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NIMCET Previous Year Questions (PYQs)

NIMCET Mathematics PYQ




NIMCET PYQ 2020
The expression  tanA1cotA+cotA1tanA can be written as 





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NIMCET PYQ 2023
If \vec{a}=\hat{i}-\hat{k}, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k} and \vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}, then \begin{bmatrix}{\vec{a}} & {\vec{b}} & {\vec{c}}\end{bmatrix} depends on





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NIMCET PYQ 2020
Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB and BC is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

According to the given information, the figure should be as follows.  
Let the height of tower = h



NIMCET PYQ 2023
If \vec{a}, \vec{b} are unit vectors such that 2\vec{a}+\vec{b} =3 then which of the following statement is true?





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NIMCET PYQ 2020
The area enclosed between the curves y2 = x and y = |x| is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Solving y2 = x and y = x, 
we get, y = 0, x = 0, y = 1, x = 1  Therefore, 




NIMCET PYQ 2023
\int f(x)\mathrm{d}x=g(x), then \int {x}^5f({x}^3)\mathrm{d}x





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2020
Test the continuity of the function at x = 2 
f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 & \text{ if } x=2 \\ x-\frac{3}{2}& \text{ if } x>2 \end{cases}





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

LHL ≠ f(2)

NIMCET PYQ 2023
\lim _{{x}\rightarrow1}\frac{{x}^4-1}{x-1}=\lim _{{x}\rightarrow k}\frac{{x}^3-{k}^2}{{x}^2-{k}^2}=, then find k





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NIMCET PYQ 2020
The value of 
2tan-1[cosec(tan-1x) - tan(cot-1x)]





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NIMCET PYQ 2023
The graph of function f(x)=\log _e({x}^3+\sqrt[]{{x}^6+1}) is symmetric about:





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NIMCET PYQ 2020
If 3 sin x + 4 cos x = 5, then 6tan\frac{x}{2}-9tan^2\frac{x}{2} 





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NIMCET PYQ 2023
If the equation |x^2 – 6x + 8| = a has four real solution then find the value of a?





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NIMCET PYQ 2020
If A is a subset of B and B is a subset of C, then cardinality of A ∪ B ∪ C is equal to





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NIMCET PYQ 2023
Largest value of cos^2\theta -6sin\theta cos\theta+3sin^2\theta+2 is





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NIMCET PYQ 2023
Given to events A and B such that odd in favour A are 2 : 1 and odd in favour of A \cup B are 3 : 1. Consistent with this information the smallest and largest value for the probability of event B are given by





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NIMCET PYQ 2023
If A and B are square matrices such that B=-A^{-1} BA, then (A + B)^2 is





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NIMCET PYQ 2023
A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen





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NIMCET PYQ 2023
Between any two real roots of the equation e^x sin x = 1, the equation e^x cos x = –1 has





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NIMCET PYQ 2023
If f(x) is a polynomial of degree 4, f(n) = n + 1 & f(0) = 25, then find f(5) = ?





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NIMCET PYQ 2023
The maximum value of f(x) = (x – 1)^2 (x + 1)^3 is equal to \frac{2^p3^q}{3125}  then the ordered pair of (p, q) will be





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NIMCET PYQ 2023
The coefficient of x^{50} in the expression of {(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001x^{1000}}





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NIMCET PYQ 2023
If {{x}}_k=\cos \Bigg{(}\frac{2\pi k}{n}\Bigg{)}+i\sin \Bigg{(}\frac{2\pi k}{n}\Bigg{)} , then \sum ^n_{k=1}({{x}}_k)=?





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NIMCET PYQ 2023
Number of point of which f(x) is not differentiable f(x)=|cosx|+3 in [-\pi, \pi]





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NIMCET PYQ 2023
If n_1 and n_2 are the number of real valued solutions x = | sin^{–1} x | & x = sin (x) respectively, then the value of n_2– n_1 is





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NIMCET PYQ 2023
The negation of \sim S\vee(\sim R\wedge S) is equivalent to





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NIMCET PYQ 2023
A point P in the first quadrant, lies on y^2 = 4ax, a > 0, and keeps a distance of 5a units from its focus. Which of the following points lies on the locus of P?





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NIMCET PYQ 2023
If \int x\, \sin x\, sec^3x\, dx=\frac{1}{2}\Bigg{[}f(x){se}c^2x+g(x)\Bigg{(}\frac{\tan x}{x}\Bigg{)}\Bigg{]}+C, then which of the following is true?





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NIMCET PYQ 2023
Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lies in the fourth quadrant and is equidistance from the two are then





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NIMCET PYQ 2023
\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)} is the angle between \vec{a}=\hat{i}-2x\hat{j}+2y\hat{k} & \vec{b}=x\hat{i}+\hat{j}+y\hat{k} then possible values of (x,y) that lie on the locus





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NIMCET PYQ 2023
Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then





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NIMCET PYQ 2023
If | x - 6|= | x - 4x | -| x^2- 5x +6 | , where x is a real variable





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NIMCET PYQ 2023
The range of values of \theta in the interval (0,\pi) such that the points (3, 2) and (cos\theta ,sin\theta) lie on the samesides of the line x + y – 1 = 0, is





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NIMCET PYQ 2023
Which of the following number is the coefficient of x^{100} in the expansion of \log _e\Bigg{(}\frac{1+x}{1+{x}^2}\Bigg{)},\, |x|{\lt}1 ?





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NIMCET PYQ 2023
A real valued function f is defined as f(x)=\begin{cases}{-1} & {-2\leq x\leq0} \\ {x-1} & {0\leq x\leq2}\end{cases}Which of the following statement is FALSE?





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NIMCET PYQ 2023
A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. Top of the pillar subtends angles tan^{–1} 3 and tan^{–1} 2 at A and B respectively. Which of the following choice represents the height of the pillar?





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NIMCET PYQ 2023
If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes,then the sum of the magnitude of the projections on each of the axis is





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NIMCET PYQ 2023
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred is red, is:





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NIMCET PYQ 2023
Let f(x)=\frac{x^2-1}{|x|-1}. Then the value of lim_{x\to-1} f(x) is





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NIMCET PYQ 2019
The mean of 5 observation is 5 and their variance is 12.4. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:





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NIMCET PYQ 2019
In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


Let the total number of experts be N.
E is the set of experts who voted for miss A.
F is the set of experts who voted for miss B.
Since 6 did not vote for either, n(EF)=N6.
n(E)=N2,n(F)=23N and n(EF)=10
.
So, N6=N2+23N10
Solving the above equation gives 

NIMCET PYQ 2023
A circle touches the x–axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is





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NIMCET PYQ 2019
The value of non-zero scalars α and  β such that for all vectors  and  such that  is





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NIMCET PYQ 2019

A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnitude of its moment about the line joining the origin to the point (12,3,4) is






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NIMCET PYQ 2019
Number of real solutions of the equation  is





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NIMCET PYQ 2019
The sum of infinite terms of a decreasing GP is equal to the greatest value of the function  in the interval [-2,3] and the difference between the first two terms is f'(0). Then the common ratio of GP is





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NIMCET PYQ 2019
Number of onto (surjective) functions from A to B if n(A)=6 and n(B)=3, is





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NIMCET PYQ 2019
If |z|<\sqrt{3}-1, then |z^{2}+2z cos \alpha| is





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NIMCET PYQ 2019
A computer producing factory has only two plants T1 and T2 produces 20% and plant T2 produces 80% of the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T1 10P(computer turns out to be defective given that it is produced in plant T2 ). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2 is  





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NIMCET PYQ 2019
If A > 0, B > 0 and A + B = \frac{\pi}{6} , then the minimum value of tanA + tanB





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

On differentiating 
x= tanA + tan(π/6-A) 
we get : 
dx/dA = sec²A-sec²(π/6-A) 
now putting 
dx/dA=0 
we get 
cos²(A) = cos²(π/6-A) so 0≤A≤π/6 
therefore 
A=π/6-A from here we get A = π/12 = B 
so minimum value of that function is 
2tanπ/12 which is equal to 2(2-√3)

NIMCET PYQ 2022
Inverse of the function f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}} is 





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Let f(x)=y, then 

⇒ \frac{10^x-10^-x}{10^x+10^-x}=y

⇒ \frac{10^{2x}-1}{10^{2x}+1}=y

⇒ 10^{2x}=\frac{1+y}{1-y}   By Componendo Dividendo Rule 

⇒ x=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}

⇒ {f}^{-1}(y)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}

⇒ {f}^{-1}(x)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+x}{1-x}\Bigg{)}


NIMCET PYQ 2019
The tangent at the point (2,  -2) to the curve x^2 y^2-2x=4(1-y) does not passes through the point





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NIMCET PYQ 2019
The integral \int \sqrt{1+2 cot x(cosec x+cotx)} dx , (0<x<\frac{\pi}{2}) (where C is a constant of integration) is equal to





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NIMCET PYQ 2019
If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in  English Dictionary, then the position of the word QUEEN is





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


Letters of the word QUEEN are E,E,N,Q,U

Words beginning with E (4!) = 24

Words beginning with N (4!/2!)=12

Words beginning with QE (3!) =  6

Words beginning with QN (3!/2!)= 3

Total words = 24+12+6+9=45

QUEEN is the next word and has rank 46th.


NIMCET PYQ 2019
The curve satisfying the differential equation  and passing through the point (1,1) also passes through the point __________





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NIMCET PYQ 2019
If S and S' are foci of the ellipse , B is the end of the minor axis and BSS' is an equilateral triangle, then the eccentricity of the ellipse is 





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NIMCET PYQ 2019
The equation of the circle passing through the point (4,6) and whose diameters are along x + 2y - 5 =0 and 3x - y - 1=0 is





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NIMCET PYQ 2019
In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =





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NIMCET PYQ 2019
The median AD of ΔABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =





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NIMCET PYQ 2019
Let X_i, i = 1,2,.. , n be n observations and w_i = px_i +k, i = 1,2, ,n where p and k are constants. If the mean of x_i 's is 48 and the standard deviation is 12, whereas the mean of w_i 's is 55 and the standard deviation is 15, then the value of p and k should be





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NIMCET PYQ 2019
If , then the values of A1, A2, A3, A4 are





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NIMCET PYQ 2019
If  then x =





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NIMCET PYQ 2019
Equation of the tangent from the point (3,−1) to the ellipse 2x2 + 9y2 = 3 is





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NIMCET PYQ 2019
The position vectors of the vertices





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NIMCET PYQ 2019
The sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx , x \in (0 , \pi), then x





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NIMCET PYQ 2019
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is






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NIMCET PYQ 2019
Suppose A1 , A2 , A3 , …..A30 are thirty sets each having 5 elements with no common elements across the sets and B1 , B2 , B3 , ..... , Bn are





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NIMCET PYQ 2019
Let  ,where [x]denotes the greatest integer





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NIMCET PYQ 2019
Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following statements is true?






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NIMCET PYQ 2019
If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket?






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NIMCET PYQ 2019
If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to






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NIMCET PYQ 2019
If  and , then a possible value of n is among the following is 





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NIMCET PYQ 2019
Let S be the set \{a\in Z^+:a\leq100\}.If the equation [tan^2 x]-tan x - a = 0 has real roots (where [ . ] is the greatest integer function), then the number of elements is S is





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NIMCET PYQ 2019
The solution set of the inequality  is






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NIMCET PYQ 2019
If a, b, c are in GP and log a - log 2b, log 2b - log 3c and log 3c - log a are in AP, then a, b, care the lengths of the sides of a triangle which is





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NIMCET PYQ 2019
If (1 + x – 2x2)= 1 + a1x + a2x+ ... + a12x12, then the value a+ a+ a+ ... + a12





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


NIMCET PYQ 2019

Not Available






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NIMCET PYQ 2019
A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps, he is one step away from the starting point is





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NIMCET PYQ 2019
If x, y, z are distinct real numbers then  = 0, then xyz=





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Solution



NIMCET PYQ 2019
If a, a, a_2, ., a_{2n-1},b are in AP, a, b_1, b_2,...b_{2n-1}, b are in GP and a, c_1, c_2,... c_{2n-1}, b are in HP, where a, b are positive, then the equation a_n x^2-b_n+c_n has its roots





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NIMCET PYQ 2019

For the two circles x^2+y^2=16 and x^2+y^2-2y=0, there is/are






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NIMCET PYQ 2019







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NIMCET PYQ 2022
Let \vec{a}, \vec{b}, \vec{c} be distinct non-negative numbers. If the vectors a\hat{i}+a\hat{j}+c\hat{k} , \hat{i}+\hat{k} and c\hat{i}+c\hat{j}+b\hat{k} lie in a plane, then c is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

\vec{a}=a\hat{i}+a\hat{j}+c\hat{k}\, ,\, \vec{b}=\hat{i}+\hat{k}\, \&\, \vec{c}=c\hat{i}+c\hat{j}+b\hat{k} are coplanar.

\Rightarrow\begin{vmatrix}{a} & {a} & {c} \\ {1} & {0} & {1} \\ {c} & {c} & {b}\end{vmatrix}=0

\Rightarrow-ac-ab+ac+{c}^2=0

\Rightarrow{c}^2=ab

NIMCET PYQ 2019

A particle P starts from the point






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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution



NIMCET PYQ 2022
The correct expression for cos^{-1} (-x) is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

You should learn it as an important formula.

