List of top Mathematics Questions asked in NIMCET

There are two sets $A$ and $B$ with $|A|=m$ and $|B|=n$. If $|P(A)|-|P(B)|=112$, choose the wrong option.

A survey is done among 200 people. 60% like tea and 72% like coffee. Let $x$ be the number who like both. Let $m\le x\le n$. Find the correct option.

If $A \subseteq B$ and $B \subseteq C$, then cardinality of $A \cup B \cup C$ is equal to:

From the word ARRANGEMENT, how many distinct 9-letter words can be formed?

Suppose $ t_1, t_2, t_3, \dots, t_{55} $ are in AP such that $ \sum_{l=0}^{18} t_{3l+1} = 1197 $ and $ t_7 + 3t_{22} = 174 $. If $ \sum_{l=1}^{9} t_l^2 = 947b $, then the value of $ b $ is

A sum of money was divided into 2 parts in the ratio 2:5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years so that the interest earned in both cases is the same?

If $ 8^{x-1} = \left( \frac{1}{4} \right)^x $, then the value of \[ \frac{1}{\log_{x+14} x - \log_{x+15}} \div \frac{1}{\log_{1-x} 4 - \log_{1-x} 5} \] is

Which one of the following is NOT a correct statement?

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

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

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

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships as 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is

Let $ g: \mathbb{R} \to \mathbb{R} $ and $ h: \mathbb{R} \to \mathbb{R} $ be two functions such that $ h(x) = s \cdot g \cdot n(g(x)) $, where $ \mathbb{R} $ denotes the set of all real numbers and $ s $ and $ n $ stand for the signum and the sine functions respectively. Then, select which of the following is not true?

Let $ A = (1, 2, 3, \dots, 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:

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

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

Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. What is Ram's present age?

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

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

The circle $ x^2 + y^2 + ax + by + \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)

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 the triangle is:

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

Let $ \mathbf{a} = e\hat{i} + 3\hat{j} + 4\hat{k}, \mathbf{b} = \hat{i} + 2\hat{j} - \hat{k}, \mathbf{c} = 3\hat{i} + \hat{j} + \lambda \hat{k} $ be the co-terminal edges of a parallelepiped whose volume is 5 units. Then the value of $ \lambda $ is:

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:

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?