List of top Mathematics Questions

If \( z + \bar{z} = 6 \) and \( z - \bar{z} = 4i \), then \( |z|^2 = \)

The modulus of the complex number \( (2\sqrt{2} + i2\sqrt{2})^2 \) is equal to

Let \( z = 1 - i \). Then the value of \( z^4 \) is equal to

Let \( f(x)=\log_5 x \, (x > 0) \) and \( g(x)=\cos^{-1}(x) \, (-1\le x \le 1) \). Then the domain of \( g \circ f \) is

Let \( f(x) = \cos x \). Then the value of \( \frac{1}{2}[f(x+y) + f(y-x)] - f(x)f(y) \) is equal to

Let \( f(x) = x^2 - 10x - 19, \, x \in \mathbb{R} \). Then the inverse image of 5, \( f^{-1}(5) = \)

Let \( A, B, C \) be any three finite sets. If \( n(A \times B) = 160\), \( n(B \times C) = 80 \) and \( n(C \times A) = 200\), then \( n(A) = \)

If \[ \lim_{x \to \infty} \left( \frac{e}{1 - e} \left( \frac{1}{e} - \frac{x}{1 + x} \right) \right)^x = \alpha, \] then the value of \[ \frac{\log_e \alpha}{1 + \log_e \alpha} \] equals:

If \( A = \begin{bmatrix} 4 & \lambda & -3 0 & 2 & 5 1 & 1 & 3 \end{bmatrix} \), then \( A^{-1} \) exists if:

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

AB and CD are diameters of a circle with centre O and radius 7 cm. If \(\angle BOD = 30^\circ\), then find the area and perimeter of the shaded region.

Solution of the differential equation \( \frac{dy}{dx} + x = 0 \) represents a family of

One card is drawn from a well shuffled deck of 52 cards. Then the probability that the card will be a face card is ________

If two unbiased dice are thrown at a time, then find the probability of getting the sum of the number on the dice is 10?

A sector of a circle with radius 14 cm makes an angle 90° at the centre. Then the perimeter of the sector is (in cm).

Match the following:

Find the total surface area of the cuboid if length is 12 cm, breadth 8 cm and height is 10 cm (in cubic cm.)

The area of the triangle whose vertices are A(2, 3), B(−1, 0) and C(2, −4) (in square units) is

The median of the given data is
89, 45, 56, 67, 89, 45, 78, 45, 78, 45, 67

If \( \sin x = \dfrac{3}{5} \), then \( \tan x + \cot x = \)

If \(p(x) = 4x^{11} - 8x^9 + 7x^5 + 6x^3 + 4x^2 + 5x + 6\), then the number of zeros is ________.

For \((k \neq 0)\), if the quadratic equation \(kx(x - 2) + 6 = 0\) has two equal roots, then find the value of \(k\).

If \[ \frac{3}{x + y} + \frac{12}{2x - y} = \frac{7}{3} \text{ and } \frac{6}{x + y} + \frac{18}{2x - y} = \frac{11}{3}, \text{ then } x^2 + y^2 = \]

The roots of the equation \( x^4 - 5x^2 + 4 = 0 \) are