sample paper class xi – 11 section – i …sample paper class xi – 11th std (engineering) head...

SAMPLE PAPER CLASS XI – 11th STD (ENGINEERING)

Head Office: 364, 1st Floor, Kohat Enclave, Pitampura, New Delhi -110034 – [ 2 ] – Contact: 08586984577, 09643103458, www.futureedge.in

Branch Office: Indirapuram, Plot No. - 16, Ahinsa Khand, Habitat Center, Near Shipra Mall. Contact: 09643103452/51

SECTION – I MENTAL APTITUDE

1 On a certain planet, there are nine months in a year, and seven days in a week (which are same as the weekdays on the earth). The alternate months have 29 and 30 days, (starting with 29 days). In a leap year, 2 days are added to the third, the sixth and the ninth month. If 3rd of the first month is a Tuesday and if it is leap year, 10th of the 7th month will be a

(A) Sunday (B) Monday (C) Friday (D) Wednesday

Directions for questions 2 to 4: These questions are based on the following data. A large cube painted red on all sides is cut into smaller cubes of side 1cm and it is found that there are 729 small cubes which do not have any surface painted red.

2 How many small 1cm cubes are required to completely cover the original large cube placed on the table?

(A) 866 (B) 697 (C) 1016 (D) None of these

3. If the original large cube required 726 litres of red paint, then how much paint would be required to completely paint all surfaces of all the small cubes? (In litres)

(A) 2662 (B) 1331 (C) 7986 (D) None of these

4. How many small cubes from the original large cube have at least one side painted red?

(A) 702 (B) 602 (C) 729 (D) 840

5 Two different views of a cube are given. The cube is numbered from 1 to 6.

Which is the correct view of the cube given above?

(A)

(B) (C) (D)

6 What is the time observed in the reflection of a mirror when the clock shows 5 hours 38 minutes?

(A) 6 hours 32 minutes (B) 7 hours 12 minutes

(C) 6 hours 26 minutes (D) 6 hours 22 minutes

http://www.futureedge.in




7. In a town, 65% people watch the news on television, 40% read a newspaper and 25% read a newspaper and watch the news on television also. What percent of the people neither watch the news on television nor read a newspaper?

(A) 5 (B) 10 (C) 15 (D) 20

8 In the following question, a matrix of certain characters is given. These characters follow a certain trend, row-wise or column-wise. Find out this trend and choose the missing character accordingly.

1 3 7

5 12 15

25 ? 28

125 192 56

(A) 64 (B) 56 (C) 48 (D) 40

Directions for Questions 9 to 11: In one of the Personality Development classes held at Zion Tutorials, 10 students are sitting around a circular table for Group Discussion according to the following conditions.

(i) There are two students between X and U. (ii) Y is neither adjacent to X nor opposite T. (iii) P and T are the only persons adjacent to W. (iv) Q is opposite to S who is to the right of V. (v) R and W have four persons between them.

9 Who is three places to the right of U? (A) X (B) P (C) W (D) Cannot be determined 10 Who is to the right of S? (A) V (B) X (C) W (D) Cannot be determined 11 Who are the only two persons sitting in between R and V? (A) X and S (B) only S (C) X and Y (D) Cannot be determined

Directions (Q. 12 and 13): Which is the number that comes next in the sequence?

12 (2,3), (3,5), (5,7), (7,11), (11,13), (.....)

