List of top Mathematics Questions asked in KEAM

The set of all real numbers satisfying the inequality \( x - 2 < 1 \) is:

The integral \( \int \frac{x+1}{x^{1/2}} \, dx \) is equal to:

If \( \int_{0}^{x} f(t)dt = x^2 + e^x (x > 0) \), then \( f(1) \) is equal to:

If \( \frac{|x-3|}{x-3} > 0 \), then:

The mode of the data 8, 11, 9, 8, 11, 9, 7, 8, 7, 3, 2, 8 is:

If the mean of six numbers is 41, then the sum of these numbers is:

If \( z = i^9 + i^{19} \), then \( z \) is equal to:

The sum of odd integers from 1 to 2001 is:

The number of words that can be formed by using all the letters of the word PROBLEM only once is:

The number of diagonals in a hexagon is:

The mean for the data 6, 7, 10, 12, 13, 4, 8, 12 is:

Let S be the set of all \( 2 \times 2 \) symmetric matrices whose entries are either zero or one. A matrix X is chosen from S. The probability that the determinant of X is not zero is:

Two distinct numbers \( x \) and \( y \) are chosen from 1, 2, 3, 4, 5. The probability that the arithmetic mean of \( x \) and \( y \) is an integer is:

In a class, 60% of the students know lesson I, 40% know lesson II and 20% know lesson I and lesson II. A student is selected at random. The probability that the student does not know lesson I and lesson II is:

From 4 red balls, 2 white balls and 4 black balls, four balls are selected. The probability of getting 2 red balls is:

A single letter is selected from the word TRICKS. The probability that it is either T or R is:

Three unbiased coins are tossed. The probability of getting at least 2 tails is:

The number of \( 3 \times 3 \) matrices with entries \( -1 \) or \( +1 \) is:

The solution of \( 3^{2x-1} = 81^{1-x} \) is:

Three numbers are in arithmetic progression (A.P.). Their sum is 21 and the product of the first number and the third number is 45. Then the product of these three numbers is:

If \( a+1, 2a+1, 4a-1 \) are in arithmetic progression, then the value of \( a \) is:

The sixth term in the sequence \( 3, 1, \frac{1}{3}, \dots \) is:

The arithmetic mean (A.M.) of two numbers \( x \) and \( y \) is \( 3 \) and their geometric mean (G.M.) is \( 1 \). Then \( x^2+y^2 \) is equal to:

Two numbers \( x \) and \( y \) have arithmetic mean 9 and geometric mean 4. Then \( x \) and \( y \) are the roots of:

If \( A = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), then the value of \( A^{2017} \) is equal to: