List of top Mathematics Questions

To draw a pair of tangents to a circle which are inclined to each other at an angle of $ 50^\circ $, it is required to draw tangents at end points of those two radii of the circle. What should be the angle between these two radii?
The angle of elevation of a 15 m high tower from a point 15 m away from its foot is:
If \(\sec(7^\circ - 2\alpha) = \csc(5\alpha - 7^\circ)\), then the value of \(\alpha\) is:
The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?
If the angle between the hands of a clock be $54^{\circ}$ and the time it reads between $7$ and $8$, find the time indicated by the clock.
The integral part of $(8+3\sqrt{7})^n$ is
Find the.
  1. Probability of the pointer stopping on D in (Question 1-(a))?
  2. Probability of getting an ace from a well shuffled deck of \(52\) playing cards?
  3. Probability of getting a red apple. (See figure below)
Image of Red Apples
If $C_{0}$, $C_{1}$, $C_{2}$, $C_{3}$, $\cdots$ are binomial coefficients in the expansion of $(1 + x)^n$, then $\frac{C_{0}}{3}- \frac{C_{1}}{4}+ \frac{C_{2}}{5}- \frac{C_{3}}{6}+ \cdots$ is equal to
Four writers must write a book containing $17$ chapters. The first and third writer must write $5$ chapters each, the second writer must write $4$ chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is
The sum of the first \( n \) terms of an arithmetic progression is \( S_n = 3n^2 + 2n \). Find the 5th term of the sequence.
If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
Evaluate \( \int_{1}^{2} \frac{1}{x^2} \, dx \).

Find the derivative of the function \(f(x) = \sqrt{3x^2 + 2x + 1}\).

If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
The sum of the first 20 terms of an arithmetic progression is 610. If the first term is 7, what is the common difference?
The integral $ \int (3x^2 - 2x + 1) \, dx $ is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) have a difference of 2, find the value of \( k \).
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
A box contains 4 white and 6 black balls. If 3 balls are drawn at random with replacement, what is the probability that at least one is white?
If \( z = 1 + i \), find the modulus of \( z^2 \).