List of top Mathematics Questions

The sum of first 'n' natural numbers is

The distance between the points (2, 3) and (4, 1) is

In an A.P. if the first term is 4 and 9^th term is 20 then 15^th term is

If A is a skew symmetric matrx, then \(A^ {2021}\) is

Let L₁ be the line joining (0, 0, 0) and (1, 2, 3) and L₂ be the line joining (2, 3, 4) and (3, 4, 5). The point of intersection of L₁ and L₂ is

How many numbers greater than 50000 can be formed by using digits 2, 5, 5, 6, 7?

Total number of elements in the power set of a set $A$ containing 17 elements is

Evaluate the integral \( \int \frac{1}{x \sqrt{ax^2 - x^2}} \, dx \)

Evaluate the integral \( 3 \int \frac{3^x}{\sqrt{1 - 9^x}} \, dx \)

Evaluate the integral \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x \, dx \)

The solution of the differential equation \( \frac{d^2y}{dx^2} = 0 \) represents

The solution of the differential equation \( \frac{dy}{dx} + \sqrt{\frac{1 - y^2}{1 - x^2}} = 0 \) is

The solution of the differential equation \( x \frac{dy}{dx} = \cot y \) is

If \( \sin A + \sin B = a \) and \( \cos A + \cos B = b \), then \( \cos(A + B) \) equals?

What is \( \frac{\cos \theta}{1 - \tan \theta} + \frac{\sin \theta}{1 - \cot \theta} \) equal to?

Find the general solution of \( \sin 2x + \cos x = 0 \).

If \( f(x) + 2f(1 - x) = x^2 + 5 \) for all real values of \( x \), then \( f(x) \) is given by:

Evaluate $\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3$

If \( U_{n+1} = 3U_n - 2U_{n-1} \) and \( U_0 = 2, U_1 = 3 \), then \( U_n \) is equal to

If \( 4^n + 15n + P \) is divisible by 9 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is

\( (2^{3n} - 1) \) is divisible by

If \( S = \frac{2^2 - 1}{2} + \frac{3^2 - 2}{6} + \frac{4^2 - 3}{12} + \ldots\) \text{ upto 10 terms, then S is equal to}

\( \sum_{n=1}^{m} n \cdot n! \) is equal to

The first and fifth terms of an A.P. are -14 and 2 respectively and the sum of its $n$ terms is 40. The value of $n$ is

The probability of choosing randomly a number \( c \) from the set \( \{1, 2, 3, \dots, 9\} \) such that the quadratic equation \( x^2 + 4x + c = 0 \) has real roots, is