List of top Mathematics Questions asked in KCET

The value of \(\int\limits_0^1\frac{\log(1+x)}{1+x^2}\ dx\) is

The value of \(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos x}{1+e^x}\ dx\) is

The value of \(\int\limits^{\frac{1}{2}}_{-\frac{1}{2}}\cos^{-1}x\ dx\) is

The value of \(\int e^{\sin x}\sin 2x\ dx\) is

If \(\int\frac{3x+1}{(x-1)(x-2)(x-3)}dx\) = A log |x - 1| + B log |x - 2| + C log |x - 3| + C, then the values of A, B and C are respectively.

The value of \(\int\frac{1+x^4}{1+x^6}dx\) is

If the side of a cube is increased by 5%, then the surface area of a cube is increased by

The maximum value of \(\frac{\log_ex}{x}\), if x > 0 is

If the curves 2x = y² and 2xy = K intersect perpendicularly, then the value of K² is

If y = 2xⁿ⁺¹ + \(\frac{3}{x^n}\) then x²\(\frac{d^2y}{dx^2}\) is

If (xe)^y = e^x, then \(\frac{dy}{dx}\) is

If f(x) = sin^-1\((\frac{2x}{1+x^2})\), then f'\((\sqrt3)\) is\(\)

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 f(x) = \(\left\{ \begin{aligned}     & \frac{1-\cos Kx}{x\sin x} ,\ \ \text{if x}\neq0 \\     &\ \ \ \ \ \  \ \frac{1}{2}\ \ \ \ \ \ \ \ \  ,\ \ \  \text{if x=0} \end{aligned} \right.\) is continuous at x = 0, then the value of K is

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