The area of region bounded by two curves \(y^2=x\) and \(x^2=y\) is:

The function \(f(x)=\frac{x^2-25}{(x+5)}, x \neq-5\) is:

\(\int\left(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\right) d x=\)
(Given that c is an arbitrary constant )

If \(x=a \sin ^3 t\) and \(y=a \cos ^3 t\), then \(\frac{d y}{d x}\) is equal to :

How many times a person must toss a fair coin so that the probability of having at least one head is more than 80% ?

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-l with List-ll

List - I	List - II
(A) P(y > 2)	(I) \(\frac{2}{5}\)
(B) k	(II) \(\frac{2}{3}\)
(C) \(P(y \leq 3)\)	(II) \(\frac{8}{15}\)
(D) \(P(2 \leq y \leq 4)\)	(II) \(\frac{1}{15}\)

Choose the correct answer from the options given below

The remainder when \(2^{340}\) is divided by 341 is :

Which of the following pairs of transition metal ions is the strongest oxidizing agent?

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders
A colour blind man marries a carrier woman. Choose the possible progeny outcome.

Which of the following statements are true?
(A) The potential energy for a system of two negative point charges is negative
(B) Electrostatic force is a conservative force
(C) Negative potential energy between two charges implies that the force between them is repulsive
(D) Electrostatic potential energy is a scalar quantity
Choose the correct answer from the options given below:

Arrange the following in increasing order of their \(pK _a\) values.
(A) o-nitrophenol
(B) m-nitrophenol
(C) Phenol
(D) Ethanol
Choose the correct answer from the options given below:

A runs 5 times faster than B . If A gives B a start of 100 m , how far must the goal be so that A and B reach there at the same time.

Which of the following statements are correct?
A. In a region of free space with electric field E, there is an energy density \( \frac{1}{2}\epsilon_0 E^2 \)
B. An electromagnetic wave contains both electric and magnetic field.
C. Electromagnetic waves do not exert pressure
D. Hertz could not establish the wave nature of radiation.
E. No material medium is required for vibrations of electric field and magnetic field.