1 For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation of δm=A. Which of the following options is/are correct? A) For the angle of incidence i1=A, the ray inside the prism is parallel to the base of the prism B) At minimum deviation , the incident angle i1 and refracting angle r1 at the first refracting surface are realated by r1=(i12) 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 i1=sin−1[sinA√4cos2A2−1−cosA] D) For this prism, the refractive index μ and the angle prism A are related as A=12cos−1(μ2)
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
3 An electron in a hydrogen atom undergoes a transition from an orbit with quantum number ni to another with quantum number nf . vi and vf are respectively, the initial and final potential energies of the electron. If vivf=6.25 then the smallest possible nf is A) 5 B) 8 C) 4 D) 3
4 A drop of liquid of radius R=10-2m having surface tension S=0.14π Nm-1 divides itself into K identical drops. In this process the total change in the surface energy △U=10−3 J . If K=10α, then the value of α is A) 5 B) 7 C) 6 D) 3
5 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 δT=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 δLLis closet to A) 1% B) 5% C) 3% D) 0.2%
6 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 −Q2ϵ0(1−1√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 Qϵ0 D) The circumference of the flat surface is an equipotential
7 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 τ 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 τ is zero B) if the force is applied tangentially at point S then τ≠0 but the wheel never climbs the step C) If the force is applied at point P tangentially , then τ decreases continously as the wheel climbs D) If the force is applied normal to the circumfernce at point X , then τ is constant
8 if y=y(x) satisfies the differential equation 8√x(√9+√x)dy=(√4+√9+√x)−1 dx,x >0 and y(0)=√7 , then y(256)= A) 16 B) 3 C) 9 D) 80
9 Let S={1,2,3.......,9} For k=1,2,...5 , Let Nk 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
10 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
11 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 A) −32 B) 32 C) 53 D) −53
12 Let f:R→ R be a differentable function such that f(0)=0, f(π2)=3 and f ' (0)=1 if g(x)=∫π20f′(t)cosec tf(t)−cot tcosec tf(t)]dt for xϵ(0,π2], then lim A) 4 B) 2 C) 1 D) 3
13 The order of basicity among the following compound is A) II>I>IV>III B) I>IV>III>I C) IV>I>II>I D) IV>I>II>III
14 Among the following , the correct statement(s) is (are) A) 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} C) AlCl_{3} has the three centre two electron bonds in its dimeric structure D) BH_{3} has the three centre two electron bonds in its dimeric structure
15 The option (s) with only amphoteric oxides is (are) A) NO,B_{2}O_{3},PbO,SnO_{2} B) Cr_{2}O_{3},CrO,SnO,PbO C) Cr_{2}O_{3},BeO,SnO,SnO_{2} D) ZnO,Al_{2}O_{3},PbO,PbO_{2}