List of top Mathematics Questions

The value of \(\lim_{x \to \pi/6} \frac{\sin x + \sin 2x - 1}{\sin 2x - \sin 3x + 1}\) is

Tangent to the ellipse \(\frac{x^2}{32} + \frac{y^2}{18} = 1\) having slope \(-\frac{3}{4}\) meet the coordinate axis at A and B. Then, the area of \(\triangle AOB\), where O is the origin, is

In a \(\triangle ABC\), if \(b = 2\), \(\angle B = 30^\circ\), then the area of the circumcircle of \(\triangle ABC\) (in sq units) is

The value of \(\int \frac{\cos x + \sin x}{\cos x + x \sin x} \, dx\) is

If \(\sin A + \cos B = a\) and \(\sin B + \cos A = b\), then \(\sin(A + B)\) is equal to

A letter lock contains 5 rings each marked with four different letters. The number of all possible unsuccessful attempts to open the lock is

If \(y^{1/m} + y^{-1/m} = 2x\), then \((x^2 - 1)y'' + xy'\) is equal to

The condition that the straight line \(cx - by + b^2 = 0\) may touch the circle \(x^2 + y^2 = ax + by\) is

If \(0 < \alpha, \beta, \gamma < \frac{\pi}{2}\), such that \(\alpha + \beta + \gamma = \frac{\pi}{2}\) and \(\cot \alpha, \cot \beta, \cot \gamma\) are in AP, then the value of \(\cot \alpha \cot \gamma\) is

The value of \(S = \frac{1}{6} \left( \frac{\pi}{2} - \sin^2 \frac{2\pi}{7} - \cos^2 \frac{2\pi}{7} \right)\) is

Fifteen coupons are numbered 1, 2, …, 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

The solution of the differential equation \(\frac{dy}{dx} = \sin(x + y) \tan(x + y) - 1\) is

Let \(h(x) = \min(x, x^2)\), for every real number \(x\). Then,

The area bounded by the parabolas \(y^2 = 4a(x + a)\) and \(y^2 = -4a(x - a)\) is

Area bounded by the curves \(y = x^2\) and \(y = 2 - x^2\) is

The value of \(\int \frac{\sin x + \cos x}{3 + \sin 2x} dx\) is

The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are

The equation of the circle passing through the point \((2a, 0)\) and whose radical axis is \(x = \frac{a}{2}\) with respect to the circle \(x^2 + y^2 = a^2\), will be

\(\lim_{n \to \infty} \left( \frac{1^2}{1 - n^3} + \frac{2^2}{1 - n^3} + \dots + \frac{n^2}{1 - n^3} \right)\) is equal to

The differential equation of the family of curves \(y = Ae^{3x} + Be^{5x}\), where \(A\) and \(B\) are arbitrary constants, is

The derivative of \(\sin^{-1}(2x\sqrt{1-x^2})\) with respect to \(\sin^{-1}(3x - 4x^3)\) is

If \(\begin{bmatrix} \alpha & \beta \gamma & -\alpha \end{bmatrix}\) is to be the square root of the two-rowed unit matrix, then \(\alpha, \beta\) and \(\gamma\) should satisfy the relation

Total number of regions in which 'n' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to

Total number of polynomials of the form \(x^3 + ax^2 + bx + c\) that are divisible by \(x^2 + 1\), where \(a,b,c \in \{1, 2, 3, \dots, 10\}\) is equal to

The statement \(p \rightarrow (q \rightarrow p)\) is equivalent to