List of top Mathematics Questions

Convert the non-linear equation \( xy' + y = x^4 y^3 \) into a linear one using the transformation \( z = y^{-2} \).
The linear equation is ...........

If \( A = \begin{pmatrix} -3 & 2 \\ 1 & 0 \end{pmatrix} \) is a \( 2 \times 2 \) matrix, then \( A \) satisfies the relation ...........

Let \( i \) be an imaginary number such that \( i = \sqrt{-1} \). Let \( a \) and \( b \) be real numbers satisfying \( a^2 + b^2 = 1 \).
Then, the eigenvalues of the matrix \[ \begin{bmatrix} -a & b \\ b & a \end{bmatrix} \] are ...........

The directional derivative of \( f(x, y, z) = xyz \) at the point \( (1, 2, 3) \) in the direction of the vector \( 2\hat{i} + \hat{j} - 2\hat{k} \) is ...........

If \( \sin x \) is a solution of the differential equation \[ \dfrac{d^4 y}{dx^4} + 2 \dfrac{d^3 y}{dx^3} + 6 \dfrac{d^2 y}{dx^2} + 2 \dfrac{dy}{dx} + 5y = 0, \] then the general solution is ...........

In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?

A company's sales increased by 20% in 2022 compared to 2021 and by 25% in 2023 compared to 2022. If the sales in 2021 were ₹10 lakhs, what were the sales in 2023?

Solve the following differential equation:
\[ \frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0 \]

A real valued function $ f: A \to B $ defined by $ f(x) = \frac{4 - x^2}{4 + x^2} \ \forall x \in A $ is a bijection. If $ -4 \in A $, then $ A \cap B = $

Evaluate: \[ \sqrt{\sin^4 x + 4\cos^2 x} - \sqrt{\cos^4 x + 4\sin^2 x} = ? \]

Among the following, the correct picture representation of the number of school teachers in Delhi is:

Calculate the compound interest on ₹ 1000 for a period of one year at the rate of 10% per annum, if interest is compounded quarterly.

If \( A : B : C = 2 : 3 : 4 \), then find the value of \( \frac{A}{B} \div \frac{B}{C} \div \frac{C}{A} \):