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CBSE 7
th
The Aspire Scholarship
Test 2015
(Maths + Science)
(Solved)
General Instructions:
 The question paper contains 90 objective multiple choice questions.
 There are three parts in the question paper consisting of
 Section-A MATHEMATICS (1 to 45)
 Section-B SCIENCE (45 to 90),
 Each right answer carries 4 marks and Minus 1 for every wrong answer.
 The paper consists of 90 questions. The maximum marks are 360.
 Maximum Time 2.30 Hrs.
Give your response in the OMR Sheet provided with the Question Paper.
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Section-A Mathematics
1.
A  P, B  Q, C  R, AB = PQ, BC, = QR, AC = PR, A  P, B  Q and C  R, then ABC is
congruent to
(a) QPR
(b) RQP
(c) PQR
(d) none of these
(c) 10ac
(d) 6 < 10 × a – 6
Solution :
AP
BQ
CR
AB = PQ
BC = QR
AC = PR
A  P
B  Q
C  R
 ABC  PQR.
2.
3.
6 less than ten times a’ is written as
(a) 6 – 10a
(b) 10a – 6
Ans. (b)
2
3
Nine boards are stacked on the top of each other. The thickness of each board is 3 cm. Then the
height of the stack is
(a) 33 cm
(b) 32 cm
Ans. (a)
Solution :
(c) 31 cm
(d) 11 cm
2
3
Thickness of each board = 3 cm
=
11
cm.
3
Since nine boards are stacked an the top of each other.

4.
height = 9 
11
 33 cm.
3
The diameter of the wheel of a car is 77 cm. Number of revolutions it will make to travel 121 km is
(a) 500
(b) 1000
(c) 3000
(d) 50, 000
Ans. (d)
Solution:
Diameter = 77 cm
 Radius =
77
cm.
2
Total distance travelled = 121 km
= 121000 m
= 12100000cm
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
Number of Revolutions =
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12100000
2
2  77
12100000
2r
12100000

22 77
2

7
2

5.
6.
Regular polygons have the same order of rotational symmetry as the number of __________
(a) sides
(b) vertices
(c) diagonals
(d) none of these
Ans. (a)
The constant term in 7x2 – 10 is
(a) 7
(b) – 10
(c) 10
(d) – 7
Ans. (b)
1
7.
1
____________number should be multiplied by   so that the product is
2
5
2
2
(a)
(b)
(c)
5
2
5
 5 
 4 
 
1
(d) 1
Ans. (a)
Solution:
1
8.
1
4
2
1
 5 
 2   x   4   2x  5  x  5
 
 
In the given fig. ABCD is a parallelogram. DL  AB and DM  BC. If AB = 18 cm, BC =12 cm and DM = 10
cm. Find DL.
1
2
(a) 6 cm
(b) 6 cm
2
3
(c) 6 cm
(d) None
Ans. (c)
Solution:
Area of gm ABCD
= AB × DL
 BC × MD = AB × DL
 12 × 10 = 18 × DL
DL 
120
18
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9.
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The number of independent measurements required to construct a triangle is
(a) 3
(b) 4
(c) 2
(d) 5
Ans. (a)
10. If the radius of a circle is
(a) 154 cm2
(b)
7
cm, then the area of the circle is

49 2
cm

(c) 22 cm2
(d) 49 cm2
Ans. (d)
2
Area of the circle = r   
7
7

 49 cm2
11
11
11. The perimeter of a rectangular plot is 48 m and its area is 108 m2. The dimensions of the plot are
(a) 12 and 9
(b) 18 and 6
(c) 27 and 4
(d) 36 and 3
Ans. (b)
Solution:
Area = 108m2 = L × B; Perimeter = 2(L + B) = 48 m
 108 

108
 2 
 B  48
L × B = 108  L 

B
 B 

 B2  108  24B  B  18, 6  L  6, 18
dimensions are 18, 6 or 6, 18.
12. The area of the shaded region in the figure given below is

(a) 150 m2
(b) 156 m2
(c) 160 m2
(d) 180 m2
Ans. (b)
Solution:
Area of shaded region = 2 × 30 + 2 × 50 = 160 m2.
13. A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its
area will be
(a) 3520 cm2
(b) 6400 cm2
(c) 8800 cm2
(d) 7744 cm2.
Ans. (d)
Solution :
Circumference = 2 

22
 56  352 cm
7
4a  352  a  88

Area of a2 = (88)2 = 7744 cm2.
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14. In the given diagram ABCD is a rectangle; and ADEF, CDHG, BCLM, ABNO are four squares. If the
perimeter of ABCD is 16 cm and the total area of the four squares is 68 cm2, then the area of ABCD is
equal to
(a) 15 cm2
(b) 20 cm2
(c) 25 cm2
Ans. (a)
Solution:
2a2 + 2b2 = 68  a2 + b2 = 34 also 2(a + b) = 16  a + b = 8
 (a + b)2 = 64  a2 + b2 + 2ab = 64  ab = 15 cm2.
(d) 30 cm2.
5
15. Which is greater 5 or 2
5
(a) 5
Ans. (b)
Solution:
(b)
Raising both
we get
 5
5
10
5
5 and
2
(c) both are equal
(d) can’t say.
2 to the 10th power
 52  25 and
 2
10
 210  25  32 and since 32 > 25, 2  5 5.
16. In a problem involving division, the divisor is eight times the quotient and four times the remainder. If
the remainder be 12, then the dividend is
(a) 300
(b) 288
(c) 512
(d) 524.
Ans. (a)
Solution:
Remainder = 12  divisor = 4 × 12 = 48.
 8 × quotient = 48  q = 6.
 dividend = 6 × 48 + 12 = 300.
17. If a five digit number 2785x is divisible by 11, then the value of x is
(a) 1
(b) 2
(c) 3
(d) 5.
Ans. (b)
Solution :
2785 x is divisible by 11 only if x= 2.
18. The value of x – yx–y when x = 2 and y = – 2 is :
(a) –18
(b) –14
(c) 14
(d) 18
Ans. (b)
Solution:
2 – (–2)4 = 2 – 16 = – 14.
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19. In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The
number of cows was :
(a) 5
(b) 7
(c) 10
(d) 12
Ans. (b)
Solution :
Let a be the number of cows and b the number of chickens. Then 4a + 2b is the total number of legs and
4a + 2b = 14 + 2(a + b), 2a = 14, a = 7 (cows).
Note: The number of chickens is indeterminate.
20. The expressions a + bc and (a + b) (a + c) are :
(a) always equal
(b) never equal
(c) equal when a + b + c = 1
(d) equal when a + b + c = 0
Ans. (c)
Solution:
For the equality a + bc = a2 + ab + ac + bc to hold, we must have
a = a2 + ab + ac or 1 = a + b + c.
21. If the Highest Common Divisor of 6432 and 132 is diminished by 8, it will equal :
(a) – 6
(b) 6
(c) – 2
(d) none of these
Ans. (d)
Solution:
132 = 22. 3. 11 and 6432 = 25. 3. 67.
Their H.C.F. = 22. 3 =12 and 12 – 8 = 4.
22. [5 81/3  271/3  ]1/ 4 is :
3
(a) 25
Ans. (b)
Solution :

(b) 5

5 81/3  271/3 3 




3
= 5 2  3 


(d) 625
(c) 2
(d) cannot be determined
1/4
1/3
1/3 3 
= 5 23   33 


(c) 125
1/4
1/4
= 5  53 
1/ 4
= 54 
1/ 4
5
23. The degree of the polynomial 5x3 – 6x3y – 8 is :
(a) 3
(b) 4
Ans. (b)
Solution:
Since the highest power is 3 + 1 = 4.
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24. If the angles of a triangle are in the ratio 2 : 3 : 4, then the difference between the greatest and smallest
angle is :
(a) 100
(b) 200
(c) 300
(d) 400
Ans. (d)
Solution:
Let the angles be 2x, 3x, 4x
 2x + 3x + 4x = 1800
 9x = 1800
 x = 200
 2x = 400 and 4x = 800
 4x – 2x = 800 – 400 = 400
25. If
2
of a number is 20 less then the original number, then the number is :
3
(a) 60
(b) 40
Ans. (a)
Solution:
Let the number be x.
A.T.Q.
(c) 80
(d) 120
2
 x  x  20
3
x  2x 3x  2x x
20 


3
3
3
 x  60
26. The perimeter of a gm is 180 cm, one side exceeds another by 10 cm. The sides of the gm are :
(a) 40, 50
(b) 45 each
(c) 50 each
(d) None
Ans. (a)
Solution:
Let one side of gm be x cm
other side is (10 + x) cm
Also, Perimeter = 180
 2{x + (10 + x)} = 180
 2(10 + 2x) = 180
 10 +2x = 90
 x = 40
and other side = 40 + 10 = 50 cm.
27. C is the centre of circle shown in the diagram below : Then x + y is equal to :

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(a) 900
Ans. (a)
Solution:
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(b) 1000
(c) 1300
(d) 450
1350  x  1800  x  450
 Also x= y
y = 450
 x + y = 450 + 450 = 900
28. The order of rotational symmetry for the given figure is __________
(a) 3
(b) 4
(c) 6
(d) 12
Ans. (c)
Solution:
Since the number of times a figure fits onto itself in one full turn is 6.
 is order of rotational symmetry is 6.
29. The rational number
0
7
(a) has a positive numerator
(b) has a negative numerator
(c) has either a positive numerators or a negative numerator
(d) has neither a positive numerator nor a negative numerator.
Ans. (c)
30. The solution of
0.2(2x – 1) – 0.5(3x – 1) = 0.4 is
(a)
1
11
(b) 
1
11
(c)
3
11
(d) –
Ans. (b)
Solution:
0.2(2x – 1) – 0.5(3x – 1) = 0.4
0.4x – 0.2 – 01.5x + 0.5 = 0.4
–1.1x = 0.4 – 0.3
–1.1x = 0.1
x= 
0.1
1

1.1
11
31. Find: 113
(a) 10 . 54
Ans. (b)
(b) 10. 64
(c) 10.84
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Solution :
10
 113  11

113  11 
2
= 11 
2
121  113
2  11
8
4
 11 
2  11
11
= 11 – 4 × 0.0909
= 11 – 0.3636
= 10.6364
 10.64
3
32. Find: 29791
(a) 21
Ans. (c)
Solution:
3
(b) 41
(c) 31
(d) None of these.
29791  ?
From unit digit of 29, 791, we ascertain that last digit of its cube root will be 1
Now, 33 < 29 < 43
 our first digit thus comes to 3 and the answer is 31.
33. Find:
3
592904
1764
(a) 1
Ans. (a)
Solution:
(b) 2
(c) 3
(d) 4
3
34.
35.
36.
37.
592904 84.009

