List of top Questions asked in KCET

The function f(x) = |cos 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 \(\lim\limits_{x \to 0}\frac{f(x)}{x^2}\)=

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

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

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

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 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

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

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

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 $f^{-1}(1)$

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

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

If ΔABC is right angled at C, then the value of tan A + tan B is

The real value of ‘α’ for which $\frac{1 -isinα}{1+ 2isinα}$ is purely real 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

The annual net primary productivity of the biosphere is approximately

The sequence of communities of primary succession in water is

Which of these enzymes is required to cleave a plasmid?

Match the type of adaptation given in List-I with their examples given in List-II. Select the option showing correct combination.

List-1 (Types of adaptation)		List-II (Examples)
1	Biochemical adaptation	p	Desert lizards
2	Behavioural adaptation	q	Deep sea fishes
3	Physiological adaptation	r	Opuntia
4	Morphological adaptation	s	Kangaroo rats

Choose the correct option from the following: