List of top Mathematics Questions asked in KCET

If 2^x + 2^y = 2^x+y, then $\frac{dy}{dx}$ is

The right hand and left hand limit of the function
f(x) = $\left\{ \begin{aligned} & \frac{e^{1/x}-1}{e^{1/x}+1}\ \ ,\ \ \text{if x}\ne0 \\ & \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ ,\ \ \text{if x = 0} \end{aligned} \right.$ are respectively

If A is a square matrix of order 3 and |A| = 5, then |A adj.A| is

If a₁a₂a₃ …….. a₉ are in A.P. then the value of $\begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \\ \end{vmatrix}$ is

If f(x) =

\[\begin{vmatrix} x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0 \\ \end{vmatrix}\]

then

If $\begin{pmatrix} 2 & 1 \\ 3 & 2 \\ \end{pmatrix}A=\begin{pmatrix} 1 & 0 \\ 0 & 1 \\ \end{pmatrix}$, then the matrix A is

If A and B are square matrices of same order and B is a skew symmetric matrix, then A’BA is

If A = $\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{pmatrix}$, then A⁴ is equal to

The value of $\cos(\sin^{-1}\frac{\pi}{3}+\cos^{-1}\frac{\pi}{3})$ is

The domain of the function defined by f(x) = $\cos^{-1}\sqrt{x-1}$ is

If A = {a, b, c}, then the number of binary operations on A is

Let f : [2, ∞) → R be the function defined by f(x) = x² - 4x + 5 , then the range of f is

If a relation R on the set {1, 2, 3} be defined by R = {(1, 1)}, then R is

If A, B, C are three mutually exclusive and exhaustive events of an experiment such that P(A) = 2P(B) = 3P(C),then P(B) is equal to

The standard deviation of the data 6, 7, 8, 9, 10 is

The negation of the statement “For all real numbers x and y, x + y = y + x” is

$\lim\limits_{x\rightarrow0}(\frac{\tan x}{\sqrt{2x+4}-2})$ is equal to

If the parabola x² = 4ay passes through the point (2, 1), then the length of the latus rectum is

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

If the sum of n terms of an A.P is given by S_n = n² + n, then the common difference of the A.P is

If $ z = x + iy $, then the equation $ |z + 1| = |z - 1| $ represents:

If f(x) = $\sin^{-1}$ $\left(\frac{2x}{1+x^{2}}\right)$, then f' $(\sqrt{3})$ is

If the sum of n terms of an A.P is given by $S_n = n^2 + n$, then the common difference of the A.P is

If a relation R on the set {1, 2, 3} be defined by R={(1, 1)}, then R is

Rain is falling vertically with a speed of $12 \,ms^{-1}$. A woman rides a bicycles with a speed of $12 \,ms^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?