 2.
42
1764
B is the husband of P.Q is the only grandson of E, who is wife of D and mother-in-law of P. How is B
related to D?
(a) Nephew
(b) cousin
(c) Son-in-law
(d) Son
Ans. (d)
Choose the pair in which the words are differently related
(a) Chaff: Wheat
(b) Grit: Pulses
(c) Grain : Crop
(d) Dregs: Wine
Ans. (c)
Choose out the odd one
(a) Mumbai
(b) Cochin
(c) Kandla
(d) Mysore
Ans. (d)
Going 50 m to the south of her house, Radhika turns left and goes another 20 m. Then turning to the
North, she goes 30 m and then starts walking to her house. In which direction is she walking now ?
(a) North-west
(b) North
(c) South east
(d) East
Ans.
Solution:
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To reach her house, she should travel in North-West direction.
38. If a person is walking towards North, what direction should he follow so that he is walking towards
West ?
(a) right, right, left (b) left, left, right
(c) left, right, left
(d) left, left, left
Ans. (b) or (c)
39. In a certain language, MIRACLE is coded as NKUEHRL, then how is GAMBLE coded in that language?
(a) JDOCMF
(b) CLEMNK
(c) HCPFQK
(d) AELGMN
Ans. (c)
Solution :
M
I
R
A
C
L
E
, G
A
M
B
L
E
 1  2  3  4   5  6  7
B
K
U
E
H
R L
 1   2   3   4   5   6
H
C
P
F
Q
K
40. If ‘rat’ is called ‘dog’, ‘dog’ is called ‘mongoose’, ‘mongoose’ is called ‘lion’, ‘lion’ is called ‘snake’ and
‘snake’ is called ‘elephant’, which is reared as pet ?
(a) Rat
(b) Dog
(c) Mongoose
(d) Lion
Ans. (c)
Solution :
Since Dog is reared as pet and Dog is called mongoose
 Mongoose is the correct answer.
41. If DRIVER = 12, PEDESTRIAN = 20, ACCIDENT = 16, then CAR = ?
(a) 3
(b) 6
(c) 8
(d) 10
Ans. (b)
Solution :
DRIVER = 12
PEDESTRAIN = 20
ACCIDENT = 16
Since in each case, no. is 2 the no. of letters in the respective words
 CAR = 2 × 3 = 6
42. Find the mirror image of DL9CG4728
Ans. (c)
3
43. Find 17576  729
(a) 1
(b) –1
(c) 2
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Ans. (b)
Solution:
3
17576  729  26  27  1
44. Find the HCF of 12576 and 4052
(a) 2
(b) 4
(c) 6
(d) 8
Ans. (b)
Solution:
12576 = 25 × 3 × 131
4052 = 22 × 1013
 HCF = 22 = 4
45. Nidhi travels 10 km to the north, turns left and travels 5 km, and then again turns right and covers
another 5 km, and then turns right, and travels another 5 km. How far is she from the starting point ?
(a) 15 km
(b) 4 km
(c) 5 km
(d) 10 Km
Ans. (a)
Solution:
AB + BC
= AB + ED
= 10 + 5
= 15 km.
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Section – B {Science}
46. The process of depositing a layer of zinc on iron is called :
(a) galvanization
(b) neutralization
(c) crystallization
(d) none of these
Ans. (a)
47. Anaerobic bacteria digests animal waste and produces biogas (Change-A). The biogas is then burnt as fuel
(Change-B). The following statements pertain to these changes. Choose the correct one.
(a) Process-A is a chemical change
(b) Process-B is a chemical change
(c) Both processes A and B are chemical changes
(d) None of these processes are chemical changes.
Ans. (c)
48. ____________ aerates the soil and allows the air to each the roots of plants:
(a) earth worm
(b) bacteria
(c) fungi
(d) virus
(c) sandy soil
(d) all of these
Ans. (a)
49. The bests kind of soil for plant
(a) loamy soil
(b) clayey soil
Ans. (a)
50. The hard layer of rocks below the C horizon is called :
(a) bottom rock
(b) substratum
(c) bed rock
(d) gravel
Ans. (d)
51. Insects have small openings on the outside of their bodies. These openings are called :
(a) spiracles
(b) trachea
(c) gills
(d) none of these
Ans. (a)
52. The seed of which of the following plants has monocotylendon :
(a) maize
(b) bean
(c) pea
(d) gram
(c) pumpkin
(d) all of these
Ans. (a)
53. The plants which have unisexual flowers are :
(a) torial
(b) lauki
Ans. (d)
54. Which of the appliances does not use on electro magnet?
(a) washing
(b) refrigeration
(c) room heater
(d) electric bell
Ans. (c)
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55. Which of these is not circuit element?
(a) potential difference(b) voltmeter
(c) resistor
(d) battery
Ans. (c)
56. The image formed by a concave lens is always virtual, erect and:
(a) bigger in size
(b) smaller in size
(c) medium in size
(d) all of these
Ans. (b)
57. The most common example of a curved mirror is a :
(a) concave mirror
(b) erect mirror
(c) convex mirror
(d) spherical mirror
(c) sea water
(d) spring water
(c) under storeys
(d) all of these
Ans. (d)
58. Purest form of natural water is:
(a) rain water
(b) ground water
Ans. (a)
59. Small trees and grass and shrubs form the :
(a) canopy
(b) lowest canopy
Ans. (c)
60. Dried sludge is used as :
(a) sludge
(b) sewers
(c) waste water treatment plant
(d) manure
Ans. (d)
61. Which of the following is NOT in uniform motion?
(a) A bullet travelling with a constant speed in a straight line.
(b) A swinging pendulum
(c) The rotation of earth
(d) Both B & C
Ans. (d)
62. Which of the following letters will be seen without any change in a plane mirror?
(a) S
(b) T
(c) L
(d) P
Ans. (b)
63. In which circuit will the bulb or bulbs glow the brightest?
(a) A simple circuit with one bulb and one cell.
(b) A simple circuit with one bulb and two cells.
(c) A simple circuit with two bulbs and one cell.
(d) A simple circuit with two bulbs and two cells
Ans. (b)
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64. To lower the freezing point of water ___________ is added.
(a) sand
(b) salt
(c) sugar
(d) sawdust
(c) salt + O2
(d) salt + H2
Ans. (b)
65. Acid reacts with metal to form :
(a) salt + CO2
(b) salt + water
Ans. (c)
66. A student poured alcohol on a plant continuously for a long time. The plant could not prepare food on its
own. What has happened?
(a) alcohol absorbed all the food prepared by the plant
(b) alcohol does not let the plant to absorb carbon dioxide from the air
(c) alcohol dissolved all the minerals present in the plant
(d) alcohol dissolved chlorophyll present in the plant
Ans. (b)
67. Leguminous plants have their roots modified into :
(a) fibrous roots
(b) stilt roots
(c) nodulated roots
(d) prop roots
Ans. (c)
68. Shadows are formed because :
(a) opaque bodies allow the light to pass through them
(b) light can bend around the opaque bodies
(c) light rays cannot pass through the opaque bodies
(d) light shows the phenomenon of diffraction around large objects.
Ans. (c)
69.
Lichens are
(a) symbiotic algae and fungi
(b) carnivorous plants
(c) animals which can perform photosynthesis
(d) interdependent algae
Ans. (a)
70. Which of the following is NOT a chemical change?
(a) Digestion of food
(b) Precipitation of rain and snow
(c) Rusting of iron
(d) Burning of paper
Ans. (b)
71. Consider the following statements:
A person in a spaceship located half way between the earth and the sun will notice that the
(1) Sky is jet black.
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(2) Stars do not twinkle.
(3) Temperature outside the spaceship is much higher that on the surface of the earth. Of these
statements,
(a) 1 and 3 are correct (b) 1 and 2 are correct
(c) 3 along is correct
(d) 1,2and3are correct
Ans. (d)
72. An electric current is the rate of flow of electric charges and it is measured in volts.
(a) In this statement, the.' first part is true and the second part is false
(b) True
(c) False
(d) First part is false, second part is lure
Ans. (a)
73. On a half-moon night the angle between the moon and the sun when
measured from earth is about
(a) 90°
(b) 60°
(c) 45°
(d) 180°
Ans. (a)
74. 'Black holes' refers to
(a) Collapsing object of high density
(b) Bright spots on the sun
(c) Holes occurring in heavenly bodies
(d)Collapsing object of low density
Ans. (a)
75. Atmospheric pressure exerted on earth is due to the
(a) Gravitational pull
(b) Revolution of earth
(c) Rotation of earth
(d) Uneven heating of earth
Ans. (a)
76. A cricketer lowers his hands while holding a catch because
(a) The momentum decreases with time
(b) The velocity decreases with time
(c) The force decreases as time increases
(d) It is a style of holding a catch
Ans. (c)
77. In Thomson's e/m experiment,
(a) The uniform magnetic field is produced by a magnet
(b) The electric and magnetic fields arc parallel
(c) The electric and magnetic fields are perpendicular
(d) The uniform magnetic field is produced by two parallel circular current -carrying coils
Ans. (c)
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78. The phenomenon of bending of light at the surface of separation of two media is called
(a) Refraction of light
(b) Reflection of light
(c) Deflection of light
(d) Absorption of light
Ans. (a)
79. Which of the following transformations of energy takes place in a microphone?
(a) Mechanical energy into sound
(b) Sound into electrical energy
(c)Electrical energy into sound
(d)Sound into mechanical energy
Ans. (b)
80. The sound waves which cannot be heard by a human ear are called
(a) Ultrasonic sounds
(b) Infrasonic sounds
(c) Extraordinary sounds
(d) Both (a) and (c)
Ans. (d)
81. Food item when kept carefully get spoiled is a :
(a) chemical change
(b) physical change
(c) both (a) and (b)
(d) none of these
(c) cotton crop
(d) all of these
Ans. (a)
82. Loamy soil is most suitable for planting :
(a) rice crop
(b) pulse crop
Ans. (a)
83. The mountaineer carry oxygen with them because :
(a) At an attitude of more than 5 km there is no air
(b) The amount of air available to a person is less than that available on the ground
(c) The temperature of air is higher than that on the ground
(d) The pressure of air is higher than that on the ground
Ans. (b)
84. The vascular tissue for that transports the food synthesized by the leaves to all parts of the plants is :
(a) Phloem
(b) xylem
(c) stomata
(d) root hairs
Ans. (a)
85. Why you add yeast to dough, it rises because:
(a) yeast cell reproduce by budding
(b) budding yeast cells from chains
(c) The rapidly reproducing yeast cells release carbon dioxide due to respiration
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(d) Of the bulk of the new yeast cells.
Ans. (c)
86. Rose and lemon are grown from:
(a) tubers
(b) bulbs
(c) stem cuttings
(c) leaf buds
Ans. (c)
87. Which of the following liquid is bad conductor of electricity :
(a) salted water
(b) orange juice
(c) lemon juice
(d) none of these
(c) variable battery
(d) current
Ans. (d)
88.
Symbol represents
(a) Resistance
(b) variable resistance
Ans. (b)
89. If a boy is standing 5 m away from the mirror then what is its distance from his image?
(a) 5 m
(b) 10 m
(c) 15m
(d) no image all form
Ans. (b)
90. Bending of light when it travel from one medium to another is known as
(a) reflection
(b) refraction
(c) dispersion
(d) diffraction
Ans. (b)
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