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HALF COURSE TEST – VII

Paper 1

Time Allotted: 3 Hours Maximum Marks: 246  Please r ead the inst ruct ions carefu l l y . You are a l lot ted 5 minutes

speci f i ca l l y for th is purpose.  You are not a l lowed to leave the Exam inat ion Hal l before the end of

the test .

INSTRUCTIONS

A. General Instructions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets. 2. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 4. Each part is further divided into three sections: Section-A, Section-B & Section-C 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be

provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic

devices, in any form, are not allowed. B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers

on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your

Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts.

1. Section – A (01 – 07) contains 7 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and – 1 mark for wrong answer.

Section – A (08 – 11) contains 4 multiple choice questions which have one or more than one correct answer. Each question carries +3 marks for correct answer. There is no negative marking.

Section-A (12 – 16) contains 2 paragraphs. Based upon paragraph, 2 and 3 multiple choice questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer and – 1 mark for wrong answer.

2. Section – B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2

columns. Statements in the first column have to be matched with statements in the second column. Each question carries +8 marks for all correct answer. For each correct row +2 marks will be awarded. There may be one or more than one correct matching. No marks will be given for any wrong matching in any question. There is no negative marking.

3. Section-C (01 – 06) contains 6 Numerical based questions with answers as numerical value from 0 to 9 and each question carries +3 marks for correct answer. There is no negative marking.

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Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6  1019 C

Mass of electron me = 9.1  1031 kg

Permittivity of free space 0 = 8.85  1012 C2/N-m2

Density of water water = 103 kg/m3

Atmospheric pressure Pa = 105 N/m2

Gas constant R = 8.314 J K1 mol1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol1 = 0.0821 Lit atm K1 mol1 = 1.987  2 Cal K1 mol1 Avogadro's Number Na = 6.023  1023 Planck’s constant h = 6.625  1034 Js = 6.625  10–27 ergs 1 Faraday = 96500 coulomb 1 calorie = 4.2 joule 1 amu = 1.66  10–27 kg 1 eV = 1.6  10–19 J Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92.

Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.

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PPhhyyssiiccss PART – I

SECTION – A

Straight Objective Type

This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct 1. At the middle of the mercury barometer tube there is a little

column of air with the length l0 and there is vacuum at the top as shown. Under the normal atmospheric pressure and the temperature of 300 kelvin, l0 = 10 cm. Neglect expansion of the tube. The length of the air column if the temperature rises to 330 Kelvin will be:

(A) 100 11

cm (B) 11 cm

(C) 10 cm (D) 12 cm

air column

vacuum

l0

2. Two cars A and B are moving towards each other with same speed 25 m/s. Wind is blowing with

speed 5 m/s in the direction of motion of car A. The car A blows horn of frequency 300 Hz and the sound is reflected from car B. The wavelength of the reflected sound received by the driver of car A is (velocity of sound in air = 330 m/s)

(A) 25 m 36

(B) 31m 36

(C) 35 m 36

(D) 37 m 36

3. A particle is moving along the x axis is acted upon by a single force F = F0e–kx, where F0 and k are

constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of :

(A) 0F k

(B) 0k F ke

(C) 0k kF e

(D) kekF0

Space for rough work

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4. First 10 cm piece of a uniform meter strick is cut and kept on the other end as shown in figure. Find the shift in the x-coordinate of center of mass

(A) 5 cm (B) 10 cm (C) 9 cm (D) 45 cm 5. A satellite is in a circular orbit very close to the surface of a planet with speed v0. At some point it is

given an impulse along its direction of motion, causing its velocity to increase  times (that is, its speed becomes v0). It now goes into an elliptical orbit. The maximum possible value of  for satellite to move in the elliptical orbit is:

(A) 2 (B) 2

(C) 2 + 1 (D) 1 2 1

6. An elevator is moving upward with an acceleration a. It has velocity v at t = 0. A man inside the

elevator lifts a body of mass m through a height h in interval t = 0 to t = t0. The average power developed by the man is in elevator ref. frame :

(A) 0

m(g a)h t  (B) m(g + a) (v + 1

2 at0)

(C) 0

mgh t

(D) mg (v + 1 2

at0)

7. A thermally insulated vessel contains some water at 0°C. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at 0°C = 21 × 105 J/kg and latent heat of freezing of water = 3.36 × 105 J/kg. The maximum percentage amount of water that will be solidified in this manner will be :

(A) 86.2% (B) 33.6% (C) 21% (D) 24.36%

Space for rough work

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Multiple Correct Choice Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct 8. As a wave propagates : (A) The wave intensity remains constant for a plane wave (B) The wave intensity decreases as the inverse of the distance from the source for a spherical wave (C) The wave intensity decreases as the inverse square of the distance from the source for a

spherical wave (D)