NIMCET PYQ 2024
If (4, 3) and (12, 5) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2019

If \Delta=a^2-(b-c)^2, where \Delta is the are of the triangle ABC, then tanA=






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Solution


NIMCET PYQ 2024
The number of one - one functions f: {1,2,3} → {a,b,c,d,e} is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2019
Two numbers a and b are chosen are random from a set of the first 30 natural numbers, then the probability that a^2 - b^2 is divisible by 3 is





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution




NIMCET PYQ 2022
Suppose that the temperature at a point (x,y), on a metal plate is T(x,y)=4x^2-4xy+y^2, An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The value of the limit \lim _{{x}\rightarrow0}\Bigg{(}\frac{{1}^x+{2}^x+{3}^x+{4}^x}{4}{\Bigg{)}}^{1/x} is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The value of m for which volume of the parallelepiped is 4 cubic units whose three edges are represented by a = mi + j + k, b = i – j + k, c = i + 2j –k is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60° respectively. The ratio of AB and BC is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The number of distinct real values of \lambda for which the vectors {\lambda}^2\hat{i}+\hat{j}+\hat{k},\, \hat{i}+{\lambda}^2\hat{j}+j and \hat{i}+\hat{j}+{\lambda}^2\hat{k} are coplanar is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If the foci of the ellipse \frac{x^2}{25}+\frac{y^2}{b^2}=1 and the hyperbola \frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25} are coincide, then the value of b^2





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
There are 9 bottle labelled 1, 2, 3, ... , 9 and 9 boxes labelled 1, 2, 3,....9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their
corresponding numbered boxes is 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
A particle is at rest at the origin. It moves along the x −axis with an acceleration x-x^2 , where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If the perpendicular bisector of the line segment joining p(1,4) and q(k,3) has yintercept -4, then the possible values of k are





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If a{\lt}b then \int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
Let C denote the set of all tuples (x,y) which satisfy x^2 -2^y=0 where x and y are natural numbers. What is the cardinality of C?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The domain of the function f(x)=\frac{{\cos }^{-1}x}{[x]} is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
If x=1+\sqrt[{6}]{2}+\sqrt[{6}]{4}+\sqrt[{6}]{8}+\sqrt[{6}]{16}+\sqrt[{6}]{32} then {\Bigg{(}1+\frac{1}{x}\Bigg{)}}^{24} =





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If the volume of the parallelepiped whose adjacent edges are \vec{a}=2\hat{i}+3\hat{j}+4\hat{k}, \vec{b}=\hat{i}+\alpha \hat{j}+2\hat{k} and \vec{c}=\hat{i}+2\hat{j}+\alpha \hat{k} is 15, then \alpha is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The number of solutions of {5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25 for x\in(-\mathrm{\pi},\mathrm{\pi}) is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Let a be the distance between the lines −2x + y = 2 and 2x − y = 2, and b be the distance between the lines 4x − 3y= 5 and 6y − 8x = 1, then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The system of equations x+2y+2z=5, x+2y+3z=6, x+2y+\lambda z=\mu has infinitely many solutions if 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If cosec\theta-\cot \theta=2, then the value of cosec\theta is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Which of the following is TRUE?
A. If f is continuous on [a,b], then \int ^b_axf(x)\mathrm{d}x=x\int ^b_af(x)\mathrm{d}x
B. \int ^3_0{e}^{{x}^2}dx=\int ^5_0e^{{x}^2}dx+{\int ^5_3e}^{{x}^2}dx
C. If f is continuous on [a,b], then \frac{d}{\mathrm{d}x}\Bigg{(}\int ^b_af(x)dx\Bigg{)}=f(x)
D. Both (a) and (b)





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The solution of the equation {4\cos }^2x+6{\sin }^2x=5 are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If F|= 40N (Newtons), |D| = 3m, and \theta={60^{\circ}}, then the work done by F acting
from P to Q is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The function f(x)=\begin{cases}{{(1+2x)}^{1/x}} & {,x\ne0} \\ {{e}^2} & {,x=0}\end{cases}, is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Let \vec{a}=2\hat{i}+2\hat{j}+\hat{k} and \vec{b} be another vector such that \vec{a}.\vec{b}=14 and \vec{a} \times \vec{b}=3\hat{i}+\hat{j}-8\hat{k} the vector \vec{b} =





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
Find the cardinality of the set C which is defined as C={\{x|\, \sin 4x=\frac{1}{2}\, forx\in(-9\pi,3\pi)}\}.





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Which term of the series \frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ... is \frac{\sqrt{5}}{13} ?





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
At how many points the following curves intersect \frac{{y}^2}{9}-\frac{{x}^2}{16}=1 and \frac{{x}^2}{4}+\frac{{(y-4)}^2}{16}=1





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If for non-zero x, cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3, where c\ned, then \int ^e_1f(x)dx=





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let m{\leq x\leq n}, then choose the correct option.





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
A critical orthopedic surgery is performed on 3 patients. The probability of recovering a patient is 0.6. Then the probability that after surgery, exactly two of them will recover is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The value of \cot \Bigg{(}{cosec}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\Bigg{)} is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The value of \tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)} is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If 0{\lt}P(A){\lt}1 and 0{\lt}P(B){\lt}1 and P(A\cap B)=P(A)P(B), then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If \sin x=\sin y and \cos x=\cos y, then the value of x-y is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
Which of the following is NOT true?





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
For an invertible matrix A, which of the following is not always true:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
f(x)=x+|x| is continuous for





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
For what values of \lambda does the equation 6x^2 - xy + 2y^2 = 0 represents two perpendicular lines and two lines inclined at an angle of \pi/4.





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If {{a}}_1,{{a}}_2,\ldots,{{a}}_n are any real numbers and n is any positive integer, then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If D={\begin{vmatrix}{1} & 1 & {1} \\ 1 & {2+x} & {1} \\ {1} & {1} & {2+y}\end{vmatrix}}\, for\, x\ne0,\, y\ne0 then D is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The two parabolas y^2 = 4a(x + c) and y^2 = 4bx, a > b > 0 cannot have a common normal unless





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Area of the parallelogram formed by the lines y=4x, y=4x+1, x+y=0 and x+y=1





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
A man starts at the origin O and walks a distance of 3 units in the north- east direction and then walks a distance of 4 units in the north-west direction to reach the point P. then \vec{OP} is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20, leaves the remainders 4, 5, 10, and 15, respectively





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
For a\in R (the set of al real numbers), a \ne 1, \lim _{{n}\rightarrow\infty}\frac{({1}^a+{2}^a+{\ldots+{n}^a})}{{(n+1)}^{a-1}\lbrack(na+1)(na+b)\ldots(na+n)\rbrack}=\frac{1}{60} . Then one of the value of a is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The value of \sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!} is:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If \vec{a}=\lambda \hat{i}+\hat{j}-2\hat{k} , \vec{b}=\hat{i}+\lambda \hat{j}-2\hat{k} and \vec{c}=\hat{i}+\hat{j}+\hat{k} and \begin{bmatrix}{\vec{a}} & {\vec{b}} & {\vec{c}}  \end{bmatrix}=7, then the values of the \lambda are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Let A and B be two events defined on a sample space \Omega. Suppose A^C denotes the complement of A relative to the sample space \Omega. Then the probability P\Bigg{(}(A\cap{B}^C)\cup({A}^C\cap B)\Bigg{)} equals





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
The function f(x)=\log (x+\sqrt[]{{x}^2+1}) is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Let Z be the set of all integers, and consider the sets X=\{(x,y)\colon{x}^2+2{y}^2=3,\, x,y\in Z\} and Y=\{(x,y)\colon x{\gt}y,\, x,y\in Z\}. Then the number of elements in X\cap Y is:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The value of f(1) for f\Bigg{(}\frac{1-x}{1+x}\Bigg{)}=x+2 is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
The area enclosed within the curve |x|+|y|=2 is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Given a set A with median m_1 = 2 and set B with median m_2 = 4
What can we say about the median of the combined set?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If {\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1, (a{\gt}b) and {x}^2-{y}^2={c}^2 cut at right angles, then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

