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Engineering BITSAT
BITSAT 2013 Question Paper with Answers
10183 By AglaSem EduTech - September 5 2016
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BITSAT 2013 Question Paper with Answers
BITSAT 2009 Question Paper with Answers are given below
BITSAT 2013 Question Paper
Mathematics
1. If α β are the roots of ax + bx + c 0 then -1/α -1/β are the roots of
a ax – bx + c 0
b cx – bx + a 0
c cx + bx + a 0
d ax – bx – c 0
2. The number of real roots of the equation
x – 1 + x – 2 + x – 3 0 is
a 1
b 2
c 3
d None of these
3. If S is the set containing values of x satisfying x – 5x + 6 ≤ 0 where x denotes GIF then S contains
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2
2
2
2
2
2 2 2
2
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a 2 4
b 2 4
c 2 3
d 2 4
4. Seven people are seated in a circle. How many relative arrangements are possible
a 7
b 6
c P
d C
5. In how many ways can 4 people be seated on a square table one on each side
a 4
b 3
c 1
d None of these
6. Four different items have to be placed in three different boxes. In how many ways can it be done such that any box can have any number of items
a 3
b 4
c P
d C
7. What is the probability that if a number is randomly chosen from any 31 consecutive natural numbers it is divisible by 5
a 6/31
b 7/31
c 6/31 or 7/31
d None of these
8. The mean of a binomial distribution is 5 then its variance has to be
a 5
b 5
c 5
d 25
9. If a is the single A.M. between two numbers a and b and S is the sum of n A.M ‘s between them then S/A depends upon
a n a b
b n a
c n b
d n
10. 2 4 8 16 .. upto ∞ equal to
7
6
7
6
4
3
4
3
4
3
1/4 1/8 1/16 1/32
slide 3: a 1
b 2
c 3/2
d 5/2
11. The odds in favour of India winning any cricket match is 2 : 3. What is the probability that if India plays 5 matches it wins exactly 3 of them
12. For an A.P. S 3 S . The value of S /S is equal to
a 4
b 6
c 8
d 10
13. 1 + sin x + sin x + sin x + … 4 + 2√3 0 x π x ≠ π/2 then x
a π/6 π/3
b π/6 5π/6
c π/3 2π/3
d π/3 5π/6
14.
a x
b x
c log 1 + x
d log x
15. The ends of a line segment are P1 3 and Q1 1. R is a point on the line segment PO such that PR : QR 1 : λ. If R is an interior point of the parabola y
4x then
a λ ∈ 0 1
b λ ∈ -3/5 1
c λ ∈ -1/2 -3/5
d None of these
16. Set of values for which
is true is
a φ
b nπ + π/4 n ∈ Z
c π/4
d 2nπ + π/4 n ∈ Z
17. The distance between the lines 3x + 4y 9 and 6x + 8y + 15 0 is
2n n 3n n
2 3
2
e
e
2
2
slide 4: a 3/10
b 33/10
c 33/5
d None of these
18. Let A 3 -4 B1 2 and P 2k – 1 2k + 1 is a variable point such that PA + PB is the minimum. Then k is
a 7/9
b 0
c 7/8
d None of these
19. The length of the y-intercept made by the circle x + y – 4x 6y – 5 0 is
a 6
b √14
c 2√14
0 3
20. If x + y k is normal to y 12x then k
a 3
b 6
c 9
d None of these
21. The number of values of c such that the straight line y 4x + c touches the curve x /4 + y 1
a 1
b 1
c 2
d infinite
22.
a 0
b √2
c 1/2
d 1/√2
23. Locus of the point z satisfying Re i/z k is a non-zero real number is
a a straight line
b a circle
c an ellipse
d a hyperbola
24. The points of z satisfying arg
lies on
2 2
2
2 2
slide 5: a an arc of a circle
b a parabola
c an ellipse
d a straight line
25. The coefficients of the 3rth term and the r + 2th term in the expansion 1 + x are equal then
a n 2r
b n 3r
c n 2r + 1
d None of these
26.
a 2e
b e
c e – 1
d 3e
27. If a 13 b 12 c 5 in ∠ABC then sinA/2
a 1/√5
b 2/3
c √32/35
d 1/√2
28. 2tan 3/4
a sin 24/25
b sin 12/13
c cos 24/25
d cos 12/13
29. Two pairs of straight lines have the equations y + xy – 12x 0 and ax + 2hxy + by 0. One line will be common among them if
a a -32h + 3b
b a 8h – 2b
c a 2 b + h
d Both a and b
30. If a circle passes through the point 3 4 and cuts x + y 9 orthogonally then the locus of its centre is 3x + 4y λ X. Then λ
a 11
b 13
c 17
d 23
31. For what value of x the matrix A is singular
2n
-1
-1
-1
-1
-1
2 2 2 2
2 2
slide 6: a x 0 2
b x 1 2
c x 2 3
d x 0 3
32. 1f 7 and 2 are two roots of the following equation
then its third root will be
a -9
b 14
c 1/2
d None of these
33. Period of fx sin x cos x
a π
b π/2
c 2π
d None of these
34. The range Of log sin x
a - ∞ ∞
b - ∞ 1
c - ∞ 0
d - ∞ 0
35.
a 1/8
b -1/8
c 2/3
d 3/2
36. Let y log sinx 0 x ≤ π/2. The value of dy/dx at x √π/2 is
a 0
b 1
c π/-4
d√π
37. For the curve x t – 1 y t – t tangent is parallel to x-axis where
a t 0
b t 1/√3
c t 1/2
d t -1/√3
38. fx x – 6x + 12x – 16 is strictly decreasing for
4 4
e
2
2 2
3 2
slide 7: a x ∈ R
b X ∈ R – 1
c x ∈ R
d x ∈ φ
39. The value of b for which the function fx sinx – bx + c is a strictly decreasing function ∀ x ∈ R is
a b ∈ -1 1
b b ∈ -α 1
c b ∈ 1 α
d b ∈ 1 α
40. Maximum value of the expression 2 sinx + 4 cosx + 3 is
a 2√5 + 3
b √5 – 3
C √5 + 3
d None of these
41. If sin θ 3 sinθ + 2 α then the value of tanθ + α+ 2 tanα is
a 3
b 2
c 1
d 0
42.
a 10
b 1/10
c 1
d -1
43. If √1 + x + √1 + y a then find dy/dx
44. Length of the subtangent to the curve y e is
a e
b a
c 2/a
d None of these
45. The value of c of mean value theorem when fx x – 3x – 2 in -2 3 is
a √7/3
b √3/7
+
2 2
x/a
x/a
3
slide 8: c √7/3
d √3/7
Physics
46. A gold coin has a charge of + 10 C. The number of electrons removed from it is
a 10
b 625 x 10
c 1.6 x 10
d 1.6 x 10
47. A small sphere of mass m and electric charge q is suspended by a light thread. A second sphere carrying a charge q is placed directly below the first sphere
at a distance ‘d’ away. Then
a tension in thread may reduce to zero if the spheres are positively charged
b tension in thread may reduce to zero if the spheres are oppositely charged
c tension in thread can never be zero
d tension in thread is independent of the nature of the charges
48. A pitch ball covered with a tin foil having a mass m kg hangs by a fine silk thread of length l metres in an electric field E. When the ball is given an electric
charge of q coulomb it stands out d metre apart from the vertical line. The magnitude of an electric field will be
49. The current I and voltage V graphs for a given metallic wire of two different temperatures T and T are shown in the following figure. It is concluded that
