List of top Mathematics Questions

From a group of 10 persons, in how many ways can a selection of 4 persons to be made such that a particular person is always included?

There are twelve friends. On the eve of Diwali, they exchanged greeting cards among themselves. How many cards did they exchange altogether?

In Super 30 movie, Anand sir asks every of 30 students to do handshake among themselves, find total number of handshakes.

There are 23 buses available between Dinu's house and his school. How many ways are possible for Dinu to go from his house to school and return using different buses?

Babita has to go to a party. She decides to wear either a Saree or a dress. If Babita has 5 Sarees and 6 dresses, in how many ways can she choose her outfit?

Ram has 4 formal shirts and 5 formal trousers, in how many ways can he choose his outfit for the interview?

Find the direction cosines of a line that makes equal angles with the coordinate axes.

In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.

(3, −4) and (4, −a) lie on line. Find a?

The locus of the mid-point of a chord of the circle \( x^2 + y^2 = 4 \), which subtends a right angle at the origin is

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

What is the probability of an impossible event?

Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]

The end-points of a diameter of a circle are \( (-1, 4) \) and \( (5, 4) \). Then the equation of the circle is

A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

Given: \( P(B) = 0.8 \) and \( P(A \cup B) = 0.8 \), find \( P(A' \cup B') \).

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]

Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

Given that \( |AB| = 21 \) and \( |A^{-1}| = 7 \), find \( |B| \).

The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.

Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]