List of top Mathematics Questions asked in CBSE CLASS XII

If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).
A relation \( R \) on set \( A = \{1, 2, 3, 4, 5\} \) is defined as \[ R = \{(x, y) : |x^2 - y^2| <8\}. \] Check whether the relation \( R \) is reflexive, symmetric, and transitive.
A function \( f \) is defined from \( R \to R \) as \( f(x) = ax + b \), such that \( f(1) = 1 \) and \( f(2) = 3 \). Find the function \( f(x) \). Hence, check whether the function \( f(x) \) is one-one and onto.
Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]
E and F are two independent events such that \( P(\overline{E}) = 0.6 \) and \( P(E \cup F) = 0.6 \). Find \( P(F) \) and \( P(\overline{E} \cup \overline{F}) \).
If \( x^{1/3} + y^{1/3} = 1 \), find \( \frac{dy}{dx} \) at the point \( \left( \frac{1}{8}, \frac{1}{8} \right) \).
Evaluate: \[ \int_0^{\frac{\pi^2}{4}} \frac{\sin\sqrt{x}}{\sqrt{x}} \, dx \]
Find: \[ \int x \sqrt{1 + 2x} \, dx \]
A linear programming problem deals with the optimization of a/an:
If \( P(A|B) = P(A'|B) \), then which of the following statements is true?
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
If \( f(x) \) is an odd function, then: \[ \int_{-\pi/2}^{\pi/2} f(x) \cos^3 x \, dx \, \text{equals:} \]
Let \( f(x) \) be a continuous function on \([a, b]\) and differentiable on \((a, b)\). Then, this function \( f(x) \) is strictly increasing in \((a, b)\) if:
Let \( \theta \) be the angle between two unit vectors \( \hat{a} \) and \( \hat{b} \) such that \( \sin \theta = \frac{3}{5} \). Then, \( \hat{a} \cdot \hat{b} \) is equal to:
If a matrix has 36 elements, the number of possible orders it can have, is:
The number of corner points of the feasible region determined by constraints \( x \geq 0, y \geq 0, x + y \geq 4 \) is:
The distance of point \( P(a, b, c) \) from the y-axis is:
If matrices \( A \) and \( B \) are of order \( 1 \times 3 \) and \( 3 \times 1 \) respectively, then the order of \( A'B' \) is:
If \( x = at, y = \frac{a}{t} \), then \( \frac{dy}{dx} \) is:
The solution of the differential equation \( \frac{dy}{dx} = \frac{1}{\log y} \) is:
The interval in which \(y=x^2e^{-x}\) is increasing is
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.
A function \( f : \mathbb{R}_+ \to \mathbb{R} \) (where \( \mathbb{R}_+ \) is the set of all non-negative real numbers) defined by \( f(x) = 4x + 3 \) is:
Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]
If \( P(A | B) = P(A' | B) \), then which of the following statements is true?