B_tech Sample Paper

7/30/2019 B_tech Sample Paper

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ALL INDIA TERII SCHLORSHIP EXAM - 2013

SAMPLE PAPER FOR B.TECH

PHYSICS1. (i) The maximum horizontal range of projectile is 3times the maximum height attained by a

projectile when it is thrown at an angle to have maximum possible range.(ii) A rocket suffered an engine failure at a height of 1000m from ground. It is sure to

circulate in the space around the earth.(1) true, true (2) true, false(3) false, false (4) false, true

2. A string can withstand a tension of 25 N. The greatest speed at which a 1 kg body can bein a horizontal circle using 1 m length of string.

(1) 5 ms-1 (2) 2.5 ms-1

(3) 10 ms-1 (4) 7.5 ms-1

3. The bob A of a simple pendulum is released when the string makes an angle of 045 withvertical. It hits the another bob B of the same mass and same material kept at rest on thetable. If the collision is elastic(1) both A and B rise to same height(2) both A and B come to rest at B(3) both A and B move with same velocity A(4) A comes to rest and B moves with the velocity of A

4. Four spheres each of mass M and radius R are placed with their centers’ on the four

corners A,B,C and D of a square of side ‘b’. The spheres A and B are hollow and C & Dare are solid. The MOI of the system about side AD of a square is

(1)8 22 23

Mb MR + (2)8 22 25

Mb MR +

(3)32 22 215

Mb MR + (4) 2232 4 Mb MR +

5. Velocity of efflux through an orifice does not depend upon(1) acceleration due to gravity (2) density of the liquid (3) height of the liquid in the vessel (4) viscosity of the liquid

# Read the following paragraph:

The temperature of an isotropic cubical solid of length L, density d and co-efficient of expansion is raised by .At this temperature, to a good approximation, Now answers thefollowing Questions:

6. Length is

(1) ( )1 10 L a + (2) ( )1 10 L a -

(3) ( )1

1 10 L a -

- (4) 10 L a ´

7. Density is



(1) ( )1 30d a + (2) ( )21 30d a +

(3) ( )21 20d a + (4) ( )1

1 30d a -

+

8. A second harmonic has to be generated in a string of length l stretched between two rightsupports. The points where the string has to be plucked and touched are(1) pluck at l/4,touch at l/2 (2) pluck at l/4,touch at l/4(3) pluck at l/2,touch at l/4 (4) pluck at l/2,touch at 3l/4

9. A ball of mass m kg hangs from a spring of constant k. The ball oscillates with a period of T seconds. If the ball is removed the spring is shortened by (in metre)

(1)( )

2

22

gT

p (2)

( )

2

2

3

2

T g

p (3)

Tm

k (4)

Tk

m

10. Capacitance of a parallel plate capacitor becomes 4/3 times its original value if adielectric slab of thickness t=d/2 is inserted between the plates(d is the separation between the plates).The dielectric constant of the slab is(1) 2 (2) 6 (3) 4 (4) 8

11. A charge +q is uniformly distributed over a thin ring of radius r. A particle of mass m and charge -q was initially at rest at infinity on the axis of the ring. Velocity of the particle atthe moment it passes through the centre of the ring is given by

(1)2q

mr (2)

122

0

2

4

q

mr pe

æ öç ÷è ø

(3)

122

0

2

4

q

mr pe

æ öç ÷è ø

(4)

12

0

2

4

q

mr pe

æ öç ÷è ø

12. A pure resistive circuit element X when connected to an a.c. supply of peak voltage 200Vgives a peak current of 5 A which is in phase with the voltage second current element Y,when connected to same a.c. supply also gives the same value of peak current lags behind by . If the series combination of X and Y is connected to the same supply, Whatwill be the r.m.s. value of current?(1) 1.5A (2) 3.5A (3) 2.5A (4) 0.5A

# Read the statement 1 and statement 2 carefully to mark the correct optionsgiven below:

(1) if both statement 1 and statement 2 are true and the statement 2 isthe correct explanation of the statement 1(2) if both statement 1 and statement 2 are true but statement 2 is notthe correct explanation of statement 1(3) if statement 1 is true but statement 2 is false(4) if both statements are false

13. Statement 1 : Induced e.m.f. can be produced mainly in three ways :

Statement 2 : ( cos )d d

e BAdt dt

f q = - = - with usual notations:

(1) 1 (2) 2 (3) 3 (4) 414. Statement 1 : Stopping potential depends upon the frequency of incident light i.e. 0V an

Statement 2 : Photo electric current depends upon the intensity of incident light.



