NIMCET 2025 Previous Year Question Paper and Solution with PDF

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NIMCET Previous Year Questions (PYQs)

NIMCET 2025 PYQ

Qus : 1NIMCET PYQ 2025

The length of the projection of $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ on $\vec{b} = -2\hat{i} + \hat{j} + 2\hat{k}$, is equal to:

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 2NIMCET PYQ 2025

If $8^{x-1}=(1/4)^{x}$, then the value of $\frac{1}{log_{x+1}4-log_{x+1}5}+\frac{1}{log_{1-x}4-log_{1-x}5}$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 3NIMCET PYQ 2025

Consider the matrix $$B=\begin{pmatrix}{-1} & {-1} & {2} \\ {0} & {-1} & {-1} \\ {0} & {0} & {-1}\end{pmatrix}$$. The sum of all the entries of the matrix $B^{19}$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 4NIMCET PYQ 2025

The curve $y=\frac{x}{1+x\tan x}$ attains maxima

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Qus : 5NIMCET PYQ 2025

The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

Solution

Probability Between 450 and 500 (Normal Distribution)

The exam scores are normally distributed with a mean $ \mu = 500 $ and standard deviation $ \sigma = 100 $.
Given: $ P(Z \leq 0.5) = 0.691 $
We need to find: $ P(450 \leq X \leq 500) $

Step 1: Convert scores to Z-scores

Use the formula: $$ Z = \frac{X - \mu}{\sigma} $$

For $ X = 500 $: $$ Z = \frac{500 - 500}{100} = 0 $$ For $ X = 450 $: $$ Z = \frac{450 - 500}{100} = -0.5 $$

Step 2: Find the probability using cumulative values

We calculate: $$ P(450 \leq X \leq 500) = P(-0.5 \leq Z \leq 0) = P(Z \leq 0) - P(Z \leq -0.5) $$

From symmetry: $$ P(Z \leq -0.5) = 1 - P(Z \leq 0.5) = 1 - 0.691 = 0.309 $$ and $$ P(Z \leq 0) = 0.5 $$

Step 3: Final Calculation

$$ P(-0.5 \leq Z \leq 0) = 0.5 - 0.309 = \boxed{0.191} $$

✅ Final Answer:

The probability that a randomly selected student scored between 450 and 500 is: 0.191

Qus : 6NIMCET PYQ 2025

Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is

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Qus : 7NIMCET PYQ 2025

Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and $B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix $C= BA+2B+2A+4I$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 8NIMCET PYQ 2025

The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?

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Qus : 9NIMCET PYQ 2025

The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$

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Qus : 10NIMCET PYQ 2025

There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and for red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting head is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 11NIMCET PYQ 2025

The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 12NIMCET PYQ 2025

Let A = {1,2,3, ... , 20}. Let $R\subseteq A\times A$ such that R = {(x,y): y = 2x - 7}. Then the number of elements in R, is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 13NIMCET PYQ 2025

If $\vec{a}, \vec{b}$ and $\vec{c} $ are three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ , $\vec{a}.\vec{c} = 2$ and $\vec{b}.\vec{c} = 1$. If $|\vec{b}| = 1$, then the value of $|\vec{a}| $ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 14NIMCET PYQ 2025

If x, y and z are three cube roots of 27, then the determinant of the matrix $\begin{bmatrix}{x} & {y} & {z} \\ {y} & {z} & {x} \\ {z} & {x} & {y}\end{bmatrix}$ is

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Qus : 15NIMCET PYQ 2025

Let $A=\{{5}^n-4n-1\colon n\in N\}$ and $B=\{{}16(n-1)\colon n\in N\}$ be sets. Then

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 16NIMCET PYQ 2025

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be unit vectors such that the angle between them is ${\cos }^{-1}\Bigg{\{}\frac{1}{4}\Bigg{\}}$. If $\vec{b}=2\vec{c}+\lambda \vec{a}$, where $\lambda$ > 0 and $\vec{b}=4$, then $\lambda$ is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 17NIMCET PYQ 2025

A tower subtends angles $\alpha, 2\alpha$ and $3\alpha$ respectively at points A, B and C which are lying on a

horizontal line through the foot of the tower. Then $\frac{AB}{BC}$ is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 18NIMCET PYQ 2025

If $\vec{a}$ and $\vec{b}$ are twp vectors such that |$\vec{a}$|=3, |$\vec{b}$|=4 and |$\vec{a}+\vec{b}$|=1, then the value of $|\vec{a}-\vec{b}|$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 19NIMCET PYQ 2025

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$, then a vector of magnitude $\sqrt{22}$ which is parallel to $2\vec{a}-\vec{b}+3\vec{c}$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 20NIMCET PYQ 2025

Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely. Let A = {x ≥ 2} and B = {y > x} be two events. Then which of the following is NOT true?

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 21NIMCET PYQ 2025

Let the line $\frac{x}{4}+\frac{y}{2}=1$ meets the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line x + y = 1. Let the point P lie on the line x + y = 1 such that the $\Delta$ABP is an isosceles triangle with AP = BP. Then the distance between M' and P is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 22NIMCET PYQ 2025

Which one of the following is NOT a correct statement?

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 23NIMCET PYQ 2025

An equilateral triangle is inscribed in the parabola $y^2 = x$. One vertex of the triangle is at the vertex of the parabola. The centroid of triangle is

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Qus : 24NIMCET PYQ 2025

The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° and 45°, respectively. What is the height of the multistoried building and the distance between the two buildings?

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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Qus : 25NIMCET PYQ 2025

The number of accidents per week in a town follows Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is $ke^{-6}$, then the value of k is

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NIMCET Previous Year PYQNIMCET NIMCET 2025 PYQ

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NIMCET Previous Year Questions (PYQs)

NIMCET 2025 PYQ

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Probability Between 450 and 500 (Normal Distribution)

Step 1: Convert scores to Z-scores

Step 2: Find the probability using cumulative values

Step 3: Final Calculation

✅ Final Answer:

Solution

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