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For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation of $\delta_{m}=A$ . Which of the following options is/are correct?

A) For the angle of incidence

$i_{1}=A$ , the ray inside the prism is parallel to the base of the prism

B) At minimum deviation , the incident angle

$i_{1}$ and refracting angle

$r_{1}$ at the first refracting surface are realated by

$r_{1}=(\frac{i_{1}}{2})$

C) For the prism, the emergent ray at the second surface will be tangent to the surface when the angle of incidence at the first surface is

$i_{1}= \sin^{-1}[\sin A\sqrt{4\cos^{2}\frac{A}{2}-1}-cos A]$

D) For this prism, the refractive index

$\mu$ and the angle prism A are related as

$A=\frac{1}{2}\cos^{-1}(\frac{\mu}{2})$

A flat plane is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at very low pressure. The speed of the plane v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

A) At a later time the external force F balances the resistive force

B) The plate will continue to move with constant non-zero acceleration at all times.

C) The resistive force experienced by the plate is proportional to v

D) The pressure difference between the leading and trailing faces of the plate is proportinal to uv

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number n_i to another with quantum number n_f . v_i and v_f are respectively, the initial and final potential energies of the electron. If $\frac{v_{i}}{v_{f}}=6.25$ then the smallest possible n_f is

A) 5

B) 8

C) 4

D) 3

A drop of liquid of radius R=10^-2m having surface tension $S= \frac{0.1}{4\pi}$ Nm^-1 divides itself into K identical drops. In this process the total change in the surface energy $\triangle U= 10^{-3}$ J . If $K=10^{\alpha}$ , then the value of $\alpha$ is

A) 5

B) 7

C) 6

D) 3

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T= 0.01s$ and he measures the depth of the well to be L=20 m. Take the acceleration due to gravity g=10 ms^-2 and the velocity of sound is 300 ms^-1. Then the fractional error in the measurement

$\frac{\delta L}{L}$ is closet to

A) 1%

B) 5%

C) 3%

D) 0.2%

A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statement is/are correct?

A) The electric flux passing through the curved surface of the hemisphere is

$-\frac{Q}{2\epsilon_{0}}(1-\frac{1}{\sqrt{2}})$

B) The component of the electric field normal to the flat surface is constant over the surface

C) Total flux through the curved and the flat surface is

$\frac{Q}{\epsilon_{0}}$

D) The circumference of the flat surface is an equipotential

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $\tau$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct ?

A) If the force is applied normal to the circumference at point P then

$\tau$ is zero

B) if the force is applied tangentially at point S then

$\tau\neq 0$ but the wheel never climbs the step

C) If the force is applied at point P tangentially , then

$\tau$ decreases continously as the wheel climbs

D) If the force is applied normal to the circumfernce at point X , then

$\tau$ is constant

if y=y(x) satisfies the differential equation

$8\sqrt{x}(\sqrt{9+\sqrt{x}})dy=(\sqrt{4+\sqrt{9+\sqrt{x}}})^{-1}$

dx,x >0 and $y(0)=\sqrt{7}$ , then y(256)=

A) 16

B) 3

C) 9

D) 80

Let S={1,2,3.......,9} For k=1,2,...5 , Let N_k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N₁+N₂+N₃+N₄+N₅ =

A) 210

B) 252

C) 126

D) 125

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR,RP,PQ respectively of triangle PQR.

(ox × oy)=

A) sin(P+Q)

B) sin(P+R)

C) Sin(Q+R)

D) sin2R

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR,RP,PQ respectively of triangle PQR.

I f the triangle PQR varies, then the minimum value of $\cos(P+Q)+\cos(Q+R)+\cos(R+P)$ is

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{5}{3}$

$-\frac{5}{3}$

Let f:R→ R be a differentable function such that f(0)=0, $f(\frac{\pi}{2})=3$ and f ' (0)=1

if $g(x)=\int_{0}^{\frac{\pi}{2}} f'(t) cosec$ $t f(t)-\cot$ $t cosec$ $t f(t)] dt$

for $x\epsilon(0,\frac{\pi}{2}]$ , then $\lim_{x \rightarrow0 }g(x)=$

A) 4

B) 2

C) 1

D) 3

The order of basicity among the following compound is

1822020575_compound 1.JPG

A) II>I>IV>III

B) I>IV>III>I

C) IV>I>II>I

D) IV>I>II>III

Among the following , the correct statement(s) is (are)

$Al(CH_{3})_{3}$ has the three centre two -electron bonds in its dimeric structure

B) The lewis acidity of

$BCl_{3}$ is greater than that of

$AlCl_{3}$

$AlCl_{3}$ has the three centre two electron bonds in its dimeric structure

$BH_{3}$ has the three centre two electron bonds in its dimeric structure

The option (s) with only amphoteric oxides is (are)

$NO,B_{2}O_{3},PbO,SnO_{2}$

$Cr_{2}O_{3},CrO,SnO,PbO$

$Cr_{2}O_{3},BeO,SnO,SnO_{2}$

$ZnO,Al_{2}O_{3},PbO,PbO_{2}$

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