Suppose that A, B and C are matrices of order \(m \times n, n \times 5\) and \(5 \times q\) respectively. The restriction on m, n and q so that AB - BC is defined are

Match List-I with List-II

List I (Function)	List II (Derivative with respect to ' x ')
(A) \(f(x)=x^x\)	(I) \(a x^{a-1}\)
(B) \(f(x)=a^x\)	(II) 0
(C) \(f(x)=a^a\)	(III) \(a^x \log _e a\)
(D) \(f(x)=x^a\)	(IV) \(x^x\left(1+\log _e x\right)\)

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A random variable X has the following probability distribution

X	0	1	2	3	4	5
P(X)	0.1	k	0.2	2k	0.3	k

Then \(P(X<3)\) is

If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then

Let \(\left|\begin{array}{cc}3 x & -7 \\ 1 & 4\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & x\end{array}\right|\), then value of \(x\) is :

The slope of the normal to the curve \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\) at \(\theta=\frac{\pi}{4}\) is :

The present value of a sequence of payments of Rs. \(2000\) made at the end of every \(6\) months and continuing forever, if money is worth \(8 \%\) per annum compounded semi-annually, is:

An angular magnification of 30 X is desired using an objective lens of focal length 1.25 cm and an eyepiece of focal length 5 cm. What should be the separation between objective and eyepiece when the final image is formed at the near point ?

If \(A = \begin{bmatrix} 2a & 0 & 0 \\ 0 & 2a & 0 \\ 0 & 0 & 2a \end{bmatrix}\), then the value of \(|\text{adj A}|\) is:

The solution of the differential equation \(\frac{d y}{d x}=\frac{6}{x^2} ; y(1)=3\) is :

The value of \(\left[\begin{array}{lll}1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b)\end{array}\right]\) is

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
The major product in the reaction of anisole with bromine in ethanoic acid, is :

Match List-l with List-II:

List-I (Concepts)	List-II (Explanation)
(A) Standing state	(I) Available biomass for the consumption of heterotrophs
(B) Secondary productivity	(II) Rate of formation of organic matter by consumers
(C) Standing crop	(III) Mass of living matter in a trophic level at a given time
(D) Net primary productivity	(IV) Amount of mineral nutrients in the soil at a given time

Choose the correct answer from the options given below: