List of top Questions asked in KEAM- 2017

The number of diagonals in a hexagon is:

Two balls are selected from two black and two red balls. The probability that the two balls will have no black ball is:

The sum of odd integers from 1 to 2001 is:

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

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

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

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

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:

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

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

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:

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

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

The \( 30^{th} \) term of the arithmetic progression \( 10, 7, 4, \dots \) is:

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

Three numbers \( x, y, \) and \( z \) are in arithmetic progression (A.P.). If \( x+y+z = -3 \) and \( xyz = 8 \), then \( x^2+y^2+z^2 \) is equal to:

If \( |z| = 5 \) and \( w = \frac{z-5}{z+5} \), then \( \text{Re}(w) \) is equal to:

If \( a = e^{i\theta} \), then the expression \( \frac{1+a}{1-a} \) is equal to:

If \( \begin{vmatrix} 3i & -9i & 1 \\ 2 & 9i & -1 \\ 10 & 9 & i \end{vmatrix} = x + iy \), then:

Let \( \Delta = \begin{vmatrix} 1 & 1 & 1 \\ 1 & -1-w^2 & w^2 \\ 1 & w & w^4 \end{vmatrix} \), where \( w \neq 1 \) is a complex number such that \( w^3 = 1 \). Then \( \Delta \) equals: