List of top Mathematics Questions asked in KCET

If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

The two lines $l x+my=n$ and $l'x+m'y=n'$ are perpendicular if

$\displaystyle \lim_{x\to0}\left(\frac{\tan \,x}{\sqrt{2x +4} - 2}\right)$ is equal to

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

The third term of a G.P. is 9. The product of its first five terms is

If cos x = |sin x| then, the general solution is

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is

If $A = \{ x | x \in N, x \le 5 \}, B = \{ x | x \in Z, x^2 - 5x + 6 = 0\}$, then the number of onto functions from A to B is

$\sqrt{3}\, cosec \,20^{\circ} - \sec\, 20^{\circ}$ =

If $| 3x -5| \le 2$, then

The interval in which the function $f(x) = x^3 - 6x^2 + 9x + 10$ is increasing in

If $a + \frac{\pi}{2} < 2 \tan^{-1} x + 3 \cot^{-1} x < b $ then 'a' and 'b' are respectively.

The domain of the function f : R $\to$ R defined by $f(x) = \sqrt{x^2 - 7x + 12} $ is

If $P$ and $Q$ are symmetric matrices of the same order then $PQ - QP$ is

On the set of positive rationals, a binary operation * is defined by a * b = $\frac{2ab}{5}$ . If 2 * x = $3^{-1}$ then x =

The eccentricity of the ellipse $9x^2 + 25y^2 = 225$ is

The distance of the point (1, 2, 1) from the line $\frac{x-1}{2} = \frac{ y-2}{1}=\frac{ z-3}{2} $ is

If $3A + 4B' = $$\begin{bmatrix}7&-10&17\\ 0&6&31\end{bmatrix} $ and $2B - 3A'$ $ \begin{bmatrix}-1&18\\ 4&0\\ -5&-7\end{bmatrix}$ then $B =$

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