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NIMCET Previous Year Questions (PYQs)

NIMCET 2024 PYQ


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





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





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





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





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





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