Consider the curves, \(x^2+y^2=1\) and \((x-1)^2+y^2=1\).
Area enclosed by the two curves is :

Let f : R → R be defined as f(x) = [x], where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?
(A) f is one-one but not onto
(B) f is not onto
(C) f is not one-one
(D) f is one-one and onto
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Matrix)	List-II (Inverse of the Matrix)
(A) \(\left[\begin{array}{cc}1 & 7 \\ 4 & -2\end{array}\right]\)	(I) \(\left[\begin{array}{cc}2 / 15 & 1 / 10 \\ -1 / 15 & 1 / 5\end{array}\right]\)
(B) \(\left[\begin{array}{cc}6 & -3 \\ 2 & 4\end{array}\right]\)	(II) \(\left[\begin{array}{cc}1 / 5 & -2 / 15 \\ -1 / 10 & 7 / 30\end{array}\right]\)
(C) \(\left[\begin{array}{cc}5 & 2 \\ -5 & 4\end{array}\right]\)	(III) \(\left[\begin{array}{cc}\frac{1}{15} & \frac{7}{30} \\ 2 / 15 & -1 / 30\end{array}\right]\)
(D) \(\left[\begin{array}{ll}7 & 4 \\ 3 & 6\end{array}\right]\)	IV) \(\left[\begin{array}{cc}2 / 15 & -1 / 15 \\ 1 / 6 & 1 / 6\end{array}\right]\)

Choose the correct answer from the options given below:

A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement.
The probability that first is blue and second is green is

Match List - I with List - II. Match the integrating factors :

List - I (Differential Equation)	List - II (Integrating factor)
(A) \(\frac{d y}{d x}+3 y=e^{-2 x}\)	(I) \(\frac{1}{x}\)
(B) \(x \frac{d y}{d x}+y=3 x^2\)	(II) \(e^{-x}\)
(C) \(x \frac{d y}{d x}-y=3 x^2\)	(III) \(x\)
(D) \(\frac{d y}{d x}-y=x\)	(IV) \(e^{3 x}\)

Choose the correct answer from the options given below :

\(\int_0^{\pi / 2} \frac{\sin ^8 x}{\sin ^8 x+\cos ^8 x} d x\) is equal to

The value of \(x\), for which the function \(f(x)=x(x-2)\) attains its minimum value, is:

Read the Passage carefully and answer the Questions:
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^{ a }[B]^{ y }\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The unit of rate constant for first order reaction is:

\(\int_0^2\left(x^2+1\right) d x\) is equal to

In India, the number of biosphere reserves and national parks are -

The unequivocal proof that DNA is the genetic material came from the experiments of __________.

Two point charges + 200 \( \mu \)C are placed at a distance of 2 mm from each other in a uniform electric field of \( 10^5 \text{ N/C} \), such that the line joining the negative to positive charge makes an angle 30° with the field. The torque acting on the system is:

In an experiment with a convex lens, the length of an image is 1 cm, and the object length is 5 cm. If the object is placed at a distance of 40 cm from the lens, then the focal length of the lens is