The value of the integral \(I=\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\) is :

Evaluate \(\int_1^{\sqrt{3}} \frac{1}{1+x^2} d x\)

Let \(A=\left[a_{i j}\right]_{3 \times 2}\) and \(B=\left[b_{i j}\right]_{3 \times 4}\) be two matrices.
Then the order of the matrix \(\left(A^T \cdot B\right)^T\) is :

Which of the following is not the specification of the Sinking Fund?

\(\int \frac{x^3-1}{x^2} d x\) is equal to

The function \(f(x)=|x-1|, x \in R\) is:

Let \(X\) denotes the number of hours you study during a randomly selected school day. The random variable \(X\) has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List - I with List - II.

LIST - I	LIST - II
(A) Value of K	(I) \(\frac{1}{4}\)
(B) Probability you study at least two hours	(II) \(\frac{1}{8}\)
(C) Probability you study exactly two hours	(III) \(\frac{3}{8}\)
(D) Probability you study at most one hour	(IV) \(\frac{5}{8}\)

Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions
The separated DNA fragments can be visualized only after staining the DNA with ethidium bromide followed by exposure to UV radiation. Bright orange colored bands of DNA in ethidium bromide stained gel exposed to UV light can be seen. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. This step is known as elution. The DNA fragments purified in this way are used in constructing recombinant DNA by joining them with a cloning vector.
The natural polymer used in the agarose gel is extracted from:

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance that absorbs. In physiosorption the attractive forces are mainly van der Waal's forces while in chemisorption ionic/covalent bonds are formed between particles of adsorbent and adsorbate. The catalytic activity of finely divided iron in Haber's process of ammonia manufacture can be explained by adsorption theory. Adsorption being an exothermic process, the heat of adsorption is utilised in enhancing the rate of the reaction. Adsorption has many applications being used in gas masks, control of humidity, chromatograph separation, curing diseases etc.
Which of the following is not a surface phenomenon?

The interval in which the function \(g(x)=x^2 e^{-x}\) is increasing is :

Which one of the following is not an example of terrestrial ecosystem?

The solution of \(y^{\prime}-y^{\prime \prime}=2 x\) is:
A. \(y=x^2+2 x+2\)
B. \(y=x^2+2 x+1\)
C. \(y=x+2\)
D. \(y=x^2-2 x+1\)
Choose the correct answer from the options given below :

Which metal has the highest oxidation state in the first row transition series?