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Consider a hydrogen atom with its electron in the n^th orbital. An electromagnetic radiation of wavelength 90mm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc= 1242 eV nm)

A) 2

B) 3

C) 1

D) 4

A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet's gravity is $\frac{1}{4}$ th of its value at the surface of the planet. If the escape velocity from the planet is $v_{sec}=v\sqrt{N}$ , then the value of N is (ignore energy loss due to atmosphere)

A) 4

B) 3

C) 2

D) 1

A nuclear power plant supplying electrical power to a village uses a radioactive material of half-life T years as fuel.The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is

A) 4

B) 2

C) 3

D) 1

A ring of mass M and radius R is rotating with angular speed ω about a fixed vertical axis passing through its centre O with two-point masses each of mass $\frac{M}{8}$ at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure.

At some instant , the angular speed of the system is $\frac{8}{9}\omega$ and one of the maases is at a distance of $\frac{3}{5}R$ from O. At this instant , the distance of the other mass from O is

$\frac{2}{3}R$

$\frac{1}{3}R$

$\frac{3}{5}R$

$\frac{4}{5}R$

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement is/are

A) The average energy per mole of the gas mixture is 2RT

B) The ratio of speed of sound in the gas mixture to that in helium gas is

$\sqrt{\frac{6}{5}}$

C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is

$\frac{1}{2}$

D) The ratio of the rms speed of helum atoms to that of hydrogen molecules is

$\frac{1}{\sqrt{2}}$

The total number of stereoisomers that can exist for M is

A) 2

B) 1

C) 0

All the energy released from the reaction

$X\rightarrow Y,\triangle_{r}G^{0}=-193kJmol^{-1}$

is used for oxidising M⁺ as $M^{+}\rightarrow M^{3+}+2\overline{e}$ , E⁰ =-0.25 V.

Under standard conditions , the number of moles of M⁺ oxidised when one mole of X is converted to Y is [F=96500 C mol^-]

A) 4

B) 3

C) 2

D) 1

Let y(x) be a soilution of the differential equation $(1+e^{x})y^{'}+ye^{x}=1,$ .If y(0)=2 , then which of the following statement(s) is/are true?

A) y(-4)=0

B) y(-2)=0

C) y(x) has a critical point in the interval (-1,0)

D) y(x) has no critical point in the interval (-1,0)

Consider the family of all circles whose centres lie on the straight line y=x, If this family of circles is represented by the differential equation $Py"+Qy'+1=0$ , where P,Q are the functions of x, y and y' (here, $y'=\frac{dy}{dx},y''=\frac{d^{2}y}{dx^{2}})$ , then which of the following statement (s) is /are true?

A) P=y+x

B) P=y-x

$P+Q=1-x+y+y'+(y')^{2}$

$P-Q=x+y-y'-(y')^{2}$

In terms of potential difference V, electric current i, Permittivity $\epsilon_{0}$ , permeability $\mu_{0}$ and speed of light c, the dimensionally correct equations is /are

$\mu_{0}I^{2}=\epsilon_{0}V^{2}$

$\epsilon_{0}I=\mu_{0}I$

$I=\epsilon_{0}cV$

$\mu_{0}cI=\epsilon_{0}V$

Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a particular value i_m are confined in the medium of refractive index n₁. The numerical aperture (NA) of the structure is defined as sin I'm.

For two structures namely S₁ with $n_{1}=\frac{\sqrt{45}}{4}$ and $n_{2}=\frac{3}{2}$ and S₂ with $n_{1}=\frac{8}{5}$ and $n_{2}=\frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1. the correct options is/are

A) NA of

$S_{1}$ immersed in water is the same as that of

$S_{2}$ immersed in a liquid of refractive index

$\frac{16}{3\sqrt{15}}$

B) NA of

$S_{1}$ immersed in liquid of refractive index

$\frac{6}{\sqrt{15}}$ is the same as that of

$S_{2}$ immersed in water.

C) NA of

$S_{1}$ placed in air is the same as that

$S_{2}$ immersed in liquid of refractive index

$\frac{4}{\sqrt{15}}$

D) NA of

$S_{1}$ placed in air is the same as that of

$S_{2}$ placed in water

In the complex acetylbromidodicarbonylbis (triethylphosphine ) iron (II) , the number of Fe -C bond (s) is

A) 3

B) 4

C) 2

D) 1

Suppose that all the term of an arithmetic progression are natural numbers. If the ratio of the sum of first seven terms to the sum of the first eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this AP is

A) 9

B) 8

C) 7

D) 4

Let $f'(x)=\frac{192x^{3}}{2+\sin^{4}\pi x}$ for all x ε R with $f(\frac{1}{2})=0$ If $m\leq\int_{1/2}^{1} f(x) dx\leq M,$ , then the possible values of m and M are

A) m=13,N=24

$m=\frac{1}{4},M=\frac{1}{2}$

C) m=-11,M=0

D) m=1,M=12

Let $F:R\rightarrow R$ be a thrice differentiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)<0 for x ε (1,3) , Let f(x)=xF(X) for all x ε R.

The correct statement(s) is/are

$f^{1}(1)<0$

$f(2)<0$

$f'(x)\neq 0$ for any

$x\epsilon (1,3)$

D) f'(x) =0 for same

$x\epsilon (1,3)$

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