a T T
b T T
c T T
d T 2T
50. The resistance of a 20 cm long wire is 5 Ω.
The wire is stretched to form a uniform wire of 40 cm length. The resistance now will be
a 5 Ω
b 10 Ω
c 20 Ω
d 200 Ω
51. If a copper wire is stretched to make its radius decrease by 0.1 then the percentage increase in its resistance is approximately
-4
6
10
-25
-13
1 2
1 2
1 2
1 2
1 2
1 2
slide 9: a 0.1
b 0.2
c 0.4
d 0.8
52. When a charged particle is acted on only by a magnetic force its
a potential energy changes
b its kinetic energy changes
c total energy changes
d energy does not change
53 A positively charged particle projected towards east is deflected towards north by a magnetic field. The field may be
a towards west
b towards south
c upwards
d downward
54. The permanent magnetic moment of the atoms of a material is not zero. The material
a must be paramagnetic
b must be diamagnetic
c must be ferromagnetic
d may be paramagnetic
55. A paramagnetic material is kept in a magnetic field. The field is increased till the magnetization becomes constant. If the temperature is now
decreased the magnetization
a will decrease
b will increase
c remain constant
d may increase or decrease
56. A metallic wire bent in form of a semi-circle of radius 0.1 m is moved in a direction parallel to its plane but perpendicular to a magnetic field B 20m T with a
velocity of 10 m/sec. What is the induced e.m.f. in wire
a 4 x 10 Volts
b 4 x 10 Volts
c 4 x 10 Volts
d None of these
57. A glass rod of length l moves with a velocity V in a uniform magnetic field B what will be the emf induced in the rod
a Zero
b 0.01 volts
c 0.1 volts
d None of these
58. A 10 μF capacitor is connected across a 200 V 50 Hz A.C. supply. the peak current through the circuit is
a 0.6 A
b 0.6√2 A
-3
-2
-1
slide 10: c 0.6√2 A
d 0.6π/2
59. An alternating voltage E 200√2 sin 100t is connected to a 1 μF capacitor through an A.C. ammeter The reading of the ammeter shall be
a 10 mA
b 20 mA
c 40 mA
d 80 mA
60. The first diffraction minima due to a single slit diffraction is at θ 30° for a light of wavelength 5000 Å. The width of the slit is
a 5 x 10 cm
b 10 x 10 cm
c 2.5 x 10 cm
d 1.25 x 10 cm
61. A beam of light of wavelength 600 nm from a distant source falls on a single slit 1.00 mm wide and the resulting diffraction pattern is observed on a screen 2 M
away. The distance between the first dark fringe on either side of the central maxima is
a 1.2 cm
b 1.2 mm
c 2.4 cm
d 4.8 mm
62. A concave mirror of focal length F produces a real image n times the size of the object. The distance of the object from the mirror is
a n – 1F
b n + 1F
c n + 1/nF
d n – 1/nF
63. An object is placed at a distance of 2f from a concave mirror. Light reflected from the mirror falls on a plane mirror. The distance of the plane mirror from the
concave mirror equals f. The distance of the final image from the concave mirror due to reflection at both concave and plane mirror is
a f
b f/2
c 2f
d zero
64. A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the nth sec to the distance covered in n sec is
65. The range of a projectile when launched at angle θ is same as when launched at angle 2θ . What is the value of θ
a 15°
b 30°
c 45°
d 60°
-5
-5
-5
-5
slide 11: 66. A balloon is descending at a constant acceleration α. The mass of the balloon is M. When a mass m is released from the balloon it starts rising with the same
