List of top Questions asked in KCET

The area of the region bounded by the line y = x and the curve y=x³ is

The solution of \(e^{\frac{dy}{dx}} = x+1,y(0) =3\) is

\(\int\limits_1^5(|x-3|+|1-x|)dx\)=

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

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

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

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 given f(x) = tan x. Then $f^{-1}(1)$

$ \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

The annual net primary productivity of the biosphere is approximately

The sequence of communities of primary succession in water is

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:

Select the correct statement from the following:

enzyme

Match the nutrients given in List-I with the source in List-II:

List I		List II
1	Vitamin A	p	Bitter gourd
2	Single cell protein	q	Beans
3	Vitamin C	r	Carrots
4	Protein	s	Spirulina spp

Choose the correct option from the following:

The chemical substances which are produced by some microbes which can kill or retard the growth of other microbes are known as