GOPREP TALENT SEARCH EXAM

QUESTION PAPER

INSTRUCTIONS:

The duration of the test will be 60 minutes. Use the time accordingly.

The test paper consists of 50 questions divided into four sections, Section A, Section B, Section C & Section D.

➢ Section A contains 15 questions of Physics.

➢ Section B contains 15 questions of Chemistry.

➢ Section C contains 15 questions of Mathematics.

➢ Section D contains 5 questions of Aptitude.

Each question will have 4 choices, with the only single choice being correct.

You will get 2 marks for every correct answer.

There will be no negative marking for any wrong answer or unanswered

question.

SECTION |A|

PHYSICS

1. If in a p-n junction diode, a square input signal of 10V is applied as shown

Then the output signal across the load resistor RL will be

A.

B.

C.

D.

2. A ring made of non-conducting material and of radius ‘R’ has a charge of ‘+Q’ uniformly distributed on it. Which of the following statements is incorrect about the Electric Field ‘E’ and Electric Potential ‘V’ at any point on the ‘axis’ of the ring at a distance of ‘x’ from it’s center.

A. The Maximum value of ‘V’ is at

B. The Electric Field ‘E’ is zero at

C. The Electric Field ‘E’ is maximum for

D. The Electric Field ‘E’ is maximum for

3. The activity of a radioactive sample falls from to in 20 minutes. What

can be the possible half-life of the radioactive sample? Assume

A. 19 min B. 15 min C. 10 min D. 8.2 min

4. Three capacitor are connected as shown in the figure. When key is closed then, find the amount of charge flowing through the battery.

A.

B.

C.

D.

5. What is the ratio of the de-Broglie wavelengths of molecules of nitrogen and oxygen which are at temperature and respectively?

A.

B.

C.

D.

6. An iron-cored transformer assumed to be 100% efficient. The ratio of the secondary turns to the primary turns is 1 : 30. Find the current in the primary coil.

A. 0.01 A B. 0.1 A C. 2 .1 A D. 10 A

7. Determine approximately how much power is dissipated through the 12Ω resistance. Assume the internal resistance of the battery is 2.5Ω.

A. 3 W B. 6 W C. 10 W D. 16 W

8. In Young's double slit experiment, the central maxima occur where path difference between the interfering beams is zero. A glass plate of thickness 5 mm is inserted to cover the upper slit completely. The slit separation is 10 mm and the diffraction patterns are observed at the focal plane of the converging lens (focal length 35 mm). Which of the following statement on the position of the central maximum is true? Assume the refractive index of the glass is 2.5.

A. Central maxima will shift up by 5 mm B. The position of central maxima remains same. C. Central maxima will shift down by 15 mm D. None of these

9. When a ray of light is incident normally on one refracting surface of an equilateral prism (Refractive index of the material of the prism = 1.5)

A. Emerging ray is deviated by

B. Emerging ray is deviated by

C. Emerging ray just grazes the second refracting surface D. The rays undergoes total internal reflection at the second refracting surface

10. Following figure shows an adiabatic cylindrical container of volume V0 divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas is at pressure P1 and temperature T1 in left part and gas at

pressure P2 and temperature T2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

A. P2 B. P1

C.

D. Insufficient Data

11. The ratio of intensities between two coherent sound sources is 4:1. The difference of loudness in dB between maximum and minimum intensities when they interfere in space is

A. 10 log 2 B. 20 log 3 C. 10 log 3 D. 20 log 2

12. A pulse shown here is reflected from the rigid wall A and then from free end B. The shape of the string after these 2 Reflection will be.

A.

B.

C.

D.

13. Steel ruptures when a shear of 3.5 × 108 Nm‒2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly:

A. 1.4 × 104 N B. 2.7 × 104 N

C. 3.3 × 104 N D. 1.1 × 104 N

14. A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A. t = t1 – t2

B.

C.

D.

15. An aluminium container of mass 100 gm contains 200 gm of ice at -20°C . Heat is added to the system at the rate of 100 cal/s. The temperature of the system after 4 minutes will be (specific heat of ice = 0.5 and L = 80 cal/ gm, specific heat of Al = 0.2 cal/gm/°C) A. 40.5°C B. 25.5°C C. 30.3°C D. 35.0°C

SECTION |B|

CHEMISTRY

16. The Ellingham diagram reveals the curves for MgO, ZnO and CO, Answer the following questions on the basis of the given curves.

Carbon can reduce iron (II) oxide at A. 500 K B. 1000 K C. Above 1000 K D. Above 500 K and below 1000 K

17. Calculate the accelerating potential must be imparted to a proton beam to give it an effective wavelength of 0.005 nm. a. 36.8 volts b. B. 32.8 volts c. 30.2 volts d. 39.8 volts

18. The precipitate of Ag2CrO4 (Ksp = 1.9 x 10-12) is obtained when equal volumes of the following are mixed.

a. 10-4 M Ag+ + 10-4 M 24CrO −

b. 10-2 M Ag+ + 10-3 M 24CrO −

c. 10-5 M Ag+ + 10-3 M 24CrO −

d. 10-4 M Ag+ + 10-5 M 24CrO −

19.

a. 1-(S) , 2-(P,R), 3-(T), 4-(P,R,S,T) b. 1-(P,R) , 2-(R), 3-(R,S), 4-(Q,S,T) c. 1-(P,Q,R,T) , 2-(R), 3-(R,S), 4-(P,R,S,T) d. 1-( P,R,S,T) , 2-(R,S), 3-(R,S), 4-(P,Q,R,T)

