List of top Questions asked in NIMCET- 2025

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:

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

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:

If 1st January 2022 was a Saturday, what day of the week will 1st January 2023 be?

A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km. Finally, he turns left and walks 3 km. How far is he from the starting point?

A remote island has a unique social structure. Individuals are either "Truth-tellers" (who always speak the truth) or "Tricksters" (who always lie). You encounter three inhabitants: X, Y, and Z.

X says: "Y is a Trickster"
Y says: "Exactly one of us is a Truth-teller."
What can you definitively conclude about Z?

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?

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?

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.

Which of the following statements about ASCII and Unicode is correct?

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

What is the equivalent decimal value of the unsigned binary number 10101.10101?

What is the hexadecimal representation of the decimal number 265?

Which of the following sentences uses the correct form of the verb "to lay"?

Study the following sentence:

The statue of Christ the Redeemer is located on Rio de Janeiro, the largest city of Brazil. (Which of the following parts of the sentence is grammatically incorrect?)

Which of the following statements correctly explains the use of articles in the following sentence?

After earning an MBA, Srinivas was able to approach a mathematical problem from both a business and analytical perspective.

One of the employees $\underline{\hspace{1cm}}$ planning to transfer to another department.

What is the value of $\log_{X \to \infty} \left[ -(x + 1) \left( e^{x+1} - 1 \right) \right]$?

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:

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

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

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:

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

Let the line $\frac{x}{4} + \frac{y}{2} = 1$ meet 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 $\Delta ABP$ is an isosceles triangle with $AP = BP$. Then the distance between M' and P is: