Let \(f\) be a function defined by \(f(x)=2 x^3-3 x^2-36 x+2\), then which of the following are correct ?
(A) The critical points of \(f ( x )\) are \(- 2\) and 3 .
(B) The function \(f(x)\) increases in the interval \((3, \infty)\)
(C) The function \(f(x)\) decreases in the interval \((-2,3)\)
(D) The function \(f(x)\) increases in the interval \((-2,3)\)
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The integral \(I=\int \frac{e^x}{1-e^{2 x}} d x\) is equal to :

A stone is dropped into a lake and waves move in circles at a speed of \(8 cm / sec\). At the instant, when the radius of the circular wave is 10 cm , how fast is the enclosed area increasing?

If A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I - A)^3 + A^2 + I\) is:

The area (in sq. units) of the region enclosed by the curve \(9 x^2+4 y^2=36\) is

The volume of a cube is increasing at the rate of \(27 cm^3 / s\). How fast is the surface area increasing when the length of the cube is 12 cm ?

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution :
(A) The number of trials is indefinitely large.
(B) The probability of success for each trial is indefinitely small.
(C) The product of the number of trials and the probability of success for each trial is finite.
(D) The probability of success for each trial is indefinitely large.
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Identify one of the given factors which does not affect Hardy-Weinberg equilibrium.

A magnet of magnetic moment \( 50 \hat{i} \text{ A m}^2 \) is placed along the X-axis in a magnetic field \( \vec{B} = (0.5 \hat{i} + 3.0 \hat{j}) \text{ T} \). The torque acting on it is

The hybridisation of \(NCl_3\) and \(PCl_3\) are respectively :

If the system of equations \(k x+y+z=0, x+k y-z=0, x-y+z=0\) has a non-zero solution, then the possible values of \(k\) are

Read the given passage and answer the question.
ABO blood groups in human beings are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surfaces and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and I. The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles, IA and IB are completely dominant over I.
Match List - I with List - II.

List - I (Phenotype)	List - II (Genotype)
(A) Blood group A	(I) IB IB, IBi
(B) Blood group B	(II) IA, IA IA
(C) Blood group O	(III) IA IB
(D) Blood group AB	(IV) ii

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Fertilization in human female takes place in -