If \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 and \frac{x^2}{c^2}+\frac{y^2}{d^2}=1 are orthogonal.
Then 
a^2-b^2=c^2-d^2

Similarly 
If \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 and x^2-y^2=c^2 are orthogonal.
It means
\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 and \frac{x^2}{c^2}+\frac{y^2}{-c^2}=1 are orthogonal

Then 
a^2-b^2=c^2-(-c^2)
a^2-b^2=2c^2



NIMCET PYQ 2024
Let f(x)=\begin{cases}{{x}^2\sin \frac{1}{x}} & {,\, x\ne0} \\ {0} & {,x=0}\end{cases}
Then which of the follwoing is true





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If \alpha , \beta are the roots of x^2-x-1=0 and A_n=\alpha^n+\beta^n, the Arithmetic mean of A_{n-1} and A_n is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
A coin is thrown 8 number of times. What is the probability of getting a head in an odd number of throw?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If a_1, a_2, a_3,...a_n, are in Arithmetic Progression with common difference d, then the sum (sind) (cosec a_1 . cosec a_2+cosec a_2.cosec a_2+...+cosec a_{n-1}.cosec a_n) is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Consider the function f(x)={x}^{2/3}{(6-x)}^{1/3}. Which of the following statement is false?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
Solutions of the equation {\tan }^{-1}\sqrt[]{{x}^2+x}+{\sin }^{-1}\sqrt[]{{x}^2+x+1}=\frac{\pi}{2} are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The value of {{Lt}}_{x\rightarrow0}\frac{{e}^x-{e}^{-x}-2x}{1-\cos x} is equal to 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
In a Harmonic Progression, p^{th} term is q and the q^{th} term is p. Then pq^{th} term is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Consider the function f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\leq4} \\ {{e}^{-x},} & {if\, x{\gt}4}\end{cases}  Which of the following statements about f(x) is true:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If the roots of the quadratic equation x^2+px+q=0 are tan 30° and tan 15° respectively, then the value of 2 + p - q is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
If one AM (Arithmetic mean) 'a' and two GM's (Geometric means) p and q be inserted between any two positive numbers, the value of p^3+q^3 is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equation is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The equation 3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0 represents





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
The value of \int \frac{({x}^2-1)}{{x}^3\sqrt[]{2{x}^4-2{x}^2+1}}dx





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The points (1,1/2) and (3,-1/2) are





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
Coordinate of the focus of the parabola 4y^2+12x-20y+67=0 is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
How much work does it take to slide a crate for a distance of 25m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of 45° from the horizontal?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
There are two circles in xy −plane whose equations are x^2+y^2-2y=0 and x^2+y^2-2y-3=0. A point (x,y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
The vector \vec{A}=(2x+1)\hat{i}+(x^2-6y)\hat{j}+(xy^2+3z)\hat{k} is a





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Region R is defined as region in first quadrant satisfying the condition x^2 + y^2 < 4. Given that a point P=(r,s) lies in R, what is the probability that r>s?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If x^my^n=(x+y)^{m+n}, then \frac{dy}{dx} is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Lines L_1, L_2, .., L_10 are distinct among which the lines L_2, L_4, L_6, L_8, L_{10} are parallel to each other and the lines L_1, L_3, L_5, L_7, L_9 pass through a given point C. The number of point of intersection of pairs of lines from the complete set L_1, L_2, L_3, ..., L_{10} is 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
If cos^{-1} \frac{x}{2}+cos^{-1} \frac{y}{3}=\phi, then 9x^2-12xy cos\phi+4y^2 is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
If the line a^2 x + ay +1=0, for some real number a, is normal to the curve xy-=1 then





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
The value of {3}^{3-\log _35} is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
Out of a group of 50 students taking examinations in Mathematics, Physics, and Chemistry, 37 students passed Mathematics, 24 passed Physics, and 43 passed Chemistry. Additionally, no more than 19 students passed both Mathematics and Physics, no more than 29 passed both Mathematics and Chemistry, and no more than 20 passed both Physics and Chemistry. What is the maximum number of students who could have passed all three examinations?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution


NIMCET PYQ 2022
There are two sets A and B with |A| = m and |B| = n. If |P(A)| − |P(B)| = 112 then choose the wrong option (where |A| denotes the cardinality of A, and P(A) denotes the power set of A)





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NIMCET PYQ 2024
Let f\colon\mathbb{R}\rightarrow\mathbb{R} be a function such that f(0)=\frac{1}{\pi} and f(x)=\frac{x}{e^{\pi x}-1} for x\ne0, then





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
The eccentricity of an ellipse, with its center at the origin is \frac{1}{3} . If one of the directrices is x=9, then the equation of ellipse is:





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If f(x)=cos[\pi^2]x+cos[-\pi^2]x, where [.] stands for greatest integer function, then f(\pi/2)=





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is \alpha, then the height of the hill is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2024
If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If (\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c}), then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
It is given that the mean, median and mode of a data set is 1, 3^x and 9^x respectively. The possible values of the mode is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
The value of the series \frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+\cdots is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution



NIMCET PYQ 2018
The function  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2018
Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer than 20 minutes for the other. What is the probability that they meet?







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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution



NIMCET PYQ 2018
Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that  is divisible by 3 is,





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2018
A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a prize. The probability that they will not win a prize in a single trial is :





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

The total number of ways in which numbers can be choosed =25 x 25=625  The number of ways in which either players can choose same numbers = 25  
Probability that they win a prize = 25/625 = 1/25 
Thus, the probability that they will not win a prize in a single trial = 1 - 1/25 = 24/25

NIMCET PYQ 2018
The quadratic equation whose roots are  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2018
Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?





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Solution


NIMCET PYQ 2021
The area of the region bounded by x-axis and the curves defined by y=tanx-\frac{\pi}{3}\leq x\leq \frac{\pi}{3} and y=cotx-\frac{\pi}{6}\leq x\leq \frac{3\pi}{2} is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2018
Suppose that m and n are fixed numbers such that the mth  term am is equal to n and nth term an is equal to m, (m≠n), the the value of (m+n)th term  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
If \log (1-x+x^2)={{a}}_1x+{{a}}_{2{}^{{}^{}}}{x}^2+{{{}{{a}}_3{x}^3+.\ldots.}}^{}  then {{a}}_3+{{a}}_6+{{a}}_9+.\ldots. is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If A is an invertible skew-symmetric matrix, then  is a





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2021
\lim_{x\to \infty} (\frac{x+7}{x+2})^{x+5} equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If the mean of the squares of first n natural numbers be 11, then n is equal to?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
A and B are independent witness in a case. The chance that A speaks truth is x and B speaks truth is y. If A and B agree on certain statement, the probability that the statement is true is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

P(A speaks truth) = x
P(B speaks truth) = y
Since, both A and B agree on certain  statement.
Hence, Total Probability =P(A)P(B)+P(A')P(B')
=xy  + (1-x)(1-y)
If statement is true then it means both A and B speaks truth.
∴ Required Probability = 


