The following data are from a random sample : \(5,8,10,7,10,14\), then the point estimate of the population standard deviation is

The function \(f(x)=x^3+1\) is:

Match List-I with List-II
If \(P(A)=\frac{3}{7}, P(B)=\frac{4}{7}\) and \(P(A \cup B)=\frac{5}{7}\)

List-I	List-II
(A) \(P(A \cap B)\)	(I) \(\frac{2}{3}\)
(B) \(P(A \mid B)\)	(II) \(\frac{5}{7}\)
(C) \(P(B \mid A)\)	(III) \(\frac{1}{2}\)
(D) \(P\left(A^{\prime} \cup B^{\prime}\right)\)	(IV) \(\frac{2}{7}\)

Choose the correct answer from the options given below :

A person wishes to purchase a house for ₹ \(39,65,000\) with a down payment of ₹ \(5,00,000\) and balance in equal monthly installments (EMI) for 25 years.
If bank charges \(6 \%\) per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300}=4.465\) ]

The area (in sq. units) of the region bounded by the curve \(y=\sin x,-2 \pi \leq x \leq 2 \pi\) and the \(x\)-axis is :

Particular solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) given that when x = 0 y = 0 is:

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

Match List - I with List - II.

LIST I Differential equation	LIST II Integrating Factor (I.F)
A. \(\frac{d y}{d x}-\frac{y}{x}=2 x\)	I. \(x^2-1\)
B. \(\frac{d y}{d x}+\left(\frac{2 x}{x^2-1}\right) y=\frac{2}{\left(x^2-1\right)^2}\)	II. \(\sqrt{1-x^2}\)
C. \(\frac{d y}{d x}-\left(\frac{x}{1-x^2}\right) y=\frac{1}{1-x^2}\)	III. \(\frac{1}{x}\)
D. \(\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{\cot x}{1+x^2}\)	IV. \(1+x^2\)

Choose the correct answer from the options given below:

The average emf induced in a coil is 2 V when current is changed in 0.4 s.
(A) from 5 A to 2 A and the self-inductance of the coil is 0.266 mH
(B) from 4 A to 4 A in the opposite direction, the self-inductance of the coil is 0.10 mH

A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is

Read the following passage carefully and answer the given questions.
Immune System in the Body
The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The primary lymphoid organs are bone marrow and thymus where immature lymphocytes differentiate into antigen-sensitive lymphocytes. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells. The bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Hence, an antibody is represented as H2L2. Different types of antibodies are produced in our body. IgA, IgM, IgE, IgG are some of them. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs.
Which one of the following technique is not useful for the detection of cancers of internal organs?

Let \(f: R \rightarrow R\) be defined as \(f(x)=5 x^2\). Choose the correct answer :

The magnetic flux linked to a coil changes from 10 \(\times 10^{-3}\) Wb to 6 \(\times 10^{-3}\) Wb in 0.01 s. The induced emf will be :