List of top Questions asked in KCET, JIPMER

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

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 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

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

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

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

Mule is the result of

Read the following statements:
Statement I: Morphine is obtained by acetylation of Heroin.
Statement II: Cannabinoids are known for their effect on cardiovascular system
Which of the following options is correct with reference to these statements?

Identify the bacterial disease among the following:

Stanley Miller simulated the conditions of pre – biotic earth using spark – discharge apparatus. Which organic compounds were observed by him on analysing the end product of his experiment?

The principle of vaccination is based on which property of immune system?

Find the incorrect statement among the following:

Most ape - like ancestral primate was