Question Bank Categories%WP_TITLE_SEP%Class 12

Question 1: If \(\frac{d}{dx}f(x) = 2x + \frac{3}{x}\) and \(f(1) = 1\), then \(f(x)\) is: (A) \(x^2 + 3 \log |x| + 1\) (B) \(x^2 + 3 \log |x|\) (C)…

Question 1 (a): Evaluate \( \int_0^1 \frac{x e^x}{(x+1)^2} dx \). Question 1 (b): Solve the differential equation \( \frac{dy}{dx} = e^{x+y} + x^2 e^y \). Question 2: Find the present…

Question 1: If \( A \) is a square matrix of order 3 and \( |A| = 5 \), then the value of \( |2A| \) is: -10 10 -40…

SECTION A Question 1: If \( A \) and \( B \) are square matrices of the same order 3, such that \( |A| = 2 \) and \( AB…

SECTION A Question 1: Find the value of \( \tan^{-1}\sqrt{3} – \sec^{-1}(-2) \). Question 2: If \( A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 &…

Question 1: If for any \( 2 \times 2 \) square matrix \( A \), \( A(\text{adj} A) = \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix} \), then…

SECTION A Question 1: Find the maximum value of: \[ \begin{vmatrix} 1 & 1 & 1 \\ 1 & 1 + \sin\theta & 1 \\ 1 & 1 & 1…

SECTION A Question 1: If \[ \mathbf{a} = 7\mathbf{i} + \mathbf{j} – 4\mathbf{k} \quad \text{and} \quad \mathbf{b} = 2\mathbf{i} + 6\mathbf{j} + 3\mathbf{k}, \] then find the projection of \(…

SECTION A Question 1:Let ∗ be a binary operation on the set of all non-zero real numbers, given by \[ a ∗ b = \frac{ab}{5} \quad \text{for all } a,…