acceleration α. Assuming that the volume does not change when the mass is released what is the value of m
67. A heavy block of mass M is slowly placed on a conveyer belt moving with a speed v. The coefficient of friction between the block and the belt is IA . Through
what distance will the block slide on the belt
a v/μg
b v /μg
c v/2μg
d v /2μg
68. Under the action of a force a 2 kg body moves such that its position x as a function of time is given by x t /3 where x is in metre and t in second. The work
done by the force in the first 2 s is
a 1600 J
b 160 J
c 16 J
d 1.6 J
69. Three particles of mass M each are placed at corners of an equibterol triangle of side ‘d’ If the sides are increased to ‘2d’ then
a The P.E -3GM /2d
b 3GM /2d
c GM /2d
d -3GM/2d
70. The de Broglie wavelength of a neutron when its kinetic energy is K is λ . What will be its wavelength when its kinetic energy is 4k
a λ/4
b λ/2
c 2λ
d 4λ
71. According to Bohr’s theory the radius of the n orbit of an atom of atomic number Z is proportional to
a n /z
b n /z
c n/z
d n z
72. When U undergoes fission 0.1 of its original mass is changed into energy. How much energy is released if 1 kg of U undergoes fission
a 9 x 10 J
b 9 x 10 J
c 9 x 10 J
d 9 x 10 J
73. The alternating current gain of a junction transistor in common base arrangement is 0.98. What is the change in the base current corresponding to a change of 5
mA in the emitter current and a change of 4.9 mA in the collector current
2
2
3
2
2
2
th
2 2
2
2 2
235
92
235
92
10
11
12
13
slide 12: a 0.1 mA
b 0.2 mA
c 0.3 mA
d 0.4 mA
74. Fig. shows a uniform solid block of mass M and edge lengths a b and c . Its M.I about an axis through one edge and perpendicular as shown to the large face
of the block is
75. A thick walled hollow sphere has outer radius R. It rolls down an inclined plane without slipping and its speed at the bottom is u . If the inclined plane is
frictionless and the sphere slides down without rolling its speed at the bottom will be 5υ/4 What is the radius of gyration of the sphere
a R/√2
b R/2
c R/4
d √3R/4
76. How much force is required to produce an increase of 0.2 in the length of a brass wire of diameter 0.6 mm Young’s modulus for brass 0.9 x 10 N /m
a nearly 17 N
b nearly 34 N
c nearly 51 N
d nearly 68 N
77. A liquid drops at temperature T isolated from its surroundings breaks into a number of droplets. The temperature of the droplets will be
a equal to T
b greater than T
c less than T
d either a b or c depending on the surface tension of the liquid
78. In SHM the net force towards mean position is related to its displacement x from mean position by the relation
a F ∝ x
b F ∝ 1/x
c F ∝ x
d F ∝ 1/x
79. The acceleration a of SHM at mean position is
a zero
b ∝ x
c ∝ x
d None of these
80. When the temperature of air rises by 3 K from 300 K what is the percentage rise in the velocity of sound
a 0.5
b 1
11 2
2
2
2
slide 13: c 2
d None of these
81. A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is
changed to 21 cm. The frequency of tuning fork is
a 200 Hz
b 210 Hz
c 205 Hz
c 215 Hz
82. Three rods made of the same material and having the same cross-section have been joined as shown in the fig. Each rod is of the same length. The left and
right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be
a 45°C
b 60°C
c 30°C
d 20°C
83. If y be the ratio of specific heats of a perfect gas the number of degrees of freedom of a molecule of the gas is:
84. An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 x 10 cal of heat at higher temperature.
Amount of heat converted to work is:
a 2.4 x 10 cal
b 6 x 10 cal
c 1.2 x 10 cal
d 4.8 x 10 cal
85. In a room where the temperature is 30°C a body cools from 61°C to 59°C in 4 min. The time in min taken by the body to cool from 51°C to 49°C will be
a 4
b 6
c 5
d 8
Chemistry
86. The energy of first excited state of Li will be
a 13.6 eV
b 27.2 eV
c 30.6 eV
d 40.8 eV
4
4
4
4
4
2+
slide 14: 87. Which of the following phenomena will occur when two atoms of the elements having same spin of electron approach for bonding
a Orbital overlap will not occur
b Bonding will not occur
c Both a and b are correct
d None of these is correct
88. The number of octahedral sites per sphere in fcc structure are
a 8
b 4
c 2
d 1
89. Due to Frenkel defect the density of ionic solids
a decreases
b increases
c does not change
d change depends on crystal structure
90. For the given electrolyte A B the degree of dissociation ‘α’ can be given as
91. The efficiency of a heat engine is maximum when
a temperature of sink temperature of source
b temperature of source temperature of sink
c the difference between temperature of source and sink is very high
d None of these
92. If three faradays of electricity is passed through the solution of AgNO CuSO and AuCl the molar ratio of the cations deposited at the cathodes will be
a 1 : 1 : 1
b 1 : 2 : 3
c 3 : 2 : 1
d 6 : 3 : 2
93. A gas ‘X’ at 1 atm is bubbled through a solution containing a mixture of 1 M Y and 1 M Z at 25° C. If the standard reduction potential of Z Y X then
a Y will oxidize X and not Z
b Y will oxidize Z and not X
c Y will oxidize both X and Z
d Y will reduce both X and Z
94. The rate constant of a chemical reaction can be increased by
a decreasing the temperature
b increasing the temperature
x y
3 4 3
– –
slide 15: c increasing concentration of reactants
d decreasing concentration of reactants
95. Consider the two equations at a particular temperature
2N O → 4NO + O
N O → 2NO + 1/2O
If E and E represents the activation energy for the first and second reaction respectively then
a E E
b E E
c E 2E
d E E
96. Which one of the following is an example of a hydrophilic colloidal sol
a sulphur
b As S
c gold sol
d starch
97. In P O the number of oxygen atoms attached to each phosphorus atom is
a 2
b 3
c 4
D 5
98. Which of the following compound acts both as an oxidising as well as reducing agent
a SO
b MnO
c Al O
d CrO
99. Green vitriol is
a CuSO
b CuSO .7H 0
c CuSO .5H 0
d FeSO .7H 0
100. Only lanthanide which is radioactive is
a Sn
b Yb
c Pm
d Eu
101. When AI is bombarded with a particles a radioactive isotope of phosphorus P with the emission of …. is formed
a neutrons
b protons
2 5 2 2
2 5 2 2
1 2
1 2
1 2
1 2
1 2
2 2
4 10
2
2
2 3
3
4
4 2
4 2
4 2
27
13
30
15
slide 16: c positrons
d electrons
102. A freshly prepared radioactive source of half life period 2 hours emits radiations of intensity which is 64 times the permissible safe level. The minimum time
after which it would be possible to work with this source is
a 6 hours
b 12 hours
c 24 hours
d 48 hours
103. Which of the following has the highest paramagnetism
a CrH O
b FeH O
c CuH O
d ZnH O
104. Which of the following will form an octahedral complex
a d low spin
b d high spin
c d low spin
d all of these
105. The correct statement about A B C is
a A and B are identical
b A and B are diastereomers
c A and C are enantiomers
d A and B are enantiomers
106. Phenol and benzoic acid can be distinguished by
a aqueous NaHCO
b aqueous NaNO
c aqueous NaOH
d conc. H SO
a I II III IV
b IV I II III
2 6
3+
2 6
2+
2 6
2+
2 6
2+
4
8
6
3
3
2 4
slide 17: c I II IV Ill
d II III IV I
108. When acetaldehyde is heated with Fehling’s solution it gives a precipitate of
a Cu
b CuO
c Cu + Cu O + CuO
d Cu O
109. The principal organic product formed in the reaction
110. Secondary nitroalkanes on treatment with nitrous acid form
a nitrolic acids
b carboxylic acids
c pseudonitroles
d ketones
111. In HS I R – NH NH the order of proton accepting tendency will be
a I NH R — NH HS
b NH R — NH HS I
c R — NH NH HS I
D HS R NH NH I
112. In vulcanisation of rubber
a sulphur reacts to form new compound
b sulphur cross links are introduced
c sulphur forms a very thin protective layer over rubber
d All the statements are correct
113. Which of the following does not represent a disaccharide
a Maltose
b Sucrose
c Lactose
d Dextrose
114. Which one of the following vitamins contains a metal atom
a Riboflavin
b Vitamin B
c Vitamin A
d Vitamin B
2
2
– –
2 3
–
3 2
–
3 2
– –
2 3
– –
–
2 3
–
12
6
slide 18: 115. Veronal a barbiturate drug is used as
a antihistamine
b sedative
c antiseptic
d anti-malarial
116. Gay Lussac’s law of gaseous volume is derived from
a law of definite proportions
b law of multiple proportions
c law of reciprocal proportions
d experimental observation
117. One litre flask contains air water vapour and small amount of liquid water at a pressure of 200 mm Hg. If this is connected to another one litre evacuated flask
what will be the final pressure of the gas mixture at equilibrium. Assume the temperature to be 50° C.
Aqueous tension at 50°C – 93 mm Hg
a 120.56 mm
b 230 mm
c 146.5 mm
d 109.4 mm
118. The correct order of decreasing ionic radius among the following anions would be
a Se I Br F O
b F Br O Se I
C I Se Br O F
d F O Br Se I
119. l + l ⇔ l
This reaction is set up in aqueous medium. We start with 1 mole of l and 0.5 mole of l in 1 L flask. After equilibrium the excess of AgNO gave 0.25 mole of yellow
ppt. Then the equilibrium constant is
a 1.33
b 2.66
c 2.00
d 3.00
120. At 90° C pure water has H 10 M. The value of k at 90° C is
a 10
b 10
c 10
d 10
121. Nitrogen dioxide cannot be obtained by heating
a PbNO
b CuNO
c AgNO
d KNO
2- – – – 2-
– – 2- 2- –
– 2- – 2- –
– 2- – 2- –
2
– –
3
2
–
3
+ -6
w
-6
-8
-12
-14
3 2
3 2
3
3
slide 19: 122. Which of the following is heterocyclic aromatic species
123. Which of the following halides undergoes nucleophilic substitution most readily
a ρ – H CC H CI
b o – MeOC H CI
c ρ – CIC H Cl
d C H CHClCH
124. Dumas’ method involves the determination of nitrogen content in the organic compound in the form of
a NH
b N
c NaCN
d NH SO
125. Group V cations are precipitated in form of carbonates by NH CO . Why can we not use Na CO in stead of NH CO
a Because Na CO will precipitate MgCO
b Because Na CO is insoluble in water
c Because it is an ionic compound
d None of these
Logical Reasoning
126. In a certain code language MADRAS is coded as ‘ARSARS’ then how will ‘MUMBAI’ be coded in that language
a U B M U B M
b U B I U B I
c M U M M U M
d M B A M B A
127. Find the last number of the following number series
101 8 16 13 39 35
a 75
b 100
c 130
d 140
128. If ‘x’ means subtract ‘÷’ means multiply ‘+’ means divide and ‘-‘ means add then which of the following would result in a value of 10
a 15 + 12 x 3 ÷ 2 – 3
b 15 x 12 ÷ 3 + 2 – 3
c 15 + 12 x 3 – 2 ÷ 3
d 15 x 12 + 3 ÷ 2 – 3
3 6 4
6 4
6 4
6 5 3
3
2
4 2 4
4 2 3 2 3 4 2 3
2 3 3
2 3
slide 20: Directions Q. 129 – 130: In these questions there are two sets of figures. The Problem Figures and the Answer Figures. The four Problem Figures make a series.
That means they change from left to right in a specific order.
The question is if the figures continue to change in the same order what should be the third figure so that the series is completed
Study the following problem based on series.
Problem Figures
Study the position of the dot in all the Problem Figures. Note that it keeps moving around the square in the clockwise direction. Where would it be in the third
position If you observe in the second figure the dot is at the upper right corner and in the fourth figure the dot is at the bottom left corner. Hence in the third figure
it should be at the bottom right corner. Therefore the answer is b.
Now solve the following questions.
129. Problem Figures
130. Problem Figures
Directions Q. 131 – 132: In each of the following problems a related pair of figures is followed by five numbered pairs of figures. Select the pair that has a similar
relationship to that of orginal pair The best answer is to be selected from the given choices.
131.
132.