A 95% confidence interval states that the population mean is greater than 152 and less than 160.
If \(\sigma=15\) and \(Z_{0.025}=1.96\), then what sample size was used in the study?

A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then the probability of at least 3 successes is :

Amit, Sumit and Puneet were doing shooting.
Amit hits the target 4 times in 5 shots, Sumit hits the target 3 times in 4 shots and Puneet hits the target 2 times in 3 shots.
Then the probability that Amit, Sumit and Puneet all may hit the target is:

If \(r_{e f f}=\) effective rate of interest, \(r=\) nominal rate of interest and \(m=\) number of conversion periods per year, the relationship between nominal rate and effective rate of interest is :

If \(\vec{a}=2 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+\hat{k}\) then
Match List-I with List-II

List-I	List-II
(A) Projection of \(\vec{a}\) on \(\vec{b}\) is	(I) \(-7 \hat{i}+4 \hat{j}+6 \hat{k}\)
(B) \(\vec{a} \times \vec{b}\) is	(II) \(\frac{1}{\sqrt{101}}(-7 \hat{i}+4 \hat{j}+6 \hat{k})\)
(C) Unit vector along \(\vec{a}+\vec{b}\) is	(III) \(\frac{5}{3}\)
(D) Unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) is	(IV) \(\frac{1}{\sqrt{33}}(4 \hat{i}+\hat{j}+4 \hat{k})\)

Choose the correct answer from the options given below :

Let \(R\) be the set of all real numbers and \(f: R \rightarrow\) Range \(f\) be given by \(f(x)=3 x^2+1\). Then \(f^{-1}\{1,2\}\) is :

If \(y=\frac{1}{1+x^{b-a}+x^{a-a}}+\frac{1}{1+x^{a-b}+x^{a-b}}+\frac{1}{1+x^{a-c}+x^{b-c}}\) then \(\frac{d^2 y}{d x^2}\) is:

The general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is :

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
A reaction is first order in A and second order in B. If the concentration of B is doubled its initial concentration and A is reduced to 3/4th of its initial concentration, the new rate of the reaction is

Which of the following is used to make the bacterial cell as 'Competent cell' to take up DNA?

The general solution of the differential equation \(\frac{d y}{d x}=x y+x+y+1\) is

A current through a wire varies with time, as \( I = \alpha t + \beta t^2 \) where \( \alpha = 10 \, \text{A s}^{-1} \) and \( \beta = 4 \, \text{A s}^{-2} \). How much charge will cross through a section of the wire in 12 s?

If the points \((2,1),(-1,4)\) and \((a, 3)\) are collinear then the value/(s) of a is/(are) :