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NIMCET Previous Year Questions (PYQs)

NIMCET Mathematics PYQ




NIMCET PYQ
The expression  $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as 





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NIMCET PYQ
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
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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Solution

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



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





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Solution

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




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





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NIMCET PYQ
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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Solution

LHL ≠ f(2)

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





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





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





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





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





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





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





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





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





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NIMCET PYQ
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
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
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
$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ 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
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
If $| x - 6|= | x - 4x | -| x^2- 5x +6 |$ , where x is a real variable





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





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NIMCET PYQ

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
Number of real solutions of the equation  is





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





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





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





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





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





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NIMCET PYQ
If  then x =





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





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NIMCET PYQ
The position vectors of the vertices





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NIMCET PYQ
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

Not Available right now






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|

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





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





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NIMCET PYQ
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
The solution set of the inequality  is






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NIMCET PYQ
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 $a, b, c$are the lengths of the sides of a triangle which is





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Solution


NIMCET PYQ

Not Available






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





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NIMCET PYQ

Not Available






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NIMCET PYQ
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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Solution



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





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Solution



NIMCET PYQ
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

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







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NIMCET PYQ
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

A particle P starts from the point






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Solution



NIMCET PYQ
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

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






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NIMCET PYQ
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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