List of top Mathematics Questions asked in KCET

For the function \(f(x) = x^3-6x²+12x-3; x = 2\) is

The function \(x^x; x > 0\) is strictly increasing at

\(\frac{d}{dx}[cos^2(cot^{-1}\sqrt{\frac{2+x}{2-x}})]\) is

If \(f(x) = x e^{x(1-x)}\) then f(x) is

If \(A=\begin{vmatrix}x&1\\1&x\end{vmatrix}\) and \(B=\begin{vmatrix}x &1&1\\1& x&1 \\1&1&x \end{vmatrix}\),then \(\frac{dB}{dx}\) is

Let \(f(x)=\begin{vmatrix}cosx &x& 1\\ 2sinx &x& 2x \\ sinx& x& x\end{vmatrix}\).Then \(\lim\limits_{x \to 0}\frac{f(x)}{x^2}\)=

The function f(x) = |cos x| is

Let the function satisfy the equation f (x + y) = f(x)f(y) for all x, y ∈ R, where f (0)≠0. If f (5) = 3 and f'(0)=2, then f'(5) is

If $ cos^{-1}x+ cos^{-1}y+cos^{-1}z = 3 \pi$ then $ x(y+z) + y(x+z) + z(x+y) $equals to

If $2sin^{-1}x -3 cos^{-1}x =4, x∈ [-1,1] $ then $2sin^{-1}x +3cos^{-1}x $ is equal to

If A is a square matrix such that $A^2 = A$, then $(I + A)^3 $is equal to

If A = $\begin{bmatrix}1 & 1 \\1 & 1 \end{bmatrix}$ then $A^{10}$ is equal to

Let f : R ⇢ R be defined by $f (x) = x^2 +1$. Then the pre images of 17 and –3 respectively are

Let $(gof)(x) = sin x$ and $(fog)(x) = (sin \sqrt x)^2,$ Then

If f(x)= $\begin{vmatrix} x-3 & 2x^2-18 & 2x^3-81\\ x-5 & 2x^2-50 & 4x^3-500\\ 1 & 2 & 3 \\ \end{vmatrix}$ then f(1). f(3) + f(3). f(5) + f(5). f(1) is

The equation of parabola whose focus is (6, 0) and directrix is x = –6 is

The angle between the line x + y = 3 and the line joining the points (1, 1) and (–3, 4) is

$ \frac{\sqrt2 cosx -1}{cot x-1}$ is equal to

The negation of the statement “For every real number $x ; x^2 + 5$ is positive” is

Let a, b, c, d and e be the observations with mean m and standard deviation S. The standard deviation of the observations a + k, b + k, c + k, d + k and e + k is

Let f : R ⇢ R be given f(x) = tan x. Then $f^{-1}(1)$

If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the quadratic equation is

In the expansion of $\frac{C_1}{C_0} + 2\frac{C_2}{C_1} +3\frac{C_3}{C_2}+…………… n \frac{C_{n}}{C_{n-1}}$ is equal to