For the following data :

	Size	Mean	Standard Deviation
Sample 1	4	40	8
Sample 2	5	50	10

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to :

If \(\hat{a}\) is a unit vector perpendicular to both the vectors \(\vec{b}=\hat{j}+2 \hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{j}\), then \(\hat{a}\) is equal to :

The equation of the normal to the curve \(y=2 \sin x\) at \((0,0)\) is:

The relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) on the set \(A=\{1,2,3\}\) is :

Match List-I with List-II

List-I	List-II
(A) \(\int \frac{d x}{x^2-16}\)	(I) \(\frac{1}{8} \log \left|\frac{4+x}{4-x}\right|+c\)
(B) \(\int \frac{d x}{x^2+16}\)	(II) \(\log \left|x+\sqrt{x^2-16}\right|+c\)
(C) \(\int \frac{d x}{16-x^2}\)	(III) \(\frac{1}{8} \log \left|\frac{x-4}{x+4}\right|+c\)
(D) \(\int \frac{d x}{\sqrt{x^2-16}}\)	(IV) \(\frac{1}{4} \tan ^{-1}\left(\frac{x}{4}\right)+c\)

Choose the Correct answer from the options given below :

Objective function \(z=200 x+500 y\), subject to the constraints
\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),
the minimum value of \(z\) is :

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

If \(X\) is a random variable which can assume values \(0,1,2,3\) or 4 such that \(P(X=1)=P(X=2)\) and \(3 P(X=3)=4 P(X=4) =P(X=0)=\frac{1}{8}\) then \(P(X>0)\) is :

The specific DNA sequence which is responsible for initiation of replication is known as:

Question: In the complex ion \(\left[ Fe \left( C _2 O _4\right)_3\right]^{3-}\), the coordination number of Fe is:

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
Identify the statements explaining biopracy
(A) Unauthorised exploitation of bio-resoures of a country
(B) Adequate compensation is given to one country from where bioresource is taken
(C) Exploitation of traditional knowledge to develop modern applications
(D) Equal benefit sharing between developed and developing nations
Choose the correct answer from the options given below:

Match List I with List II

LIST I	LIST II
A. Heroin	I. Atropa belladona
B. Marijuana	II. Erythroxylum coca
C. Cocaine	III. Cannabis sativa
D. Hallucinogenic properties	IV. Papaver somniferum

Choose the correct answer from the options given below:

Three charges, +Q, q and +Q are placed with q at mid point of the line joining the other two charges. For the system of charges to be in equilibrium, the value of q is