MCA NIMCET 2025 Previous Year Question Paper and Solution with PDF

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MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET 2025 PYQ

Qus : 1MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 2MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 3MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 4MCA NIMCET PYQ 2025

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

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 5MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET 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 : 6MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 7MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 8MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 9MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 10MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 11MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 12MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 13MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 14MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 15MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 16MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 17MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 18MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 19MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 20MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 21MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 22MCA NIMCET PYQ 2025

Which one of the following is NOT a correct statement?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 23MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 24MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 25MCA NIMCET 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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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 26MCA NIMCET PYQ 2025

If $B=sin^2 y+cos^4 y$, then for all real y

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 27MCA NIMCET PYQ 2025

Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a point on $MF_1$ such that $MF_2\perp{{F}}_1{{F}}_2$, $MF_1\perp{{O}}{{H}}$, $|OH|=\lambda |OF_2|$ with $\lambda \in(2/5, 3/5)$, then the range of the eccentricity $e$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 28MCA NIMCET PYQ 2025

A circle with its center in the first quadrant touches both the coordinate axes and the line x -y - 2 = 0. Then the area of the circle is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 29MCA NIMCET PYQ 2025

If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic roots whose roots $\frac{1}{\alpha^3+\alpha}$ and $\frac{1}{\beta^3+\beta}$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 30MCA NIMCET PYQ 2025

The maximum value of $sinx+sin(x+1)$ is $k cos \frac{1}{2}$. Then the value of k is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 31MCA NIMCET PYQ 2025

Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}^{\beta}}} & {,x\ne0} \\ {0} & {,x=0}\end{cases}$, $\alpha , \beta \in \mathbb{R}$. Which of the following is true? ($\mathbb{R}$ denotes the set of all real numbers)

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 32MCA NIMCET PYQ 2025

The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1,2,3,4,5,6 without repetition is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 33MCA NIMCET PYQ 2025

The circle $x^2 + y^2+ \alpha x+ \beta y+ \gamma=0$ is the image of the circle $x^2 + y^2- 6x- 10y+ 30=0$ across the line 3x + y = 2. The value of $[\alpha+ \beta+ \gamma]$ is (where [.] represents the floor function.)

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 34MCA NIMCET PYQ 2025

Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}+\lambda \hat{k}$ be the co-terminal edges

of a parallelopiped whose volume is 5 units. Then the value of $\lambda$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 35MCA NIMCET PYQ 2025

The area enclosed between the curve y = sin x, y = cosx, $0\leq x\leq\frac{\pi}{2}$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 36MCA NIMCET PYQ 2025

Given the equation $x+y =1$, $x^2+y^2 =2$, $x^5 +y^5 =A$. Let N be the number of solution pairs (x,y) to this system of equations. Then AN is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 37MCA NIMCET PYQ 2025

Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits are allowed to repeat any number of times, is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 38MCA NIMCET PYQ 2025

Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = sgn(g(x))$. Then select which of the following is not true?( $\mathbb{R}$ denotes the set of all real numbers, sgn stands for signum function)

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 39MCA NIMCET PYQ 2025

An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes.

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 40MCA NIMCET PYQ 2025

Suppose $t_1, t_2, ...t_55$ are in AP such that $\sum ^{18}_{l=0}{{t}}_{3l+1}=1197$ and ${{t}}_7+{{3}}t_{22}=174$. If $\sum ^9_{l=1}{{{t}}_l}^2=947b$, then the value of $b$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 41MCA NIMCET PYQ 2025

Let E and F be two events such that P(E) > 0 and P(F) > 0. Which one of the following is NOT equivalent to the condition that $P(E) =P(E|F)$?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 42MCA NIMCET PYQ 2025

What is the general solution of the equation $tan \theta + cot \theta = 2$ ?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 43MCA NIMCET PYQ 2025

If $cos^2(10°)cos(20°)cos(40°)cos(50°) cos(70°) = \alpha+\frac{\sqrt{3}}{16} cos(10°)$, then $3\alpha^{-1}$ is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 44MCA NIMCET PYQ 2025

The slope of the normal line to the curve $x = t^2 + 3t - 8$ and $y = 2t^2 - 2t - 5$ at the point (2,-1) is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 45MCA NIMCET PYQ 2025

A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h meters above the first, the depression of the foot of the tower is 60°. What is the horizontal distance of the tower from the point?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 46MCA NIMCET PYQ 2025

There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 47MCA NIMCET PYQ 2025

Let $x$ be a positive real number such that $x^{(8log_5(x)-24)}=5^{-4}$. Then the product of all possible values of x is =

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 48MCA NIMCET PYQ 2025

The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 49MCA NIMCET PYQ 2025

What is the value of $\lim _{{x}\rightarrow\infty}-(x+1)\Bigg{(}{e}^{\frac{1}{x+1}}-1\Bigg{)}$?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 50MCA NIMCET PYQ 2025

The value of $\int ^{\frac{\pi}{2}}_0\frac{(1+2\cos x)}{({2+\cos x)}^2}dx$

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 51MCA NIMCET PYQ 2025

Read definition and all four choices carefully, and find the answer that provides the best example of the given definition. Answer the question solely on the basis of the definition given.
Definition: An informal gathering occurs when a group of people get together in a casual, relaxed manner.

Which situation below is the best example of an informal gathering?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 52MCA NIMCET PYQ 2025

In a certain code language, the word "REASON" is encoded as TDDQSK. Using the same rule, how is the word PRAYER coded?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 53MCA NIMCET PYQ 2025

Four people (P,Q,R & S) are standing in a queue. Q is ahead of P. R is between P and S. If S is at the end of the queue, who is at the front of the queue?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 54MCA NIMCET PYQ 2025

Statements:
I. The meteorological department predicts deficient rainfall during monsoon season.

II. The GDP growth estimates have been revised downwards by the government.

Choose the correct option:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 55MCA NIMCET PYQ 2025

A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 am., at what time will he first touch a flag at 120 feet from the ground?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 56MCA NIMCET PYQ 2025

In a remote research outpost, five scientists (Dr. Anand, Dr. Beena, Dr. Chirag, Dr. Dinesh, and Dr. Elango) are studying a rare phenomenon. They communicate through a secure, text-based system. Over the course of an hour, the following exchanges occur:

Dr. Anand sends a message to Dr. Beena and Dr. Chirag.
Dr. Beena replies only to Dr. Anand.
Dr. Anand sends a reminder message to who did not reply.
Dr. Chirag sends a message to Dr. Dinesh and Dr. Elango.
While replying to Dr. Chirag, Dr. Dinesh accidentally sends a "Reply All"
Dr. Elango, having received Dr. Chirag's message, sends a message to Dr. Beena.

At the end of this hour, who has received the most messages directly from other scientists within the group? (Consider only messages sent within the described hour and only between the five scientists mentioned).

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Qus : 57MCA NIMCET PYQ 2025

The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5% is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 58MCA NIMCET PYQ 2025

In a certain code language, 'SUN' is written as 'RWK' and 'MOON' is written as 'LQLR'. Following the same pattern, how will 'STAR' be written?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 59MCA NIMCET PYQ 2025

If a number is increased by 30% and then decreased by 20%, what is the net change?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

Solution

Qus : 60MCA NIMCET PYQ 2025

A two digit number is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA 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:

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