(1) 1 (2) 2 (3) 3 (4) 4

15. In a double slit experiment fringes are produced using light of wavelength0

4800 A . One

slit is covered by a thin plate of glass of refractive index 1.4 and the other with another glass plate of same thickness but of refractive index 1.7. By doing so the central brightshifts to original fifth bright from centre. The thickness of glass plate is(1) 10 mm (2) 16 mm (3) 6 mm (4) 8 mm

16. A ray of light incident in a medium of refractive index 1m , is partially reflected and

refracted at the boundary of another medium of refractive index 2m . If the reflected and

refracted rays are perpendicular to each other then the angle of incidence must be

(1) 1 2

1

sinm

m

- æ öç ÷è ø

(2) 1 1

2

sinm

m

- æ öç ÷è ø

(3) 1 1

2

cos m

m

- æ öç ÷è ø

(4) 1 2

1

tan m

m

- æ öç ÷è ø

17. When green light is incident on a certain metal surface the electrons are emitted, but noelectrons are emitted by yellow light. If red light is incident on the same metal surfacethen(1) More energetic electrons will be emitted.(2) Less energetic electrons will be emitted.(3) Emission of electrons will depend on the intensity of light.(4) No electrons will be emitted.

18. The half life of radium is 1600 years. The number of undecayed atoms of radium after

4800 years will be:(1)

1

8(2)

7

8(3)

8

7(4)

1

16

19. If in a nuclear fission process the masses of its fusion nuclei be m1and m2 and the massof the resultant nucleus be m3,then

(1)3 1 2m m m= - (2)

3 1 2m m m< +

(3)3 1 2m m m> + (4)

3 1 2m m m= +

20. Two wires P and Q made up of difference materials have some resistance at roomtemperatures. When heated, resistance of P increases and that of Q decreases. We mayconclude that

(1) P and Q are both conductors but because of being made of different materials ithappens so.

(2) P is n-type semiconductor and Q is p-type semiconductor.(3) P is semiconductor and Q is conductor.(4) P is conductor and Q is a semiconductor.

21. When n-p-n transistor is used as an amplifier (1) Electrons move from base to collector (2) Holes move from emitter to base(3) Holes move from emitter to collector (4) Electrons move from base to emitter.



22. A logic gate having two inputs A and B and output Chas the truth table as shown in figure. The given truthtable represents the gate(1) OR (2) AND(2) NOT (4) NAND

23. If E is energy, M is mass and J is angular momentum and G is universal gravitational constant then the dimensional formula of is that of (1) angle (2) area(3) acceleration (4) angular velocity

24. Side of a cube is measured by two students as ( 2.5 + 0.1 ) cm and ( 2.5 - 0.1 ) cmrespectively with the help of a Vernier Caliper. The volume of cube is

(1) ( ) 315.6 1.9 cm± (2) ( ) 315.6 1.5 cm±

(3) ( )3

15.6 0.001 cm± (4) ( )3

15.6 0.2 cm± 25. If the earth were to rotate faster than its present speed the weight of an object will

(1) increase at equator but remain same at poles.(2) decrease at equator but remain same at poles.(3) remain same at equator but decrease at poles.(4) remain same at equator but increase at poles.

26. The excess pressure inside a soap bubble is three times that inside another bubble thenthe ratio of volume of first to second bubble is(1) 3:1 (2) 7:9 (3) 1:27 (4) 27:1

27. The displacement y of a particle executing simple harmonic motion is given by

( )2 1

4cos sin 10002 y t t æ ö

= ç ÷è ø .This expression may be considered to be result of

superposition of how many waves(1) 2 (2) 3 (3) 4 (4) 5

28. A battery of electromotive force E is connected in series with a resistance R and avoltmeter. An ammeter is connected in parallel with the battery then(1) only ammeter is likely to be damaged.(2) only voltmeter is likely to be damaged.(3) both ammeter and voltmeter are likely to be damaged.(4) neither the ammeter nor the voltmeter will be damaged.

29. A charged particle of mass m and charge q travels on circular path of radius r that is

perpendicular to magnetic field B and the time taken to complete one revolution is T thenthe value of q is

(1)m

BTv

p (2)

2 m

BT

p (3)

2

BTv

mp (4)

BT

mp

30. When a thin transparent plate of thickness t and refractive index m is placed in the path

of one of the two interfering waves of light then the path difference changes by

(1) ( )1 t m + (2) ( )1 t m - (3) ( )1 / t m - (4) ( )1 / t m +

A B C

0 0 11 1 00 1 11 0 1



31. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B bethe event that the number obtained is less than 5. Then P (A∪ B) is

(1) 3/5 (2) 0 (3) 1 (4) 5/2

32. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is1/2. Then the length of the semi−major axis is

(1) 4/3 (2) 8/3 (3) 7/3 (4) 5/3

33. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertexof the parabola is at

(1) (0, 2) (2) (0, 1) (3) (1, 0) (4) (2, 0)

34. The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y − 3= 0 is

(1) (-3, -4) (2) (-3, 4) (3) (3, 4) (4) (-4, -1)

35. The conjugate of a complex number is 1/i-1. Then the complex number is

(1) -1/i-1 (2) 1/i+1 (3) 1/i-1 (4) -1/i+1

36. Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y =x + 1 and 0 < t =" {(x,">(1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not(4) T is an equivalence relation on R but S is not

37. The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) hasy−intercept − 4. Then a possible value of k is

(1) 1 (2) -4 (3) 3 (4) 2

38. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

(1) a = 0, b = 7 (2) a = 5, b = 2 (3) a = 3, b = 4 (4) a = 2, b = 4



39. The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the

point (0, 17/2, -13/2) Then

(1) a = 2, b = 8 (2) a = 4, b = 6 (3) a = 6, b = 4 (4) a = 8, b =2

40. Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 = I.Statement −1: If A ≠ I and A ≠ − I, then det A = − 1. Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.

(1) Statement −1 is false, Statement −2 is true (2) Statement −1 is tr ue, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement r1 is true, Statement a2 is true; Statement o2 is not a correct explanationfor Statement −1. (4) Statement − 1 is true, Statement − 2 is false.

41. The first two terms of a geometric progression add up to 12. The sum of the third and thefourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

(1) -2 (2) -4 (3) -12 (4) 8

42. How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have?

(1) 1 (2) 4 (3) 7 (4) 5

43. The statement p → (q → p) is equivalent to

(1) p → (p → q) (2) p → (p ∨ q)(3) p → (p ∧ q)(4) p → (p ↔ q)

44. The value of cot(cosec-1 5/3 + tan-1 2/3) is

(1) 2/17 (2) 6/17 (3) 7/17 (4) 3/17

45. The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equalto (y2 = y square)

(1) 3/5 (2) 4/3 (3) 7/3 (4) 1



46. A tangent drawn to the curve y = f(x) at P(x, y) cuts the x-axis and y-axis at A and Brespectively such that BP : AP = 3 : 1, given that f(1) = 1, then

(1) equation of curve is x dy/dx - 3y = 0(2) normal at (1, 1) is x + 3y = 4(3) curve passes through (2, 1/8)(4) equation of curve is x dy/dx + 3y = 0

47. The set of points where f(x) = x / 1+|x| is differentiable in

(1) (−∞, 0) ∪ (0, ∞) (2) (−∞, −1) ∪ (−1, ∞) (3) (−∞, ∞) (4) (0, ∞)

48. The area enclosed between curve y=loge (x+e) and the co-ordinate axes is:

(1) 4(2) 3(3) 2(4) 1

49. Three houses are available in the locality. Three persons apply for the houses. Eachapplies for one house without consulting others. The probability that all the three applyFor the same house, is:

(1) 7/9(2) 8/9(3) 1/9(4) 2/9

50. The real number x when added to its inverse gives the minimum value of the sum at xequal to

(1) 2(2) 1(3) -1(4) -2



51. The median of a set of 9 distinct observations is 20.5. If each of the largest 4observations of the set is increased by 2, then the median of the new set

(1) is increased by 2(2) is decreased by 2(3) is two times the original median(4) remains the same as that of the original set

52. Let R1 and R2 respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then R1, R, R2 are in

(1) arithmetic-geometric progression(2) A.P(3) G.P(4) H.P

53. The probability that A speaks truth is , while this probability for B is . The probability thatthey contradict each other when asked to speak on a fact is

(1) 3/20(2) 1/5(3) 7/20(4) 4/5

54. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The

relation R is

(1) a function(2) reflexive(3) not symmetric(4) transitive

55. If (1-p) is a root of quadratic equation x2 + px + (1-p) = 0 , then its roots are

(1) 0,1(2) -1,2

(3) 0,-1(4) -1, 1

56. How many ways are there to arrange the letters in the word GARDEN with the vowels inalphabetical order?

(1) 120(2) 480(3) 360



(4) 240

57. A person standing on the bank of a river observes that the angle of elevation of the top of atree on the opposite bank of the river is and when he retires 40 meter away from the treethe angle of elevation becomes . The breadth of the river is

(1) 20m(2) 30m(3) 40m(4) 60m

58. The function f(x) = x/2 + 2/x has a local minimum at

(1) x=2(2) x=-2(3) x=0(4) x=1

59. Differentiation of logx.sinx

(1) sinx.1/x(2) cosx.sinx + logx(3) sinx.1/x + logx.cos(4) cosx.(-1/x) + 1/logx

60. y = sinx then evaluate dy/dx = ? then what is Integration of ?

(1) sin x(2) cos x(3) –sin x(4) –cos x

COMMUNICATION SKILLS

61. Communication by using language is called

(1) Oral communication(2) Verbal communication(3) Written communication(4) Non verbal communication

62. He is ……………. MLA .

(1) A (2) An (3) The (4) None



63. Distribute these mangoes …………. four brothers.

(1) Among

(2) Besides(3) Between(4) After

64. Any sentence without ……………….. is incomplete.

(1) Article(2) Conjunction(3) Preposition(4) Verb

65. What is the word limit of a notice?

(1) 30 (2) 50 (3) 100 (4) 150

66. Communication is ………………………..

(1) One way process(2) Two way process(3) Three way process

(4) None of the above

67. I want ………………….. sugar in my tea.

(1) Many(2) Less(3) A(4) None

68. He is …… intelligent …… his brother.

(1) As, As

(2) So, As(3) Such, As(4) No less than, than

69. Mohan ………… a letter.

(1) Write(2) Has been written(3) Writes(4) Is Written



70. He is …….. one eyed man.

(1) A

(2) An(3) The(4) None

Directions (Q.No. 71-75) Select related words/letters/numbers from given alternatives.

71. TAP : PAT :: DAM : ?

(1) BUND (2) MAD (3) STOP (4) AMD

72. 8 : 18 : : 24 : ?

(1) 38 (2) 32 (3) 44 (4) 43

73. 08 : 09 :: ? : 25

(1) 64 (2) 16 (3) 27 (4) 36

74. ABC : HIJ : : OPQ : ?

(1) WVX (2) VWX (3) XWV (4) VXW

75. 6 : 35 : : 9 : ?

(1) 18 (2) 27 (3) 53 (4) 72



CHEMISTRY







GENERAL KNOWLEDGE

108. 30, 68, 130, 222, ? ,520, 738.

(1) 420 (2) 350 (3) 250 (4) 280

109. Rajiv Gandhi Education city is being established in the state of

(1) Rajasthan

(2) Punjab

(3) Haryana

(4) Uttar Pradesh

110. General elections 2009 for the 14th parliament of India were held in ……… stages

(1) 1 (2) 3 (3) 4 (4) 2

111. Palwal is the………. District of Haryana

(1) 20th (2) 19th (3) 21th (4) 22th

112. Abhinav Bindra who won Gold medal in Baizing Olympics is associated with

(1) Hockey (2) Boxing (3) Shooting (4) Weight lifting

113. What is the capital of Haryana?

(1) Panchkula (2) Hisar (3) Rohtak (4) Chandigarh

114. Bijender Singh who won bronze medal in 2008 olympics is belongs to

(1) Hisar (2) Panchkula (3) Bhiwani (4) Gurgaon



115. Who among the following is known as an “Iron man of India”?

(1) Bansilal

(2) Sardar Patel(3) Jawaharlal Nehru(4) Mahatma Gandhi

116. Huen Tsang stayed in Thaneswar during period 635 to 644AD . who was its ruler at that

time?

(1) Akbar (2) Pushya Mitra(3) Pulk Sen

(4) Harshvardhan

117. What is the minimum age for a candidate to became Prime – Minister of India?

(1) 35 (2) 25 (3) 40 (4) 60

118. Who among the following is famous by the name as ‘Lady of the lamp’?

(1) Florence Nightingale(2) Ani Besant(3) Mother Terasa(4) Sister Nivedita

119. Which among the following is the national game of India

(1) Cricket (2) Wrestling (3) Hockey (4) Tennis

120. Who among the following is the first Indian woman to become Miss Universe

(1) Aditi pal (2) Sania Mirza (3) Sushmita Sen (4) Dia Mirza

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