List of top Questions asked in NIMCET- 2025

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{1 + 2 \cos x}{(2 + \cos x)^2} \, dx \] lies in the interval:

Statements: 1. All cakes are ice cream 2. No ice cream is chocolate

Conclusions: 1. Some cakes are chocolate 2. No cake is chocolate Choose the correct option:

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

In computer architecture, which of the following correctly matches the fundamental unit used in the CPU, cache, and main memory respectively?

Given the equations $ 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 $ N $ is equal to:

Four people (P, Q, R & S) are standing in a queue. Q is ahead of P. R is between P and S. If 5 is at the end of the queue, who is at the front of the queue?

A tower subtends an angle of $ 30^\circ $ 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 font of the tower is $ 60^\circ $. What is the horizontal distance of the tower from the point?

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

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

If $ x, y, z $ $\text{ are the three cube roots of 27, then the determinant of the matrix}$ \[ \begin{pmatrix} x & y & z \\ y & z & x \\ z & x & y \end{pmatrix} \] $\text{is:}$

In a box, there are 8 red, 7 blue, and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

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

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:

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

If 1 man or 2 women can finish a job in 20 days, how many days will 3 men and women take to finish the same job?

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?

The value of $ \frac{d}{dx} \left( \int 2 \sin x \sin x^2 e^{t^2} \right) $ at $ t = \pi $ is:

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

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

Even though in official statements, the Presidential office has warned against violating the 25th protocol, the government's inaction against the Market group shows the government's tacit approval of the movement. (Choose the antonym of the underlined word)

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 \cap F) $?

A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

In an instruction execution pipeline, the earliest that the instruction TLB and data TLB can be accessed are:

In 8-bit two's complement arithmetic, compute the result of the following addition: $ A = 10011001 $, $ B = 11010111 $. What is the resulting 8-bit binary value?

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