List of top Mathematics Questions

Let the line \( \frac{x^2}{2} - \frac{y^2}{1} = 1 \) lie in the plane \( x + 3y - oz + \beta = 0 \). Then \( \beta \) equals:

If \( \left[ 1 \quad x \quad 1 \right] \) is equal to \( \left[ 1 \quad 3 \quad 2 \right] \), then \( x \) is:

The principal value of \( \sin^{-1} \left( \sin \frac{5\pi}{3} \right) \) is:

The interval in which the function \( f(x) = \frac{4x^2 + 1}{x} \) is decreasing is:

If the parabola \( y^2 = 4ax \) passes through the point \( (1, -2) \), then the tangent at this point is:

The eccentricity of the ellipse whose major axis is three times the minor axis is:

The equation of the hyperbola with vertices \( (3, 0), (-3, 0) \) and semi-latus rectum 4 is given by:

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of \( 0.02 \, \text{cm/s} \). The rate of increase of its volume when the radius is \( 10 \, \text{cm} \) is:

The number of points of discontinuity of the function \( f(x) = x - [x] \) in the interval \( (0, 7) \) are:

The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are:

The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:

If \( A \) and \( B \) are events such that \( P(A) = 0.42 \), \( P(B) = 0.48 \), and \( P(A \cap B) = 0.16 \), then: I. \( P(\text{not } A) = 0.58 \)
II. \( P(\text{not } B) = 0.52 \)
III. \( P(A \cup B) = 0.47 \)

The connective in the statement: \[ "2 + 7>9 \, \text{or} \, 2 + 7<9" \] is:

The value of \[ \lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x} \] is:

Amplitude of \( \frac{1 + \sqrt{3}i}{\sqrt{3} + 1} \) is:

If \( 12 \cot^2 \theta - 31 \csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:

The number of ways in which first, second and third prizes can be given to $5$ competitors is

$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to

The value of $\displaystyle\lim_{n \to\infty} \frac{1+2+3+...n}{n^{2}+100}$ is equal to :

The coefficient of $x^3$ in the expansion of $\left(x -\frac{1}{x}\right)^{7}$ is :

If $ \hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{i} + \hat{k}$ are the position vectors of the vertices of a triangle $ABC$ taken in order, then $\angle A$ is equal to

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

Eccentricity of ellipse $\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1 $ if it passes through point $(9, 5)$ and $(12, 4)$ is

If $a, b, c$ are in G.P., then

If $A = \frac{1}{3} \begin{bmatrix}1&2&2\\ 2&1&-2\\ a&2&b\end{bmatrix} $ is an orthogonal matrix, then