(A) (13, 15) (B) (15, 16) (C) (13, 17) (D) 13, 19)





13 0, 6, 24, 60, 120, 210? (A) 240 (B) 290 (C) 336 (D) 504 14 Find out the wrong term: 8, 14, 26, 48, 98, 194, 386 (A) 14 (B) 48 (C) 98 (D) 194 15 Mr. X, a mathematician, defines a number as ‘connected with 6’ if it is divisible by 6 or if the

sum of its digits is 6, or if 6 is one of the digits of the number. Other numbers are all ‘not connected with 6’. As per this definition, the number of integers from 1 to 60 (both inclusive) which are not connected with 6 is

(A) 18 (B) 22 (C) 42 (D) 43 16 Three bells toll at intervals of 36 sec, 40 sec and 48 sec respectively. They start running toll

at a particular time. They next toll together after

(A) 18 minutes (B) 12 minutes (C) 6 minutes (D) 24 minutes

Directions for questions 17 to 19: According to a survey conducted by 94.3 MY FM. In a class of 120 students, 15 students passed in

both Commerce and Accounts. The number of boys who passed in Commerce is three times those

boys who passed in both Commerce and Accounts. The number of girls who passed in only

Accounts is three times the number of girls who passed in both the subjects. 50% of girls passed in

Commerce and 50% of boys passed in Accounts. The ratio of the number of boys who failed in both

the subjects to the number of girls who failed in both the subjects is 3:2. The number of boys who

failed in both the subjects is same as the number of students who passed in both the subjects.

17 How many boys passed in both the subjects?

(A) 5 (B) 8 (C) 10 (D) 12

18 How many students passed in only Accounts?

(A) 20 (B) 40 (C) 45 (D) 55

19 How many girls passed in Commerce?

(A) 20 (B) 25 (C) 30 (D) 40

20 At the fair I bought 6 erasers and 2 pens for Rs. 15. If I could have bought 4 more erasers for

Rs. 14 than pens for Rs. 9, the price of a pen was

(A) Rs. 1.50 (B) Rs. 1.75 (C) Rs. 2.25 (D) None of these





21 Count the number of squares in the given figure

(A) 18 (B) 19

(C) 25 (D) 27

22 Find the missing character

3 c 72 D 9 E

7 I 147 K 14 M

4 D ? 7 J

(A) 66G (B) 74F (C) 33G (D) 67G 23 Sameer can do a piece of work in 9 hours. Rahul can do the same piece of work in 8 hours.

Their boss asks them to work along with Ronak and hence they finish the work in 3 hours. If their Boss offers them Rs. 7200 for the work, how much does Ronak earn?

(A) Rs. 6,900 (B) Rs. 5,000 (C) Rs. 2,100 (D) Rs. 8,000 24 Three workers at 94.3 MY FM office, P, Q and R are paid Rs. 6300 for doing a piece of work

together. P and Q start the work and continue to work together for 10 days. After that P quits while, R joins Q and they complete the remaining work. How much does Q receive for his work, given that P can do the work in 30 days, Q in 60 days and R in 90 days?

(A) Rs.2940 (B) Rs. 3000 (C) Rs. 3500 (D) Rs. 4000 25 Find the value of X in the following figure:

(A) 3 (B) 4 (C) 8 (D) 12

26 Three pipes X, Y, Z can fill a tank, individually, in 5, 10 and 15 hours respectively. A tap M can empty the tank in 20 hours individually. Pipe X was opened first and pipe Y was opened 2 hours after pipe X, pipe Z was opened 3 hours after pipe X and pipe M was opened 4 hours after pipe X was opened. How many hours after pipe X was opened did the tank get filled ?

(A) 78 hours19

(B) 47 hours11

(C) 42 hours11

(D) 72 hours19





27 Count the number of triangles in the following figure (A) 25 (B) 23 (C) 21 (D) None of these 28 The following 15 digit no. contains a hidden pattern find the last

digit 2 3 4 9 1 6 8 1 2 5 6 6 5 6 (A) 9 (B) 3 (C) 1 (D) 7 29 How many triangles can be observed in the figure? (A) 20 (B) 25 (C) 27 (D) 29 30 Complete the series 0, 4, 6, 3, 7, 9, 6, ... 12 (A) 8 (B) 10 (C) 11 (D)

14 31 Complete the series 2, 9, 28, 65, ... (A) 104 (B) 126 (C) 93 (D) 56

32

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

33 Ayush was born two years after his father’s marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married?

(A) 23 years (B) 25 year (C) 33 years (D) 35 years 34 In the series given below, how many 8s are there each of which is exactly divisible by its

immediate preceding as well as succeeding number? 2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6 (A) One (B) Two (C) Three (D) Four 35 In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D scored 5

more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score?

(A) 62 (B) 45 (C) 28 (D) 20





Directions for questions 36 and 39: During an interview round at 94.3 MY FM, three RJs put a puzzle to the person being interviewed. The following is a conversation between the three RJs Amar, Bhisham and Charan each of whom has a different surname among Sharma, Gupta and Dwivedi. Amar: I am not a Gupta. Bhisham is not a Dwivedi. Charan: I am not a Gupta. Amar is not a Dwivedi. 36 Who is Dwivedi? (A) Amar (B) Bhisham (C) Charan (D) Cannot be determined 37 Who is a Gupta? (A) Amar (B) Bhisham (C) Charan (D) cannot be determined 38 Zion Tutorials carry two packets of chocolates for distributing among children during a

particular workshop. The first packet of chocolates has 1/4 excess to as many as chocolates in the second packet. If the second packet has 3 chocolates less than the first packet, then the number of chocolates in the first packet are:

(A) 9 (B) 10 (C) 12 (D) 15 39 Find the answer from answer figure which will complete the series. Problem Figures

Answer Figures

40

(A) 6 (B) 7 (C) 8 (D) 9





SECTION – II (PHYSICS)

41. Dimensional formula for power is

(A) 1 1 –2[M L T ] (B) 1 2 –3[M L T ] (C) 1 2 –2[M L T ] (D) 2 –1[ML T ]

42. If the percentage errors in the measurements a, b and c are 1%, 3% and 2% respectively then

the percentage error in the measurement of x where 2a bxc

will be

(A) 5% (B) 3% (C) 7% (D) 2%

43. Identify the false statement from the following:

(A) Work-energy theorem is not independent of Newton’s second law.

(B) Work-energy theorem holds in all inertial frames.

(C) Work done by friction over a closed path is zero.

(D) Work done is a scalar quantity.

44. A projectile is thrown with an initial velocity of ˆ ˆV Ai Bi

, If the range of the projectile is double the maximum height reached by it then

(A) A = B (B) B = 2A (C) A= 2B (D) B= 4A

45. A body of mass 5 kg moving with a velocity of 10 ms–1 is to be stopped by a resistive force. Distance covered by it is 10 m. The magnitude of force will be

(A) 15 N (B) 20 N (C) 25N (D) 30N

46. Two blocks A and B having masses 2m and m respectively connected by a light inextensible rope passing over a smooth fixed pulley as shown in figure. The tension in the rope is

(A) 2mg3

(B) mg3

(C) 4mg3

(D) mg

47. A ball weighing 10 g hits a hard surface vertically with a speed of 5 m/s and rebounds with the same speed. The ball remains in contact with the surface for 0.01 sec. The average force exerted by the surface on the ball is:

(A) 100 N (B) 10 N (C) 1 N (D) 0.1 N





48. A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement-time curve for its motion ?

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

49. The bob of a pendulum is released from a horizontal position. If the length of pendulum is 2 m, what is the speed with which the bob arrives at the lowermost point. Assume that 10% of its energy is dissipated against air resistance. (Take g = 10 ms–2)

(A) 4 m s–1 (B) 6 m s–1

(C) 8 m s–1 (D) 10 m s–1

50. The centre of mass of triangle shown in figure has co-ordinates:

(A) b hx ; y2 2

(B) b hx ; y2 2

(C) b hx ; y3 2

(D) h bx ;y3 3

51. A ring of radius r and mass m rotates about an axis passing through its centre and perpendicular to its plane with angular velocity . Its kinetic energy is:

(A) mr (B) 21 mr2

(C) 2 2mr (D) 2 21 mr2

52. Velocity versus time graph for a body projected vertically upwards is: (A) Parabola (B) Ellipse (C) Hyperbola (D) Straight line

53. The linear mass density of a non-uniform rod of length 1 m is given by 2(x) a(1 bx ) where a and b are constants and 0 < x < 1. The centre of mass of the rod will be at

(A) 3(2 b)4(3 b)

(B) 4(2 b)3(3 b)

(C) 3(3 b)4(2 b)

(D) 4(3 b)3(2 b)





54. A body falls freely under gravity from height h. Its gravitational potential energy and kinetic energy v/s, time graph are shown in the figure. The correct variation is represented by:

(A) (B)

(C) (D)

55. Under the action of a force, a 2 kg body moves such that its position ‘x’ as a function of time is given by: 3x t /3 where ‘x’ is in metre and ‘t’ in second. The work done by the force in the first two seconds is

(A) 1600 joule (B) 160 joule (C) 16 joule (D) 1.6 joule 56. A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its

ends. Tension in the string at a distance from the end at which force is applied is: (A) Zero (B) F (C) F(L-x)/L (D) F(L-x)/M 57. A vehicle needs an engine of 7500 watt to keep it moving with a constant velocity of 20 m/sec

on a horizontal surface. The force resisting the motion is: (A) 375 dyne (B) 375 newton (C) 150000 dyne (D) 150000 newton 58. The moment of inertia of a uniform circular wire of mass M and radius r about a line

perpendicular to the plane of the circle and through the rim is

(A) 23Mr

2 (B) Mr2 (C) 2Mr2 (D) 3/4Mr2

59. A rigid ball of mass ‘2m’ is moving with speed ‘v’ collides elastically head on with another ball of mass ‘m’ at rest. Then speed of ball of mass ‘2m’ will be

(A) v/3 (B) v (C) 2v/3 (D) zero 60. The position vector of a particle is

ˆ ˆr (a cos t)i (a sin t)j

The velocity of the particle is: (A) Parallel to position vector. (B) Perpendicular to position vector. (C) Directed towards the origin. (D) Directed away from the origin.





SECTION – III (CHEMISTRY)

61. The sum of bond energies of C–H, C–C and C=O is 1500 kJ/mole The sum of bond energies of C=C, C–O and O–H is 1452 kJ/mole What can be predicted from the given data?

| |

| || |C C C CH O OH

(A) Keto form is thermodynamically more stable than enol form

(B) Keto form is thermodynamically less stable than enol form

(C) Keto form has less reactivity than enol form for nucleophilic attack

(D) Enol form has less reactivity

62. Which of the given pair of molecules have same geometry but different shape?

(A) XeF4, SF4 (B) –3 3ClF ,I (C) CCl4, CH4 (D) BH3, SF6

63. A mixture of FeO and Fe3O4 when heated in air to constant weight, gains 5% in its weight. Find out composition of mixture.

(A) 3 4

.FeO 20 25%

.Fe O 79 75%

(B)

3 4

FeO 15%

Fe O 85%

(C)

3 4

FeO 79.75%

Fe O 20.25%

(D)

3 4

FeO 40%

Fe O 60%

64. For the reaction N2O5 (g) 2NO2(g) + 0.5O2(g), calculate the mole fraction of N2O5(g) decomposed at a constant volume and temperature, if the initial pressure is 600 mm Hg and the pressure at any time ‘t’ is 960 mm Hg. Assume ideal gas behaviour.

(A) 0.5 (B) 0.6 (C) 0.7 (D) 0.4

65. A thin tube of uniform cross-sections is sealed at both ends. It lies horizontally. The middle 5 cm containing Hg and the two equal ends containing air at the same pressure P0. When the tube is held at an angle 60º with the vertical, the length of the air column above and below the mercury are 46 and 44.5 cm respectively. Calculate the pressure P0 in cm of Hg. (The temperature of the system is kept at 30ºC)

(A) 70 cm of Hg (B) 75.4 cm of Hg (C) 90 cm of Hg (D) 6.9 cm of Hg





66. Iodine molecule dissociates into atoms after absorbing light of 4500 Å. If one quantum of radiation is absorbed by each molecule, calculate the kinetic energy of iodine atoms. (Bond energy of I2 = 240 kJ mol–1)

(A) 0.216 × 10–27 J (B) 0.216 × 10–19 J (C) 0.216 × 1015 J (D) 0.216 × 10–25 J

67. Calculate the amount of energy required to convert 5 mole of sodium atom in the gaseous state to form sodium ion. Ionisation enthalpy of Na = 5.1 eV/atom.

(A) 2.46 × 1010 J (B) 2.46 × 106 J (C) 5.26 × 106 J (D) 5.26 × 1010 J

68. Which one of the following pair is isostructural?

(A) SO2, CO2 (B) 22 2CO ,CN (C) 2 2CO , NO (D) 2

2 2CN ,NO

69. The hydrogen like species that will have same velocity of electron as an electron present in first Bohr’s orbit of hydrogen atom?

(A) n = 2, Li2+ (B) n = 3, He+ (C) n = 2, Be3+ (D) n = 4, Be3+

70. For which gas density is maximum?

(A) N2at 2 atm and 27°C (C) H2at 4 atm 227°C

(C) O2at 1 atm and 0°C (D) He at 1 atm and –5°C

71. The number of tetrahedral unit present in 22 7Cr O is

(A) 2 (B) 3 (C) 1 (D) 4

72. Which is correct order of basic strength of given hydroxides?

I. NaOH II. KOH III. RbOH IV. CsOH

(A) I > II > III > IV (B) IV > III > II > I (C) IV > II > III > I (D) I > III > IV > II

73. The set of element that will not form hydride

(A) Mn, Fe, Na (B) Mn, Fe, Co (C) Sc, Ti, V (D) Ni, Cu, Zn

74. A diatomic molecule has a dipole moment equal to 1.2 D. If bond length is 1.0 Å what fraction of electronic charge ‘e’ exists on each atom ?

(A) 0.4 (B) 0.25 (C) 0.6 (D) 0.1

75. The molar heat capacity of water at constant pressure is 75 JK–1 mol–1. When 1kJ heat is supplied to 100 g of water which is free to expand, the increase in temperature of water is:

(A) 6.6 K (B) 1. 2 K (C) 2.4 K (D) 4.8 K





76. The ionization constant of 4NH in water is 5.6 × 10–10 at 25ºC. The rate constant for the reaction of 4NH and OH– to form NH3 and H2O at 25ºC is 3.4 × 1010 litre mol–1. Calculate the rate constant for proton transfer from water to NH3.?

(A) 6.07 × 106 (B) 6.07 × 105

(C) 8.07 × 109 (D) 8.07 × 108

77. The [Ag+] ion in a saturated solution of Ag2CrO4 at 25ºC is 1.5 × 10–4 M. Determine KSP of Ag2CrO4 at 25ºC.

(A) 2.688 × 10–12 mol3 L–3 (B) 1.688 × 10–12 mol3 L–3

(C) 3.688 × 10–12 mol3 L–3 (D) 2 ×10–15 mol3 L–3

78. If 20% energy of combustion of glucose [ combH 2800kJ mol–1] is available to human being and 50 kJ energy makes a runner to run only 1 km, how much glucose should he eat to run a track of 15 km ? (1 mol glucose = 180 g)

(A) 142 g (B) 241 g

(C) 410 g (D) None of these

79. Calculate the bond energy of A2 molecule from the following data:

(i) Bond energies of A2, B2 and AB are in the ratio 1 : 0.5 : 0.25.

(ii) fH of AB is – 100 kJ mol–1.

(A) 100 kJ (B) 200 kJ (C) 300 kJ (D) 400 kJ

80. Which of the following is the enthalpy of the following reaction ?

3 22Fe 3Zn 2Fe 3Zn

Given that º 3fH Fe 100kJ mol–1, o 2 1

fH Zn 15 kJ mol

(A) + 85 kJ

(B) – 115 kJ (C) + 155 kJ (D) – 155 kJ





SECTION – III (MATHEMATICS)

81. If |z2 – 1| = |z2| + 1, then z line on (A) A circle (B) The imaginary axis (C) The real axis (D) An ellipse

82. If 4z 2,z

then the maximum value of |z| is equal to

(A) 1 (B) 2 2 (C) 3 1 (D) 5 1

83. 21n n n2

represents the sum of n terms of an A.P. Their common difference can be

taken as (A) (B) (C) + (D) None of these

84. p1 i

1 i

is unity for the least positive integral value of ‘p’ as]

(A) 6 (B) 1 (C) 4 (D) 2 85. On rearranging the letters of the word RENESSANSSE, the number of ways in which a word

can be formed with all S’s not coming together is

(A) 11! 7!

4!3!2! 3!2! (B)

11! 8!4!3!2! 3!2!

(C) 11! 8!3!2! 3!2!

(D) 8!

3!2!

86. The smaller root of the equation 31x2–21x–10=0 is (A) 1 (B) – 1 (C) 10/31 (D) –10/31 87. (1, 6), (5, 6) (5, 2) and (1, 2) are vertices of a (A) Parallelogram (B) Rectangle (C) Square (D) All of these 88. The distance of point (2, 5) from 3x + y + 4 = 0 measured along the line 3x – 4y + 2 = 0 is (A) 5 units (B) 6 units (C) 4 units (D) 52 units

89. 2 2

1 sin x sin3x is equal to2 sin x cos x

(A) tan 2x (B) tan2x (C) sin x (D) sin 2x 90. If a point has sum of its distances from a pair of perpendicular lines as unity, then the locus

of this point is a (an) (A) Circle (B) Ellipse (C) Square (D) Pair of straight line





91. If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

(A) a < 2 (B) 2 < a < 3 (C) 3 < a < 4 (D) a > 4

92. The distance between points (cos 0), (0, sin ) is

(A) 1 (B) Depends upon (C) –1 (D) Zero

93. The equation x 1 x 1 4x 1,(x R)

(A) No solution (B) One solution (C) Two solutions (D) More than two solution

94. If f (x) = [x] and g(x) = |x – 2|, then fog function is [where [·] represents the greatest integer function]

(A) Even (B) Odd (C) Neither even nor odd (D) Either even or odd

95. If 3x 0

ksinx sin2xlim2x

is a finite value, then ‘k’ takes value

(A) ½ (B) –1/2 (C) –1 (D) –2

96. x x

x xx

5 3The value of lim is5 3

(A) 1 (B) –1 (C) 0 (D)

97. If the roots of the equation x2– 2ax+ a2 + a– 3 = 0 are real and less than 3, then

(A) a < 2 (B) 2 a 3 (C) 3< a 4 (D) a > 4

98. If y = (1 + x) (1 +x2) (1 +x4) (1 +x8) then dy/dx at x = –1 is

(A) 34 (B) 17 (C) 17/2 (D) 8

99. xlim x x x x

is given by

(A) 0 (B) 1/2 (C) log 2 (D) none of these

100. If S denotes the sum of infinite terms of a G.P. with its first term as a and common ratio x(|x| < 1), then the ratio of value of S as limit x tends to an infinitely small value, to when it tends to value 0.5, is given by

(A) 1 : 10 (B) 10 : 1 (C) 1 : 2 (D) 2 : 1


sample paper class xi – 11 section – i …sample paper class xi – 11th std (engineering) head...

Documents