20. The reaction of K2Cr2O7 with acidified solution of H2O2 yields a blue color substance. The change of oxidation state for Chromium observed in the above reaction is: a. 0 b. 5 c. 6 d. 2

21. Consider the following ionisation reactions:

If monovalent positive ion of A, divalent positive ion of B and trivalent positive ion of C have zero electron. Then incorrect order of corresponding I.E is : A. C3 > B2 > A1 B. B1 > A1 > C1 C. C3 > C2 > B2 D. B2 > C3 > A1

22. One mole of nitrogen gas at 0.8 atm takes 38 second to diffuse through a pin hole whereas one mole of an unknown compound of xenon with fluorine at 1.6 atm takes 57 second to diffuse through the same hole. The molecular formula of the compound is

a.

b.

c.

d.

23.

a. A – ii, B – v, C – vi, D – i, E – iii, F – iv b. A –vi, B – iv, C – v, D – iii, E – ii, F – i c. A – iii, B – iv, C – vi, D – ii, E – i, F – v d. A – ii, B – vi, C – v, D – iii, E – i, F – iv

24. .

; Identify N and M a. 6, 4 b. 6,6 c. 4, 4 d. 3,3

25. How many chiral centers are in the following compound?

a. 4 b. 5 c. 6 d. 7

26. Given: + += − = −3 2

0 0

Fe /Fe F /FeE 0.036V,E 0.439V. The value of standard electrode potential

for the change, 3 2(aq)Fe e Fe (aq)+ − ++ → will be:

A. -0.403 V B. 0.385V C. 0.77V D. 0.403V

27. The distance between adjacent, oppositely charged ions in rubidium chloride is 3.285 Å, in potassium chloride is 3.139Å, in sodium bromide is 2.981 Å and in potassium bromide is 3.293 Å. The distance between adjacent oppositely charged ions in rubidium bromide is A. 3.147 Å B. 3.385 Å C. 3.393 Å D. 3.439 Å

28. What is formed when benzoyl chloride reacts with aniline in presence of sodium hydroxide A. Acetanilide B. Benzanilide C. Benzoic acid D. Azobenzene

29. Consider the following sequence of reactions.

The products A. and B. are, respectively,

A.

B.

C.

D.

30. At the point intersection of the two curves shown, the conc. Of B is given by ________ for, A → nB:

A.

B.

C.

D. nA0

SECTION |C|

MATHEMATICS

31. If a polygon has 44 diagonals, then the number of its sides are A. 7 B. 11 C. 8 D. 10

32. The coefficient of x5 in (1+2x+3x2+……….up to infinite term)-3/2 is A. 21 B. 25 C. 26 D. 0

33. Solve :

A.

B.

C.

D. None

34. The roots of (x – a) (x – b) = abx2 A. are always real B. may be complex depending upon a & b C. are real and equal if and only if a = b = 2

D. are real and distinct if and only if

35. If is defined by , where denotes the greatest

integer function then is

A. Z, the set of all integers B. N, the set of all natural numbers

C. , the empty set D. R, the set of all real numbers

36. If , then is equal to

A. sin 1 B. 2 sin 1

C.

D. 3 sin 1

37. If = 0 , then the value of

is? A. –abc B. abc C. 0 D. none of these

38. Divide 48 into 4 parts such that third term is A.M. of first 2 and fourth term is addition of first 3. Find sum of first 2 parts. A. 16 B. 24 C. 8 D. 28

39. For let and be

three given functions. If a function, J(x) satisfies (f2oJof1)(x) = f3(x) then J(x) is equal to

: A. f1(x) B. f2(x)

C. D. f3(x)

40. Find the solution of the differential equation

at y(1)=3

A.

B.

C.

D.

41.

A.

B.

C.

D.

42. The area enclosed by y = 3x - 5, y = 0, x = 3 and x = 5 is A. 12 sq. units B. 13 sq. units

C. 1

132

sq. units

D. 14 sq. units

43.Vector of length 3 unit which is perpendicular to and lies in the plane

of and

A.

B.

C.

D.

44.Find the length of the side of an equilateral triangle whose one of the side

is and its vertex is

A.

B.

C.

D.

SECTION |D|

APTITUDE

45. If a is an integer lying in the closed interval [- 5 ,30], then the probability that the graph of y=x2+2(a+4) x-5a+64 is strictly above the x-axis is A. 2/9 B. 1/6 C. 1/2 D. 5/9

46. The sum of the ages of Ram and his father at present is 7/6 of what it was 5 years ago. Find the sum of their present ages. A. 30 B. 35 C. 60 D. 70

47. An ant is moving around a few food pieces of different shape scattered on the floor. For which food – piece would the ant have to take a longer round?

A. Food piece (P) B. Food piece (Q) C. Food piece (R) D. None of these

48. …. is equal to

A.

B.

C.

D.

49. Arrange the following words according to English Dictionary.

1. Banal

2. Banana

3. Banish

4. Bandage

5. Bandit A. 1, 3, 2, 4, 5 B. 1, 2, 4, 3, 5 C. 1, 2, 4, 5, 3 D. None of these

50.1024, ______, 64, 16, 4 A. 254 B. 236 C. 256 D. 244