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List of top Mathematics Questions

If $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ ($ a > b $) and $ x^2 - y^2 = c^2 $ cut at right angles, then

If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is $ \alpha $, then the height of the hill is

Inverse of the function $ f(x) = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} $ is

Which of the following is NOT true?

Let $ \vec{a} = 2\hat{i} + 2\hat{j} + \hat{k} $ and $ \vec{b} $ be another vector such that $ \vec{a} \cdot \vec{b} = 14 $ and $ \vec{a} \times \vec{b} = 3\hat{i} + \hat{j} - 8\hat{k} $. The vector $ \vec{b} $ is

If $ a < b $, then $ \int_a^b (|x-a| + |x-b|) dx $ is equal to

If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p² + q²)x² – 2q(p + r)x + q² + r² = 0 is also a root of the equation x² + 2x – 8 = 0, then (q² + r²)/p² is equal to _______ .

Solutions of the equation $ \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} $ are

If the volume of the parallelepiped whose adjacent edges are $ \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} $, $ \vec{b} = \hat{i} + \alpha\hat{j} + 2\hat{k} $, $ \vec{c} = \hat{i} + 2\hat{j} + \alpha\hat{k} $ is 15, then $ \alpha $ is equal to

In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30$^{\circ}$, 45$^{\circ}$ and 60$^{\circ}$ respectively. The ratio of AB and BC is

There are two circles in xy-plane whose equations are $ x^2 + y^2 - 2y = 0 $ and $ x^2 + y^2 - 2y - 3 = 0 $. A point (x, y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is

The function $ f(x) = \log(x + \sqrt{x^2 + 1}) $ is

The area enclosed within the curve $ |x| + |y| = 2 $ is

Area of the parallelogram formed by the lines $ y = 4x, y = 4x + 1, x + y = 0 $ and $ x + y = 1 $ is

The eccentricity of an ellipse, with its center at the origin is $ \frac{1}{3} $. If one of the directrices is $ x = 9 $, then the equation of ellipse is:

For $ a \in \mathbb{R} $, $ a \neq -1 $, $ \lim_{n \to \infty} \frac{1^a + 2^a + \dots + n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\dots+(na+n)]} = \frac{1}{60} $. Then one of the values of a is

If $ 0 < P(A) < 1 $ and $ 0 < P(B) < 1 $, and $ P(A \cap B) = P(A)P(B) $, then

Choose the correct answer:

1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?

Let a, b ∈ R be such that the equation ax² – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x² – 2bx + 21 = 0, then α² + β² is equal to

Domain of $cos^{-1} [x]$, where $[. ]$ denotes a greatest integer function

The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$ is _____.

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

Let
A = $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$ and B = $\begin{bmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & 14^2 \\ -15^2 & 16^2 & 17^2 \\ \end{bmatrix}$
then the value of A'BA is

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?