List of top Mathematics Questions

Which of the following is NOT true?
\( f(x) = x + |x| \) is continuous for
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
 

A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equation is
If \( a < b \), then \( \int_a^b (|x-a| + |x-b|) dx \) is equal to
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 \( a_1, a_2, \ldots, a_n \) are any real numbers and n is any positive integer, then
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

The value of \( \int \frac{(x^2-1)dx}{x^3\sqrt{2x^4 - 2x^2 + 1}} \) is
 

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 _______ .

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

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:
Solutions of the equation \( \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \) are
The function \( f(x) = \log(x + \sqrt{x^2 + 1}) \) 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
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
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
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