List of top Mathematics Questions

Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :

The value of the greatest integer \(k\) satisfying the inequation \(2^{n+4} + 12 \ge k(n + 4)\) for all \(n \in N\) is

The half of the average value of three number is 20. The second number is thrice the third number and first number is twice the second number. What is the sum of smallest and largest number?

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three time by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is

One of the roots of the equation \((x + 1)^4 + 81 = 0\) is

The internal and external radii of a hollow hemisphere are \(5\sqrt{2} \text{ cm}\) and \(10 \text{ cm}\) respectively. A cone of height \(5\sqrt{7} \text{ cm}\) and radius \(5\sqrt{2} \text{ cm}\) is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of \(\pi\). (Use \(\sqrt{2} = 1.4\))

If the system of simultaneous linear equations \(x - 2y + z = 0\), \(2x + 3y + z = 6\) and \(x + 2y + pz = q\) has infinitely many solutions, then

If \(\cos 4x = \cos 3x\), find the general solution for \(x\).

A square matrix P satisfies \(P^2 = I - P\). If \(P^n = 5I - 8P\) then n is equal to

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4 , then the sum of its first twelve terms is

The mean of some observations is 54. If each observation is increased by 8 and its sum is divided by 2, then what is the mean of the resulting observations?

Two numbers P and Q are selected from Set {1,2,3,.....,100\,then find the probability of P.Q is divisible by 5.}

Let \(n(A) = m\) and \(n(B) = n\), if the number of subsets of A is 56 more than of subsets of B, then \(m + n\) is equal to

Out of 8 students in Section Alpha, 10 students in Section Beta and 12 students in Section Gamma, a teacher wants to create a team of three to represent the school in inter-school quiz competition. In how many ways the team can be formed such that all the members of the team are not from the same section ?

A certain sum of money is borrowed by a person at 8% simple interest for 4 years. If he has to pay Rs. 7834 as interest, what is the total amount he has to pay?

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers is less than 13?

If \( \mathbf{x} \) and \( \mathbf{y} \) are positive integers then the following is always true?
{2x - 3y < 0
(1) x = (y - 1)
(2) x > y

A school sold drama tickets for Rs. 100 each for donating to an orphanage. One member sold 75% of his tickets and had 80 tickets left. How many tickets did the member collect?

If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

The average age of 15 students is 18 years. If the teacher's age is added, the average increases by 1 year. What is the teacher's age?

Which of the following numbers is a perfect square?

A batsman has a certain average of runs for 11 innings. In the 12\(^{\text{th}}\) inning. He makes a score of 90 runs, thereby increasing his average by 5. His new average is: