15 Engg Test 2016

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INSTRUCTIONS FOR STUDENTS

1. Read each question carefully.

2. It is mandatory to use Blue/BlackBall Point Pen to darken the

appropriate circle in the answer sheet.

3. Mark should be dark and shouldcomplete fill the circle.

4. Rough work must be done on theQuestion Paper, no additional sheetwill be provided for this purpose.

5. Do not use white-fluid or any other rubbing material on answer sheet.No change in the answer oncemarked.

6. Student cannot use log tables andcalculators or any other material inthe examination hall.

7. Before attempting the question paper,student should ensure that the testpaper contains all pages and no page

is missing.8. Each correct answer carries four

marks. One mark will be deducted for each incorrect answer from the totalscore.

9. Before handing over the answer sheet to the invigilator, candidateshould check the particulars havebeen filled and marked correctly.

10. Immediately after the prescribedexamination time is over, the answer sheet to be returned to the invigilator.

11. Use of Calculator and other Electronic device is not permitted.

Time : 3 Hrs. M.M. : 360

[Test No. 15]

Engineering

Entrance Exam.

2016 H

O R I Z

O N TE S T

S E R

I E S

(Divisions of Horizon Study Circle Pvt. Ltd.)

Medical IIT-JEE Foundations| |HORIZON ACADEMY

R

Since 2003

Name.

Test No.:

Subject Code.:

Date :

1

1

5

1 1

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Topics of The Test

Test No. 15

H 2 HORIZON ACADEMY :- B-3/41 A, YAMUNA VIHAR, WAZIRABAD ROAD, DELHI-53, (M) 9811139323, (O) 22922012

Maths

Physics

Chemistry

Circle, Straight lines and Pairs of straight lines,Cartesian coordinate geometry, Matrix and determinants,Quadratic equations, Sequence and series,Complex number, Binomial theorem,Permutation and combination, Inequation.

Physical world, Units and measurements, Motion in a straight line,Motion in a plane, Laws of motion, Work, Energy and power,System of particles and rotational motion, Gravitation.

Some basic concepts of chemistry, States of matter, Atomic structure,Chemical bonding, Classification of elements, Redox reaction,Equilibrium.

Test-15 (Objective) Horizon Test Series for Engineering-2016

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Space for Rough Work



Test No. 15

[PHYSICS]1. Force F is given in terms of time t and distance x by

sin cos .F A Ct B Dx Then dimensions of / A B and

/C D are

(A) 0 0 0 0 0 1[ ],[ ] M L T M L T

(B) 2 0 1 0[ ],[ ] MLT M L T

(C) 0 0 0 0 1[ ],[ ] M L T M LT

(D) 0 1 1 0 0 0[ ],[ ] M L T M L T

2. Which of the following have got same dimensions ?

a. Latent heatb. Energy per unit massc. Gravitational potentiald. Specific heat(A) “d” and “c” (B) “a” and “d”(C) “a”, “b” and “c” (D) None of these

3. Which of the following product of , , ,e h G (where is the permeability, h = planks constant,G = gravitational constant, e = charge on electron) betaken so that the dimensions of the product are sameas that of speed of light ?

(A)2 1 0

he G

(B)2 0

h eG

(C) 0 2 1h e G (D) 2 0hGe

4. A student writes four different expressions for thedisplacement y in a periodic motion as a function oftime t, a as amplitude, T as time period. Which of thefollowing can be correct ?

(A)2sin ty aT T

(B) siny a Vt

(C) sina t

y T a

(D)2 2

sin cos2a t t

yT T

5. The length of one rod is 2.53 cm and that of the other is1.27 cm. The least count of the measuring instrumentis 0.01 cm. If two rods are put together end to end, thecombined length can be expressed as

(A) (3.80 0.01) cm (B) (3.80 0.02) cm

(C) (3.80 0.03) cm (D) (3.80 0.04) cm

6. If the vectors ˆˆ ˆ4 3i j k and ˆˆ ˆ2 6mi mj k ar eperpendicular to each other, then the value of m is

(A) 3/14 (B) –1/8(C) –2/3 (D) 12

7. The resultant of the three vectors ,OA OB

and OC

,shown in the following figure, is

(A) r (B) 2r

(C) (1 2)r (D) ( 2 1)r

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8. The displacement-time graph of two bodies A and B isshown in figure. The ratio of velocity of A, to velocity of

B, is

(A) 1/ 3 (B) 3(C) 1/3 (D) 3

9. If a stone is to hit at a point which is at a distance daway and at a height h above the point from where thestone starts, then what is the value of initial speedu ifthe stone is launched at an angle ?

(A) cos 2( tan ) g d

d h

(B) cos 2( tan ) gd

d h

(C)

2

2cos

gd

h

(D)2

( ) gd

d h

10. A particle moves along x-axis obeying the equation

( 1)x t t ( 2)t , where x, in meter, is the position ofparticle at any time t in second. The time when thedisplacement of the particle is zero is(A) 0, 1 s and 2 s (B) 1 s, 3 s and 5 s(C) 5 s, 8 s and 7 s (D) 3 s, 5 s and 8 s

11. A block of metal weighing 2 kg is resting on africtionless plane. It is struck by a jet releasing waterat a rate of 1 kg/s and a speed of 5 m/s. The initialacceleration of the block will be(A) 2.5 m/s2 (B) 5 m/s2

(C) 10 m/s2 (D) 20 m/s2

12. With what minimum acceleration can a fireman slidedown a rope whose breaking strength is 2/5th of hisweight ?(A) 1 g (B) 0.4 g(C) 0.6 g (D) 0.8 g

13. Blocks A and B in the figure are connected by a bar ofnegligible weight. Mass of each block is 170 kg and

0.2 A

and 0.4,B

where A

andB

are thecoefficients of limiting friction between blocks andplane. Calculate the force developed in the bar( g = 10 m/s2)

(A) 150 N (B) 75 N(C) 200 N (D) 250 N

14. A horizontal force of 10 N is necessary to just hold ablock stationary against a wall. The coefficient of

friction between the block and the wall is 0.2. Theweight of the block is

(A) 2 N (B) 20 N

(C) 50 N (D) 100 N

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15. A marble block of mass 2 kg lying on ice when given avelocity of 6 m/s is stopped by friction in 10 s. Thenthe coefficient of friction is(A) 0.01 (B) 0.02(C) 0.03 (D) 0.06

16. The work done in moving a body of mass 4 kg withuniform velocity of 5 ms–1 for 10 s on a surface of

0.4 is (take g = 9.8 m/s2)(A) 584 J (B) 784 J(C) 684 J (D) 484 J

17. A shell explodes and many pieces fly off in differentdirections. Which of the following is conserved ?(A) Kinetic energy (B) Momentum(C) Neither momentum nor KE(D) Momentum and KE

18. A billiard ball moving with a speed of 5 m/s collideswith an identical ball elastically, originally at rest. Ifthe first ball stops dead after collision, then the second

ball will move forward with a speed of(A) 10 m/s (B) 5 m/s(C) 2.5 m/s (D) 1 m/s

For Q.No. 19 and 20

A ball moving with a velocity strikes a wall movingtowards the ball with a velocity u. Consider the massof the wall to be infinitely great. An elastic impactoccurs.

19. Determine the magnitude of velocity of the ball afterthe impact.(A) 2u (B) 2u

(C) u

(D) u

20. Calculate the change in KE of the ball after collisionwith the wall.

(A) 2 ( )m u u (B) 2 ( )m u u

(C) 2 ( 2 )m u u (D) 2 (2 )m u u

21. The separation between carbon and oxygen atoms inCO is 0.12 nm. What is the distance of the centre ofmass from carbon atom ?(A) 0.032 nm (B) 0.070 nm(C) 0.054 nm (D) 0.068 nm

22. The radius of gyration of a uniform rod of length Labout an axis passing through its centre of mass andperpendicular to its length is

(A) 12L

(B)2

12L

(C)3

L(D)

2

L

23. Four spheres each having mass m and radius r areplaced with their centres on the four corners of a squareof side a. Then the moment of inertia of the systemabout an axis along one of the sides of the square is

(A)28

5 mr (B)2 28

5 mr ma

(C) 2 28

25

mr ma (D) 2 24

45

mr ma

24. In the figure shown below, a weight W is attached toa string wrapped round a solid cylinder of mass Mmounted on a frictionless horizontal axle at O. If theweight starts from rest and falls a distance h, then itsspeed at that instant is

(A) proportional to R

(B) proportional to1R

(C) proportional to 21

R

(D) independent of R

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25. A hoop rolls on a horizontal ground without slippingwith linear speed . Speed of a particle P on thecircumference of the hoop at angle is

(A) 2 sin( /2) (B) sin

(C) 2 cos( /2) (D) cos

26. A body is broken into two parts of masses 1m and 2m .These parts are then separated by a distance r . Whatis the value of 1 2/m m so that the gravitational forcehas maximum possible value ?

(A) 1 : 1 (B) 1 : 2(C) 2 : 1 (D) 4 : 327. The adjacent figure shows two shells of masses

1m and 2m . The shells are concentric. At which point,a particle of mass m shall experience zero force ?

(A) A (B) B(C) C (D) D

28. In order to shift a body of mass m from a circular orbitof radius 3R to a higher orbit of radius 5R around theEarth, the work done is

(A)3

5GMm

R(B)

2GMm

R

(C)1

15

GMm

R

(D)

5

GMm

R

29. Two concentric shells of masses 1 and 2 are

having radii 1r and 2r . Which of the following is thecorrect expression for the gravitational field on a massm ?

(A) 1 2 12( )

,G M M

E for r r r

(B) 1 2 22( )

,G M M

E for r r r

(C) 2 1 22 ,GM

E for r r r r

(D) 1 1 22 ,GM

E for r r r r

For Q.No. 30

A uniform metal sphere of radius a and mass M issurrounded by a thin uniform spherical shell of equalmass and radius 4a. The centre of the shell falls on thesurface of the inner sphere. Find the gravitational field

30. at point 1P

(A) 210GM

a(B) 28

GM

a

(C) 22

GM

a

(D) 24

GM

a

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[CHEMISTRY]31. Gram molecular volume of oxygen at STP is

(A) 3200 cm3 (B) 5600 cm3

(C) 22400 cm3 (D) 11200 cm3

32. 74.5 g of a metallic chloride contains 35.5 g of chlorine,the equivalent weight of the metal is

(A) 19.5 (B) 35.5(C) 39 (D) 78.0

33. The empirical formula of a compound is CH2. Onemole of this compound has a mass of 56 g. Its molecularformula is

(A) C3H6 (B) C4H8(C) CH2 (D) C2H2

34. The volume of oxygen necessary for the completecombustion of 20 L of propane is

(A) 40 L (B) 60 L(C) 80 L (D) 100 L

35. Bohr’s radius of 2nd orbit of Be3+ is equal to that of

(A) 4th orbit of hydrogen

(B) 2nd orbit of He+

(C) 3rd orbit of Li2+

(D) first orbit of hydrogen36. In an atom, an electron is moving with a speed of 600

m/s with an accuracy of 0.005%. Certainity withwhich the position of the electron can be located is

(h=6.6×10–34

kg m2

s–1

, mass of electron, me = 9.1×10–31

kg )(A) 1.52×10–4 m (B) 5.10×10–3 m(C) 1.92×10–3 m (D) 3.84×10–3 m

37. The orbital angular momentum of an electron in 2sorbital is

(A)12 2

h

(B) zero

(C)2h

(D) 2

2h

38. Which of the following elements has least number ofelectrons in its M -shell ?

(A) K (B) Mn(C) Ni (D) Sc

39. An element with atomic number 21 is a(A) halogen

(B) representative element(C) transition element(D) alkali metal

40. The discovery of which of the following group ofelements gave death blow to the Newland’s law ofoctaves ?

(A) Inert gases(B) Alkali earths(C) Rare earths(D) Actinides

41. The correct order of electron gain enthalpy withnegative sign of F, Cl, Br and I, having atomic number9, 17, 35 and 53 respectively, is

(A) Cl > F > Br > I (B) F > Cl > Br > I(C) I > Br > Cl > F (D) I > Br > F > Cl

42. The pair of elements having approximately equalionisation potential is(A) Al, Ga (B) Al, Si

(C) Al, Mg (D) Al, B43. Most acidic oxide is

(A) Na2O (B) ZnO

(C) MgO (D) P2O544. Correct increasing order of first ionisation potential is

(A) Na < Mg > Al < Si(B) Na < Mg < Al < Si(C) Na > Mg > Al > Si

(D) Na < Mg < Al > Si45. The dipole moment of HBr is 1.6×10–30 cm and inter-

atomic spacing is 1 Å. The % ionic character of HBr is(A) 7 (B) 10

(C) 15 (D) 27

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H 8 HORIZON ACADEMY :- B-3/41 A, YAMUNA VIHAR, WAZIRABAD ROAD, DELHI-53, (M) 9811139323, (O) 22922012 8H 8 HORIZON ACADEMY :- B-3/41 A, YAMUNA VIHAR, WAZIRABAD ROAD, DELHI-53, (M) 9811139323, (O) 22922012


46. Shape and hybridisation of IF5 respectively are

(A) trigonal bipyramidal, 3sp d

(B) sea-saw, 3sp d

(C) square pyramidal, 3 2sp d

(D) pentagonal pyramidal, 3 3sp d

47. Which of the following has strongest hydrogenbonding ?(A) Ethylamine (B) Ammonia(C) Ethyl alcohol (D) Diethyl ether

48. The molecular electronic configuration of Be2 is

(A) 2 2 2 21 1 2 2s s s p

(B) 22KK s

(C) 2 2 2 21 1 2 2s s s s

(D) None of the above

49. Which of the following set of variables give a straightline with a negative slope when plotted ?( p = vapour pressure, T = temperature in K)

10

(A)1

(C) log

p T

pT

y - axis x - axis

10

10 10

(B) log1

(D) log log

p T

pT

y - axis x - axis

50. Dalton’s law of partial pressure is not applicable to

(A) 2 3O O (B) 2CO CO

(C) 3NH HCl (D) 2I O

51. What is kinetic energy of 1 g of O2 at 47°C ?(A) 1.24×102 J (B) 2.24×102 J(C) 1.24×103 J (D) 3.24×102 J

52. The deuiation from the ideal gas behaviour of a gascan be expressed as

(A) p

ZVRT

(B) pV

ZnRT

(C)nRT

Z pV

(D)VR

Z pT

53. Which of the following is not a physical equilibrium?

(A) Ice Water (B) 2 2( ) ( )I s I g

(C) ( ) ( )S l S g (D) 2 33 2O O

54. Equilibrium constant K , for the reaction,

2 22 ( ) ( ) ( )HI g H g I g

at room temperature is 2.85 and that at 698 K is1.4×10–2. This implies that the forward reaction is

(A) exothermic (B) endothermic(C) exergonic (D) unpredictable

55. 30 cc of3

HCl, 20 cc of2

HNO3 and 40 cc of

4NaOH solutions are mixed and the volume was

made up to 1 dm3. The pH of the resulting solution is(A) 8 (B) 2

(C) 1 (D) 356. Solubility of Al(OH)3 = , spS K will be

(A) 3108S (B) 327S

(C) 44S (D) 427S

57. In the equation,

2 24 3CrO SO

24 4( )Cr OH SO

the oxidation number of Cr changes from

(A) 6 to 4 (B) 6 to 3

(C) 8 to 4 (D) 4 to 3

58. The value of ' 'n in the reaction2 2 3 3

2 7 214 2 7Cr O H nFe Cr nFe H O will be

(A) 2 (B) 3(C) 6 (D) 7

59. How many electrons are involved in oxidation ofKMnO4 in basic medium ?(A) 1 (B) 2

(C) 5 (D) 3

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60. For redox reaction

2 24 2 4 2 2 MnO C O H Mn CO H O

coefficient of reactants in balanced states are

(A) 2 5 16

(B) 16 5 2(C) 5 16 2(D) 2 16 5

- 2- +

4 2 4MnO C O H

[MATHEMATICS]61. The solution of equation |z| – z = 1 + 2i is

(A)3

+ 2i2

(B)3

– 2i2

(C) 3 – 2i (D) None of these62. If 1, a1, a2, ..., an–1 are the n roots of unity, then the value

of (1 – a1) (1 – a2) (1 – a3) ... (1 – an–1) is equal to(A) 3 (B) 1/2

(C) n (D) 063. I f the complex numbers z1, z2, z3 satisfying

1 3

2 3

z z 1 i 3,

z z 2 then triangle is

(A) an equilateral triangle(B) a right angled triangle(C) an acute angled triangle(D) an obtuse angled isosceles triangle

64. If a, b, c are in GP, then the equation ax2

+ 2bx + c = 0and dx2 + 2ex + f = 0 have a common root, if

d e f, ,a b c

are in(A) AP (B) HP(C) GP (D) None of these

65. If ax2 + bx + c = 0 and 2x2 + 3x + 4 = 0 have a commonroot where a, b, c N (set of natural numbers), theleast value of a + b + c is(A) 13 (B) 11(C) 7 (D) 9

66. The quadratic equationsx2 – 6x + a = 0

and x2 – cx + 6 = 0have one root in common. The other roots of the firstand second equations are integers in the ratio 4 : 3.Then the common root is(A) 2 (B) 1(C) 4 (D) 3

67. If two equations x2 + a2 = 1 – 2ax and 2 2x b 1 2bxhave only one common root, then(A) a – b = 1 (B) a – b = –1(C) a – b = 2 (D) |a – b| = 1

68. If log10 (x3 + y3) – log10(x

2 + y2 – xy) 2, then themaximum value of xy, for all x 0, y 0 is(A) 2500 (B) 3000(C) 1200 (D) 3500

69. If the third term of a GP is P. Then, the product of thefirst 5 terms of the GP is(A) P3 (B) P2

(C) P10 (D) P5

70. If arithmetic mean of two positive numbers is A, theirgeometric mean is G and harmonic mean is H , then H is equal to(A) G2/A (B) A2/G2

(C) A/G2 (D) G/A2

71.

2

n 1

2n n 1n!

is equal to

(A) 2e – 1 (B) 2e + 1

(C) 6e – 1 (D) 6e + 172. Assuming that no two consecutive digits are same.The number of n digit numbers is(A) n! (B) 9!(C) 9n (D) n9

73. 20 persons are invited for a party. In how manydifferent ways can they and the host be seated atcircular table, if the two particular persons are to beseated on either side of the host ?(A) 20! (B) 2! × 18!(C) 18! (D) None of these

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74. The number of ways in which 6 rings can be worn onfour fingers of one hand, is(A) 46 (B) 6C4(C) 64 (D) 24

75. The number of diagonals that can be drawn in apolygon of 15 sides, is(A) 16 (B) 60

(C) 90 (D) 80

76. If (1 + x)15 = a0 + a1x + ... + a15x15, then

15

r

r 1r 1

ar

a is

equal to(A) 110 (B) 115(C) 120 (D) 135

77.10

20k

k 0C is equal to

(A) 19 20

10

12 C2 (B) 2

19

(C) 20C10 (D) None of these78. Using mathematical induction, the numbers an’s are

defined by a0 = 1, an+1 = 3n2 + n + an, (n 0). Then, an is

equal to(A) n3 + n2 + 1 (B) n3 – n2 + 1(C) n3 – n2 (D) n3 + n2

79. Let

1 2 a 0A and B ,

3 4 0 b a , b N. Then

(A) there exist more than one but finite number of

B’s such that AB = BA(B) there exists exactly one B such that AB = BA(C) there exists infinitely many B’s such that

AB = BA(D) there cannot exist any B such that AB = BA

80. If a b c, the value of x which satisfies the equation

0 x a x bx a 0 x c 0,x b x c 0

is

(A) x = 0 (B) x = a

(C) x = b (D) x = c

81. Given 2x – y + 2z = 2, x – 2y + 2z = –4, x + y + z = 4then the value of such that the given system ofequation has no solution, is

(A) 3 (B) 1

(C) 0 (D) –3

82. One possible condition for the three points (a, b), (b, a)and (a2, – b2) to be collinear, is

(A) a – b = 2 (B) a + b = 2

(C) a = 1 + b (D) a = 1 – b

83. A triangle with vertices (4, 0), (–1, –1), (3, 5) is

(A) isosceles and right angled

(B) isosceles but not right angled

(C) right angled but not isosceles

(D) neither right angled nor isosceles

84. The locus of the point of intersection of the linesx cot + y cosec = 2 and x cosec + y cot = 6 is

(A) a straight line (B) circle

(C) a hyperbola (D) an ellipse

85. If the equations, 12x2 – 10xy + 2y2 + 11x – 5y + k = 0represents two straight lines, then the value of k is

(A) 1 (B) 2

(C) 0 (D) 3

86. The point on the axis of x, whose perpendicular

distance from the straight lineyx 1

a b is a, are

(A) 2 2b

(a a b ,0)a

(B)2 2a (b a b ), 0

b

(C)b

(a b, 0)a

(D) 2 2a (a a b ,0)b

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87. Let P = (–1, 0), Q = (0, 0) and R (3, 3 3) be threepoints. The equation of the bisector of the angle PQRis

(A) 3x y 0 (B)3

x y 02

(C) 3 x y 02 (D) x 3y 0

88. The line ax + by + c = 0 is normal to the circle x2 + y2 +2gx + 2fy + d = 0, if(A) ag + bf + c = 0 (B) ag + bf – c = 0(C) ag – bf + c = 0 (D) ag – bf – c = 0

89. Which of the following is a point on the common chordof the circle x2 + y2 + 2x – 3y + 6 = 0 and x2 + y2 + x –8y – 13 = 0 ?

(A) (1, –2) (B) (1, 4)

(C) (1, 2) (D) (1, –4)

90. The circle x2 + y2 + 8y – 4 = 0, cuts the real circle

x2 + y 2 + gx + 4 = 0 orthogonally, if(A) for any real value of g

(B) for no real value of g

(C) g = 0

(D) g < –2, g > 2

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