List of top Mathematics Questions asked in KCET

A unit vector perpendicular to the plane containing the vectors $\hat{i} + 2 \hat{j} + \hat{k}$ and $-2 \hat{i} + \hat{j} + 3\hat{k}$ is

If the angle between $\vec{a}$ and $\vec{b}$ is $\frac{2 \pi}{3}$ and the projection of $\vec{a}$ in the direction of $\vec{b} $ is -2, the $|\vec{a}|$ =

XY - plane divides the line joining the points A (2, 3, - 5) and B (-1, -2, -3) in the ratio

The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm.

The value of $\sqrt{24 . 99}$ is

The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is

The inverse of the matrix $\begin{bmatrix}2&5&0\\ 0&1&1\\ -1&0&3\end{bmatrix} $ is

Acute angel between the line $\frac{x-5}{2} = \frac{y+1}{-1} = \frac{z+4}{1} $ and the plane 3x - 4y - z + 5 = 0 is

f : R $\to$ R and g : [0, $\infty$) $\to$ R is defined by f(x) = $x^2$ and g(x) = $\sqrt{x}$ . Which one of the following is not true?

If A and B are two events of a sample space S such that P(A) = 0.2, P(B) = 0.6 and P(A | B) = 0.5 then P(A?| B)=

If ?X? has a binomial distribution with parameters n = 6, p and P(X = 2) = 12, P(X = 3) = 5 then P =

A random variable ?X? has the following probability distribution: x 1 2 3 4 5 6 7 P(x) k-1 3k k 3k $3k^2$ $k^2$ $k^2 + k$ Then the value of k is

Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2x - y + z + 3 = 0 is

The constant term in the expansion of $\left(x^2 - \frac{1}{x^2} \right)^{16}$ is

The maximum area of a rectangle inscribed in the circle $(x + 1)^2 + (y - 3)^2 = 64$ is

In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

The negation of the statement "72 is divisible by 2 and 3" is

A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is

A bag contains 17 tickets numbered from 1 to 17. A ticket is draw at random, then another ticket is drawn at random, then another ticket is drawn without replacing the first one . The probability that both the tickets may show even numbers is

If $\left( \frac{ 1 - i}{1 + i}\right)^{96} = a + ib $ then (a,b) is

If $A = \begin{bmatrix}2&-2\\ -2&2\end{bmatrix}$ then $A^n = 2^k A,$ where k =

If $A = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix}$ , then $AA' = $

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

If A and B are mutually exclusive events , given that $P(A) = \frac{3}{5} , P(B) = \frac{1}{5}$, then P(A or B) is

The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is