If the mean of a binomial distribution is 12 and its standard deviation is 2 , then the number of trials is :

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

If the length of a simple pendulum is decreased by \(3 \backslash \%\), the percentage change in its period T is
[Note : \(T=2 \pi \sqrt{\frac{L}{g}}\) where \(L\) is the length of pendulum and \(g\) is constant]

The relationship between \(a\) and \(b\) making \(f(x)\) continuous at \(x=3\), where \(f(x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is:

\(\int \frac{e^x(1+x) d x}{\cos ^2\left(e^x x\right)}\) is equal to:

If \(x=t^{1 / 2}, y=t^{3 / 2}\), then \(\frac{d y}{d x}=\)

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

Which of the followings belong to false fruit category?
(A). Apple
(B). Cashew
(C). Strawberry
(D). Orange
Choose the correct answer from the options given below:

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 \(=k[A]^x[B]^y\)
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.
Which of the following statements are correct?
(A) Catalysts increase the rate of a chemical reaction.
(B) Catalysts can catalyze both spontaneous and non-spontaneous reactions.
(C) Higher the activation energy for a chemical reaction, lower is the rate of the reaction.
(D) Catalyst increases the potential energy barrier.
Choose the correct answer from the options given below:

Kohlrausch's Law helps to find:

The maximum value of \(4 \sin ^2 x+3 \cos ^2 x\) is:

Match List - I with List - II.

List - I (Disease)	List - II (Pathogen)
(A) Pneumonia	(I) Salmonella typhi
(B) Typhoid	(II) Plasmodium falciparum
(C) Malaria	(III) Wuchereria bancrofti
(D) Filariasis	(IV) Haemophilus influenzae

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Which of the following bond in DNA strand is broken by the action of restriction enzyme?