List of top Mathematics Questions

A particle is at rest at the origin. It moves along the x -axis with an acceleration \( x - x^2 \), where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance
If the foci of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} \) are coincide, then the value of \( b^2 \) is
Let a be the distance between the lines \( -2x + y = 2 \) and \( 2x - y = 2 \), and b be the distance between the lines \( 4x - 3y = 5 \) and \( 6y - 8x = 1 \), then
The value of \( \cot(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}) \) is
If \( \cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \phi \), then \( 9x^2 - 12xy\cos\phi + 4y^2 \) is equal to
The correct expression for \( \cos^{-1}(-x) \) is

The domain of the function \( f(x) = \frac{\cos^{-1}x}{[x]} \) is
 

The solutions of the equation \( 4\cos^2x + 6\sin^2x = 5 \) are
In a Harmonic Progression, pth term is q and the qth term is p. Then pqth term is

The function \( f(x) = \begin{cases} (1+2x)^{1/x}, & x \neq 0 \\ e^2, & x=0 \end{cases} \) is
 

A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is
A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let \( m \leq x \leq n \), then choose the correct option.
If \( \vec{a} = \lambda\hat{i} + \hat{j} - 2\hat{k} \), \( \vec{b} = \hat{i} + \lambda\hat{j} - 2\hat{k} \), \( \vec{c} = \hat{i} + \hat{j} + \hat{k} \) and \( [\vec{a}\vec{b}\vec{c}] = 7 \), then the values of \( \lambda \) are
Coordinate of focus of the parabola \(4y^2 + 12x - 20y + 67 = 0\) is

If \( D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2+x & 1 \\ 1 & 1 & 2+y \end{vmatrix} \) for \( x \neq 0, y \neq 0 \), then D is

If \( a_1, a_2, \ldots, a_n \) are in Arithmetic Progression with common difference d, then the sum \( (\sin d) (\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n) \) is equal to
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
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

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

The value of \( \int \frac{(x^2-1)dx}{x^3\sqrt{2x^4 - 2x^2 + 1}} \) 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
Which of the following is NOT true?
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