Match List I with List II

LISTI	LIST II
A. \(\int \sin ^2(2 x+1) d x\)	I. \(\frac{x}{2}+\frac{\sin (2 x+1) \cos (2 x+1)}{4}+C\)
B. \(\int \cos ^2(2 x+1) d x\)	II. \(\frac{\cos 3(2 x+1)}{24}-\frac{3 \cos (2 x+1)}{8}+C\)
C. \(\int \sin ^3(2 x+1) d x\)	III. \(\frac{x}{2}-\frac{\sin (2 x+1) \cos (2 x+1)}{4}+C\)
D. \(\int \cos ^3(2 x+1) d x\)	IV. \(\frac{\sin 3(2 x+1)}{24}+\frac{3 \sin (2 x+1)}{8}+C\)

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The probability distribution of a random variable X is given below:

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
P(X)	p	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

The area enclosed between the curve \(y=x^2+2\) and x -axis between \(x=0\) and \(x=3\) is :

For the set of all straight lines in a plane, the relation of "perpendicularity" is:
(A) reflexive but neither symmetric nor transitive.
(B) symmetric but neither reflexive nor transitive.
(C) transitive but neither reflexive nor symmetric.
(D) neither reflexive nor symmetric nor transitive.
(E) reflexive, symmetric but not transitive.
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If \(x y+\frac{x^2}{y}=x^3 y+y\), then \(\frac{d y}{d x}\) is equal to

If A and B are non-singular square matrices of the same order, then \(\left(A B^{-1}\right)^{-1}=\)

If \(P, Q\) and \(R\) are three singular matrices given by
\(P=\left[\begin{array}{cc}2 & 3 a \\4 & 3\end{array}\right], Q=\left[\begin{array}{cc}b & 5 \\2 a & 6\end{array}\right]\)
and \(R=\left[\begin{array}{cc}a^2+b^2-c & 1-c \\ c+1 & c\end{array}\right]\), then the value of \((2 a+6 b+17 c)\) is:

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

The formation of pomato is an example of:

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Identify the incorrect fact about genetic modification.

Identify the correct statements in the context of paramagnetic substances.
(A) In external magnetic field B, individual atomic dipole moment points in opposite direction of B.
(B) Susceptibility is small and positive.
(C) In non-uniform magnetic field, the paramagnetic bar will tend to move from weak field to strong.
(D) Examples of paramagnetic substances are Aluminium, Sodium and oxygen.
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Which of the following is not the characteristics of enzymes ?

Which of the following compound will undergo azo coupling reaction with benzene diazonium chloride?
(A) Aniline
(B) Phenol
(C) p-Toluidine
(D) Nitrobenzene
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