NIMCET PYQ 2021
The number of common tangents to the circle  x^2+y^2=4 and x^2+y^2-6x-8y=24 is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The set of points, where  is differential in 





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G2 = 27, then the two numbers are





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2021
In a ΔABC, if \tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k , then k is always





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution



NIMCET PYQ 2017
In an entrance test there are multiple choice questions, with four possible answer to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then the probability that he as guessing is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

NIMCET 2017 Solution

NIMCET PYQ 2021
Let \vec{a}=2\widehat{i}\, +\widehat{j}\, +2\widehat{k} , \vec{b}=\widehat{i}-\widehat{j}+2\widehat{k} and \vec{c}=\widehat{i}+\widehat{j}-2\widehat{k} are are three vectors. Then, a vector in the plane of \vec{a} and \vec{c} whose projection on \vec{b} is of magnitude \frac{1}{\sqrt{6}} is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2018
Let be defined by . Find 





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
A man is known to speak the truth 2 out of 3 times. He threw a dice cube with 1 to 6 on its faces and reports that it is 1. Then the probability that it is actually 1 is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
For what value of p, the polynomial  x^4-3x^3+2px^2-6 is exactly divisible by (x-1)





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The slope of two-lines  differ by





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
Let A and B be two events such that  ,  and 
 where  stands for the complement of event A. Then the events A and B are





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2021
If F(\theta)=\begin{bmatrix}{\cos \theta} & {-\sin \theta} & {0} \\ {\sin \theta} & {\cos \theta} & {0} \\ {0} & {0} & {1}\end{bmatrix} , then F(\theta)F(\alpha) is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If the radius of the circle changes at the rate of , at what rate does the circle's area change when the radius is 10m?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively. The P(X = 1) is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

np = 4

npq = 2

q = 1/2, p = 1/2, n = 8

p(X = 1) = 8C1 (1/2)(1/2)7


NIMCET PYQ 2021
If \frac{n!}{2!(n-2)!} and \frac{n!}{4!(n-4)!} are in the ratio 2:1, then the value of n is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The point of intersection os circle  and the line  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If  is the mean of distribution of x, then usual notation  is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Mean Deviation from mean is Zero.

NIMCET PYQ 2021
The locus of the point of intersection of tangents to the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 which meet right angles is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The number of solutions of the equation sinx + sin5x = sin3x lying in the interval  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If E1 and E2 are two events associated with a random experiment such that P (E2) = 0.35, P (E1 or E2) = 0.85 and P (E1 & E2) = 0.15 then P(E1) is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
If the position vector of A and B relative to O be \widehat{i}\, -4\widehat{j}+3\widehat{k} and -\widehat{i}\, +2\widehat{j}-\widehat{k} respectively, then the median through O of ΔABC is:





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2018
In an acute-angled ΔABC the least value of secA+secB+secC is 





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
Find a matrix X such that 2A + B + X = 0, whose A =  and B = 





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
The general value of \theta, satisfying the equation \sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution



NIMCET PYQ 2017
If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

If altitudes of a triangle are in HP then its side will be in AP because sides are inverse proportion to height as area is constant. a, b, c are sides of triangle.
a, b, c are in A.P.
sin A, sin B, sin C are in A.P.

NIMCET PYQ 2021
The area of the triangle formed by the vertices whose position vectors are 3\widehat{i}+\widehat{j}5\widehat{i}+2\widehat{j}+\widehat{k} , \widehat{i}-2\widehat{j}+3\widehat{k} is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If  then the value of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
α, β are the roots of the an equation x^2- 2x cosθ + 1 = 0, then the equation having roots αn and βn is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution



NIMCET PYQ 2021
The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation will be  





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The circles whose equations are  and  will touch one another externally, if





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
The equation (x-a)3+(x-b)3+(x-c)3 = 0 has





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


Let f(x) = (x – a)3 + (x – b)3 + (x – c)3.
Then f'(x) = 3{(x – a)2 + (x – b)2 + (x –c)2}
clearly , f'(x) > 0 for all x.
so, f'(x) = 0 has no real roots.
Hence, f(x) = 0 has two imaginary and one real root

NIMCET PYQ 2021
The function f(x)=\frac{x}{1+x\tan x} , 0\leq x\leq\frac{\pi}{2} is maximum when 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where p≠q is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Straight Line

NIMCET PYQ 2017
Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Let the three terms in A.P. be a – d, a, a + d.
given that a – d + a + a + d = 21  
a = 7
then the three term in A.P. are 7 – d, 7, 7 + d
According to given condition 9 – d, 9, 21 + d are in G.P.
(9)2 = (9 – d) (21 + d)
81 = 189 + 9d – 21d – d2
81 = 189 – 12d – d2
d2 + 12d – 108 = 0
d(d + 18) – 6 (d + 18) = 0
(d – 6) (d + 18) = 0
We get, d = 6, –18
Putting d = 6 in the term 7 – d, 7, 7 + d we get 1, 7, 13.

NIMCET PYQ 2021
If f\colon R\rightarrow R is defined by f(x)=\begin{cases}{\frac{x+2}{{x}^2+3x+2}} & {,\, if\, x\, \in R-\{-1,-2\}} \\ {-1} & {,if\, x=-2} \\ {0} & {,if\, x=-1}\end{cases} , then f(x) is continuous on the set 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
Equation of the common tangents with a positive slope to the circle and  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution



NIMCET PYQ 2021
A polygon has 44 diagonals, the number of sides are 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The area enclosed between the curves  and  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
The value of A that satisfies the equation asinA + bcosA = c is equal to






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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
The probability of occurrence of two events E and F are 0.25 and 0.50, respectively. the probability of their simultaneous occurrence is 0.14. the probability that neither E nor F occur is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
Equation of the line perpendicular to x-2y=1 and passing through (1,1) is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution



NIMCET PYQ 2021
If y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}} then \frac{dy}{dx} is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Incorrect question


NIMCET PYQ 2017
Find the principal value of  is






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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
The value of \tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}} is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is






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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


First off all select 5 boxes out 6 boxes in which 5 big ball can fit then arrange these ball in these 5 boxes and then put remaining 4 ball in any remaining box. 
So Ans is [(6C5)5!](4!) = 6!4! = 17280

NIMCET PYQ 2017
If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of the triangle , then triangle is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
Which of the following function is the inverse of itself?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution



NIMCET PYQ 2021
If H_1,H_2,\ldots,H_n are n harmonic means between a and b (b\ne a);,then \frac{{{H}}_n+a}{{{H}}_n-a}+\frac{{{H}}_n+b}{{{H}}_n-b}





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,





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Solution


NIMCET PYQ 2021
If y=\sin ^{-1}(\frac{{x}^2+1}{\sqrt[]{1+3{x}^2+{x}^4}}),\, (x>0), then  \frac{dy}{dx}=





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business. 8 students like both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is






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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If non-zero numbers a, b, c are in A.P., then the straight line ax + by + c = 0 always passes through a fixed point, then the point is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Since a, b and c are in A. P. 2b = a + c  
a –2b + c =0
The line passes through (1, –2).

NIMCET PYQ 2021
If 32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha and 3\, \cos \, 2\theta=1, then the general value of \alpha =





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If A and B are two events and , the A and B are two events which are





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If the lines x + (a – 1)y + 1 = 0 and 2x + a2y – 1 = 0 are perpendicular, then the condition satisfies by a is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
In a triangle ABC, a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2} then the sides of the triangle are in





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If  are positive real numbers whose product is a fixed number c, then the minimum of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC, then 2(r + R) equals





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
If |k|=5 and 0° ≤ θ ≤ 360°, then the number of distinct solutions of 3cos⁡θ + 4sin⁡θ = k is
NIMCET 2021





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2021
If θ is acute angle between the pair of lines x^2-7xy+12y^2=0, then \frac{2\cos \theta+3\sin \theta}{4\sin \theta+5\cos \theta}=





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If a, b, c are the roots of the equation , then the value of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If x2 + 3xy + 2y2 – x – 4y – 6 = 0 represents a pair of straight lines, their point of intersection is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
The four geometric means between 2 and 64 are 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
The coefficient of  in the expansion of is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
The equation of the tangent line to the curve y = 2x sin x at the point (π/2, π), is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
The lines px+qy=1 and qx+py=1 are respectively the sides AB, AC of the triangle ABC and the base BC is bisected at (p,q). Equation of the median of the triangle through the vertex A is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
Let  and  be the roots f the equation  and  are the roots of the equation , then the value of r,





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution



NIMCET PYQ 2017
If the graph of y = (x – 2)2 – 3 is shifted by 5 units up along y-axis and 2 units to the right along the x-axis, then the equation of the resultant graph is





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Solution

When y= f (x) is shifted by k units to the right along x
– axis, it become y= f (x - k )
Hence, new equation of
graph is y = (x - 4)2 + 2

NIMCET PYQ 2021
If the vectors a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}(a,b,c\ne1) are coplanar, then \frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=





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NIMCET PYQ 2018
How many natural numbers smaller than  can be formed using the digits 1 and 2 only?





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Solution


NIMCET PYQ 2017
The direction cosines of the vector a = (- 2i + j – 5k) are





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NIMCET PYQ 2021
Let \vec{a}=\hat{i}+\hat{j} and  \vec{b}=2\hat{i}-\hat{k}, the point of intersection of the lines \vec{r}\times\vec{a}=\vec{b}\times\vec{a}  and  \vec{r}\times\vec{b}=\vec{a}\times\vec{b}  is





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NIMCET PYQ 2017
The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and one focus (0, 4) is





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NIMCET PYQ 2021
If the system of equations 3x-y+4z=3x+2y-3z=-2 , 6x+5y+λz=-3   has atleast one solution, then λ=





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NIMCET PYQ 2018
If  and , then the value of  is







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NIMCET PYQ 2017
If \vec{a}\vec{b} and \vec{c} are vectors such that \vec{a}+\vec{b}+\vec{c} = 0 and |\vec{a}| =7, \vec{b}=5,  |\vec{c}| = 3, then the angle between the vectors \vec{b} and \vec{c}





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NIMCET PYQ 2021
If a variable takes values 0, 1, 2,…, 50 with frequencies 1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_{{{C}}_{50}}, then the AM is





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NIMCET PYQ 2017
If  ,  and 
 , (a ≠ b ≠ c ≠ 1) are co-planar, then the value of  is





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NIMCET PYQ 2021
If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)





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NIMCET PYQ 2018
Differential coefficient of  with respect to  to





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NIMCET PYQ 2017
Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a x (a x c) - b = 0, then the acute angle between a and c is





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NIMCET PYQ 2021
If n is an integer between 0 to 21, then find a value of n for which the value of n!(21-n)! is  minimum





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NIMCET PYQ 2018
 is continuous for





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Solution


NIMCET PYQ 2017
Let  and  be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is





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NIMCET PYQ 2021
Suppose A_1,A_2,\ldots,A_{30} are 30 sets each with five elements and B_1,B_2,B_3,\ldots,B_n are n sets (each with three elements) such that  \bigcup ^{30}_{i=1}{{A}}_i={{\bigcup }}^n_{j=1}{{B}}_i=S\, and each element of S belongs to exactly ten of the A_i's and exactly 9 of the B^{\prime}_j's. Then n=





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Solution


NIMCET PYQ 2018
If , and  are unit vectors, then  does not exceeds





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NIMCET PYQ 2017
If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )





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NIMCET PYQ 2021
The eccentric angle of the extremities of latus-rectum of the ellipse \frac{{x}^2}{{a}^2}^{}+\frac{{y}^2}{{b}^2}^{}=1 are given by 





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NIMCET PYQ 2018
The vector  lies in the plane of the vector  and  and bisects the angle between  and . Then which of the following gives possible values of  and ?





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NIMCET PYQ 2017
The number of elements in the power set P(S) of the set S = [2, (1, 4)] is





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Solution


NIMCET PYQ 2021
If α≠β and \alpha^2=5\alpha-3,\beta^2=5\beta-3, then the equation whose roots are \frac{\alpha}{\beta} and \frac{\beta}{\alpha} is 





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NIMCET PYQ 2017
If (1 - x + x)n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is





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NIMCET PYQ 2021
The probability that a man who is x years old will die in a year is p. Then, amongst n persons A_1,A_2,\ldots A_n each x year old now, the probability that {{A}}_1 will die in one year and (be the first to die ) is  





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NIMCET PYQ 2018
A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?





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NIMCET PYQ 2017
m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small cages and p large animal (n < p < m). The large animals are so large that they do not fit in small cage. However, small animals can be put in any cage. The number of putting the animals into cage is





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NIMCET PYQ 2021
Angle between \vec{a} and  \vec{b} is 120{^{\circ}}. If |\vec{b}|=2|\vec{a}| and the vectors , \vec{a}+x\vec{b} ,   \vec{a}-\vec{b} are at right angle, then x=





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Solution


NIMCET PYQ 2018
The value of  is





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Solution


NIMCET PYQ 2017
Let A and B two sets containing four and two elements respectively. The number of subsets of the A × B, each having at least three elements is





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Solution

n(A) = 4
n(B) = 2
Then the number of subsets in A*B is 2= 256

NIMCET PYQ 2021
If a number x is selected at random from natural numbers 1,2,…,100, then the probability for x+\frac{100}{x}{\gt}29 is





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Solution



NIMCET PYQ 2017
The slope of the function 





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Solution


NIMCET PYQ 2021
If X and Y are two sets, then X∩Y ' ∩ (X∪Y) ' is 





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NIMCET PYQ 2018
In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of  equal to?






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Solution


NIMCET PYQ 2017
What is the largest area of an isosceles triangle with two edges of length 3?






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Solution


NIMCET PYQ 2021
\int {e}^x(\sinh x+\cosh x)dx





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NIMCET PYQ 2018
Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of





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NIMCET PYQ 2017
The value of  is





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NIMCET PYQ 2021
If \vec{e_1}=(1,1,1) and \vec{e_2}=(1,1,-1) and \vec{a} and \vec{b}  and two vectors such that \vec{e_2}=\vec{a}+2\vec{b} , then angle between \vec{a} and \vec{b}





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NIMCET PYQ 2018
A line passing through P(4, 2) meets the x and y-axis at P and Q respectively. If O is the origin, then the locus of the centre of the circumcircle of ΔOPQ is -





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NIMCET PYQ 2017
Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If \lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3, then f(2) is





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Solution

Given it has extremum values at x=1 and x=2
⇒f′(1)=0  and  f′(2)=0
Given f(x) is a fourth degree polynomial 
Let  f(x)=a{x}^4+b{x}^3+c{x}^2+dx+e
Given 
\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3
\lim _{{x}\rightarrow0}\lbrack1+\frac{a{x}^4+b{x}^3+c{x}^2+\mathrm{d}x+e}{{x}^2}\rbrack=3
\lim _{{x}\rightarrow0}\lbrack1+a{x}^2+bx+c+\frac{d}{x}+\frac{e}{{x}^2}\rbrack=3
For limit to have finite value, value of 'd' and 'e' must be 0
⇒d=0  & e=0
Substituting x=0 in limit 
⇒ c+1=3
⇒ c=2
f^{\prime}(x)=4a{x}^3+3b{x}^2+2cx+d
x=1 and x=2 are extreme values,
f^{\prime}(1)=0 and $f^{\prime}(2)=0
4a+3b+4=0 and 32a+12b+8=0 
By solving these equations
we get, a=\frac{1}{2} and b=-2
So,
f(x)=\frac{x^{4}}{2}-2x^{3}+2x^{2}
f(x)=x^{2}(\frac{x^{2}}{2}-2x+2)
f(2)=2^{2}(2-4+2)
f(2)=0


NIMCET PYQ 2021
If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then 





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NIMCET PYQ 2017
The maximum value of 4 sinx + 3 cosx + sin(x/2) + cos(x/2) is





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NIMCET PYQ 2021
If a\, \cos \theta+b\, \sin \, \theta=2 and a\, \sin \, \theta-b\, \cos \, \theta=3 , then {a}^{2^{}}+{b}^2=





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NIMCET PYQ 2017
The solution of (ex + 1) y dy = (y + 1) edx is





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Solution


NIMCET PYQ 2021
If three thrown of three dice, the probability of throwing triplets not more than twice is 





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Solution



NIMCET PYQ 2020
If , then the values of n and r are:





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NIMCET PYQ 2021
\int {3}^{{3}^{{3}^x}}.{3}^{{3}^x}.{3}^xdx is equal to





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NIMCET PYQ 2017
The critical point and nature for the function f(x, y) = x2 –2x + 2y2 + 4y – 2 is





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NIMCET PYQ 2020
In a class of 50 students, it was found that 30 students read "Hitava", 35 students read "Hindustan" and 10 read neither. How many students read both: "Hitavad" and "Hindustan" newspapers?





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Solution

P(x)=50,
P(A ∩ B)' = 10 
So P(A ∪ B) = 50 - 10 = 40. 
So P(A ∩ B) = P(A) + P(B) - P(A ∪ B) 
= 30 + 35 - 40 = 25

Solution Contribution by Priyanka Soni

NIMCET PYQ 2021
There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :





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Solution


NIMCET PYQ 2017
If y = cosx, find dx/dy





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Let y = (cos x2)2
 = 2 (cos x2) sin x2 .2x 
= -4 (cos x2) sin x 

NIMCET PYQ 2020
If A = {4x - 3x - 1 : x ∈ N} and B = {9(x - 1) : x ∈ N}, where N is the set of natural numbers, then





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

A = {0,9,54...}
B = {0,9,18,27...}
So, A ⊂ B

NIMCET PYQ 2021
Consider the following frequency distribution table.
 Class Interval 10-20 20-30 30-40 40-5050-60  60-7070-80 
 Frequency 180f_1 34 180 136 f_250 
If the total frequency is 686 and the median is 42.6, then the value of f_1;and f_2 are 





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Solution


NIMCET PYQ 2017
The derivative of (x3 + ex + 3x + cotx) with respect to x is





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Solution

Let y=x+ e+ 3+ cotx
Now, 
 = 3x+ e+ 3x log3 - cosec2 x

NIMCET PYQ 2020
If A = { x, y, z }, then the number of subsets in powerset of A is





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Solution


NIMCET PYQ 2017
The solution of the differential equation  is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Variable separable

Integrating



NIMCET PYQ 2020
How many words can be formed starting with letter D taking all letters from the word DELHI so that the letters are not repeated:





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Solution


NIMCET PYQ 2017
Differentiate [- log(log x),  x > 1] with respect to x





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Let y = - log(log x), x>1
On differentiating both sides,
 = - (log (log x))
 (log x)
 

NIMCET PYQ 2020
Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


(10-3)C6= 7C6 = 7

NIMCET PYQ 2019
If the points  lie in the region corresponding to the acute angle between the lines and then





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NIMCET PYQ 2017





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Function is the form of  therefore using by L'Hospital rule
Again apply L'Hospital Rule,
Putting x = 0, we get 
 


NIMCET PYQ 2020
There is a young boy’s birthday party in which 3 friends have attended. The mother has arranged 10 games where a prize is awarded for a winning game. The prizes are identical. If each of the 4 children receives at least one prize, then how many distributions of prizes are possible?





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NIMCET PYQ 2020
A problem in Mathematics is given to 3 students A, B, and C. If the probability of A solving the problem is 1/2 and B not solving it is 1/4 . The whole probability of the problem being solved is 63/64 , then what is the probability of solving it by C?





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NIMCET PYQ 2020
A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both win a prize. The probability that they will not win a prize in a single trial is





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Solution


Probability of winning a prize = \frac{1}{25}
Thus, probability of not winning = 1-\frac{1}{25}=\frac{24}{25}

NIMCET PYQ 2020
A, B, C are three sets of values of x: 
A: 2,3,7,1,3,2,3 
B: 7,5,9,12,5,3,8 
C: 4,4,11,7,2,3,4 
Select the correct statement among the following:





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

A: 2, 3, 7, 1, 3, 2, 3 
Increasing Order : A: 1, 2, 2, 3, 3, 3, 7 
Mode = 3 (occurs maximum number of times) 
Median = 3 (the middle term) 

Mean =\frac{(1+2+2+3+3+3+7)}{7}
=\frac{21}{7} = 3

Hence. Mean=Median=Mode

NIMCET PYQ 2020
Standard deviation for the following distribution is 
 Size of item10 11 12 
 Frequency 313  8










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Solution

Total number of items in the distribution = Σ fi = 3 + 6 + 9 + 13 + 8 + 5 + 4 = 48.

The Mean (x̅) of the given set = \rm \dfrac{\sum f_i x_i}{\sum f_i}.

⇒ x̅ = \rm \dfrac{6\times3+7\times6+8\times9+9\times13+10\times8+11\times5+12\times4}{48}=\dfrac{432}{48} = 9.

Let's calculate the variance using the formula: \rm \sigma^2 =\dfrac{\sum x_i^2}{n}-\bar x^2.

\rm \dfrac{\sum {x_i}^2}{n}=\dfrac{6^2\times3+7^2\times6+8^2\times9+9^2\times13+10^2\times8+11^2\times5+12^2\times4}{48}=\dfrac{4012}{48} = 83.58.

∴ σ2 = 83.58 - 92 = 83.58 - 81 = 2.58.

And, Standard Deviation (σ) = \rm \sqrt{\sigma^2}=\sqrt{Variance}=\sqrt{2.58} ≈ 1.607.


NIMCET PYQ 2020





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NIMCET PYQ 2020
Roots of equation are ax^2-2bx+c=0 are n and m , then the value of \frac{b}{an^2+c}+\frac{b}{am^2+c} is





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NIMCET PYQ 2020
The number of values of k for which the linear equations
4x + ky + z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Since, equation has non-zero solution.
Δ = 0

NIMCET PYQ 2020
Let A = (aij) and B = (bij) be two square matricesof order n and det(A) denotes the determinant of A. Then, which of the following is not correct.





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NIMCET PYQ 2020
The tangent to an ellipse x2 + 16y2 = 16 and making angel 60° with X-axis is:





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NIMCET PYQ 2020
Find the number of point(s) of intersection of the ellipse  and the circle  x2 + y2 = 4





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NIMCET PYQ 2020
An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?





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Solution


NIMCET PYQ 2020
If a + b + c = 0, then the value of 





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Solution


NIMCET PYQ 2020
Find 





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Solution


NIMCET PYQ 2020
If  , then x = 0 is





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Solution


NIMCET PYQ 2020
If  is a continuous function at x = 0, then the value of k is





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Solution


NIMCET PYQ 2020
Find the interval(s) on which the graph y=2x3ex isincreasing





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Solution



NIMCET PYQ 2017
A cube is made up of 125 one cm. square cubes placed on a table. How many squares are visible only on three sides?





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Solution


NIMCET PYQ 2020
Evaluate 





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Solution


NIMCET PYQ 2023
A computer producing factory has only two plants T_1 and T_2. Plant T_1 produces 20% and plant T_2 produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T_1) = 10P (computer turns out to be defective given that it is produced in plant T_2). where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_2 is





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Solution


NIMCET PYQ 2020
If  where n is a positive integer, then the relation between In and In-1 is





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Solution


NIMCET PYQ 2023
The mean of 5 observation is 5 and their variance is 124. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:






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NIMCET PYQ 2020
The value of  depends on the





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NIMCET PYQ 2023
The perimeter of a \Delta ABC is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is





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NIMCET PYQ 2020
Find the area bounded by the line y = 3 - x, the parabola y = x2 - 9 and 





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NIMCET PYQ 2023
In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is





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NIMCET PYQ 2020
If  are three non-coplanar vectors, then 





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NIMCET PYQ 2023
For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are





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NIMCET PYQ 2020
Two forces F1 and F2 are used to pull a car, which met an accident. The angle between the two forces is θ . Find the values of θ for which the resultant force is equal to 





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NIMCET PYQ 2023
Consider the following frequency distribution table.
 Class interval 10-20 20-3030-40 40-50  50-60 60-7070-80 
 Frequency 180 f_1 34180  136 f_250 






If the total frequency is 685 & median is 42.6 then the values of f_1  and f_2  are





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NIMCET PYQ 2020
If  are four vectors such that is collinear with  and is collinear with  then  =





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NIMCET PYQ 2023
The sum of infinite terms of decreasing GP is equal to the greatest value of the function f(x) = x^3 + 3x – 9 in the interval [–2, 3] and difference between the first two terms is f '(0). Then the common ratio of the GP is





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NIMCET PYQ 2020
Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the point (2, −1, −3) to (5, −1, 1). The total work done by the force is





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NIMCET PYQ 2023
If f(x)=\lim _{{x}\rightarrow0}\, \frac{{6}^x-{3}^x-{2}^x+1}{\log _e9(1-\cos x)} is a real number then \lim _{{x}\rightarrow0}\, f(x)





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NIMCET PYQ 2020
The position vectors of points A and B are  and  . Then the position vector of point p dividing AB in the ratio m : n is





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NIMCET PYQ 2023
The value of \int ^{\pi/3}_{-\pi/3}\frac{x\sin x}{{\cos }^2x}dx is





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NIMCET PYQ 2020
If a, b, c are three non-zero vectors with no two of which are collinear, a + 2b  is collinear with c and b + 3c is collinear with a , then | a + 2b + 6c | will be equal to





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NIMCET PYQ 2023
The equation of the tangent at any point of curve x=a cos2t, y=2\sqrt{2} a sint with m as its slope is





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NIMCET PYQ 2020
Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is





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NIMCET PYQ 2023
If \prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]} where i=1,2,3,...,n. Then maximum value of \prod ^n_{i=1}\sin ({{\alpha}}_i).





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NIMCET PYQ 2020
If the volume of a parallelepiped whose adjacent edges are 
a = 2i + 3j + 4k,
b = i + αj + 2k
c = i + 2k + αk
is 15, then α =





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NIMCET PYQ 2023
A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely incontradict each other while narrating some incident is





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NIMCET PYQ 2020
Solve the equation sin2 x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π





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NIMCET PYQ 2023
If \overrightarrow{{a}} and \overrightarrow{{b}} are vectors in space, given by \overrightarrow{{a}}=\frac{\hat{i}-2\hat{j}}{\sqrt[]{5}} and \overrightarrow{{b}}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt[]{14}}, then the value of(2\vec{a} + \vec{b}).[(\vec{a} × \vec{b}) × (\vec{a} – 2\vec{b})] is





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NIMCET PYQ 2020
If \frac{tanx}{2}=\frac{tanx}{3}=\frac{tanx}{5} and x + y + z = π, then the value of tan2x + tan2y + tan2z is





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NIMCET PYQ 2023
Let \vec{A} = 2\hat{i} + \hat{j} – 2\hat{k} and \vec{B} = \hat{i} + \hat{j}, If \vec{C} is a vector such that |\vec{C} – \vec{A}| = 3 and the angle between A × B and C is {30^{\circ}}, then |(\vec{A} × \vec{B}) × \vec{C}| = 3 then the value of \vec{A}.\vec{C} is equal to





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NIMCET PYQ 2020
Find the value of sin 12°sin 48°sin 54°





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NIMCET PYQ 2023
Let A and B be sets. A\cap X=B\cap X=\phi and A\cup X=B\cup X for some set X, relation between A & B





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NIMCET PYQ 2020
If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =





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NIMCET PYQ 2023
If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value ofad?





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NIMCET PYQ 2020
The value of  is





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NIMCET PYQ 2023
Find foci of the equation x^2 + 2x – 4y^2 + 8y – 7 = 0





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NIMCET PYQ 2020
The value of sin 10°sin 50°sin 70° is





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Solution

sin10° sin50° sin70°
= sin10° sin(60°−10°) sin(60°+10°)
= 1/4 sin3x10°
=1/4x1/2=1/8

NIMCET PYQ 2023
The locus of the mid-point of all chords of the parabola y^2 = 4x which are drawn through its vertex is





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