List of top Mathematics Questions

If \( g(f(x)) = |\sin x| \) and \( f(g(x)) = (\sin \sqrt{x})^2 \), then:
If the graph of \( y = p(x) \) does not intersect the X-axis at all, then the zeroes of \( p(x) \) are:
If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).
The value of the integral \( \int_0^1 x^2 \, dx \) is:
If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:
Solve for $ x $ in the equation $ 2x - 3 = 5x + 12 $.
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the value of \( \frac{5}{6} + \frac{3}{4} \).
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $
Evaluate the integral: \[ \int \sqrt{x^2 + 3x} \, dx \]
If \( \mathbf{a} \) and \( \mathbf{b} \) are two non-zero vectors such that the angle between them is \( 60^\circ \), what is the probability that the dot product \( \mathbf{a} \cdot \mathbf{b} \) is positive?
Find the value of \( x \) if \( \sin(2x) = 1 \).
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).
The product of Karan’s age five years ago and his age after 9 years from now is 32. This is represented by the quadratic equation:
Let \( \alpha, \beta \) be distinct non-zero real numbers, and let \( Q(z) \) be a polynomial of degree less than 5. If the function \[ f(z) = \frac{\alpha^6 \sin \beta z - \beta^6 (e^{2az} - Q(z))}{z^6} \] satisfies Morera's theorem in \( \mathbb{C} \setminus \{0\} \), then the value of \( \frac{\alpha}{4\beta} \) is equal to (in integer).
Ram and Syam are friends. Probability that both will have same birthday is:
If $ \tan\left( \alpha - \frac{\pi}{12} \right) = \frac{1}{\sqrt{3}} $, find $ \alpha $.
Tenth term of the AP \( 1, -1, -3, -5, \dots \) is
A card is drawn from a set of 52 cards. The probability of getting a queen card is:
Which of the following has equally likely outcomes?
If \( P(E) = \), then:
Which of the following cannot be a probability?
Formula for finding mode for grouped data is:
The mode and mean of a data are 7 and 5 respectively, then median is:
A model is made with two cones each of height 2 cm attached to the two ends of a cylinder. The diameter of the model is 3 cm and its length is 12 cm. Then the volume of the model is (use \( \pi = \frac{22}{7} \)):