Quantitative aptitude question

1. Page 1LPU Set - 3
LPU Set - 3LPU Set - 3LPU Set - 3LPU Set - 3LPU Set - 3
Quantitative AptitudeQuantitative AptitudeQuantitative AptitudeQuantitative AptitudeQuantitative Aptitude
1. A circular ring of radius 3 cm is suspended from
a point I by four identical strings tied at equal
intervals on its circumference. The ring is in a
horizontal plane. The point I is 4 cm vertically
above the ring’s center. If the angle between any
two consecutive strings is θ, then find the value
of cos θ.
(a)
9
25
(b)
3
5
(c)
16
25
(d)
4
5
2. ABC∆ and ∆PQR are triangles such that PQ ||
BC, QR || AB and PR || AC as shown in the figure.
In ∆PQR, 2PD = DQ and in ABC∆ , BI = AD =
2DI. Find the ratio of areas of ∆ABC and ∆PQR.
A
B C
DP Q
R
I
(a)
49
25
(b)
4
1
(c)
25
9
(d)
29
14
No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3
Time: 90 minutesTime: 90 minutesTime: 90 minutesTime: 90 minutesTime: 90 minutes Negative mark: 1Negative mark: 1Negative mark: 1Negative mark: 1Negative mark: 1
3. In the figure (not drawn to scale) given below, if
AD = CD = BC and BCE 96∠ = o
, how much is
the value of DBC∠ ?
A
B
C
D
E
96°
(a) 32° (b) 64°
(c) 84° (d) 24°
4. A vertical tower OP stands at the center O of a
square ABCD. Let h and b denote the height of
OP and length AB respectively. Suppose
distance from top of the tower to the vertices of
the square is equal to the length of the square,
then the relationship between h and b can be
expressed as
(a) 2b2 = h2 (b) 2h2 = b2
(c) 3b2 = 2h2 (d) 3h2 = 2b2
5. There are 8436 steel balls, each with a radius of
1 centimeter, stacked in a pile, with 1 ball on
top, 3 balls in the second layer, 6 in the third
layer, 10 in the fourth, and so on. The number of
horizontal layers in the pile is
(a) 34 (b) 38
(c) 36 (d) 32

2. Page 2 LPU Set - 3
6. In the figure below, AB is the chord of a circle
with center O. AB is extended to C such that BC
= OB. The straight line CO is produced to meet
the circle at D. If ACD∠ = y degrees and
AOD∠ = x degrees such that x = ky, then the
value of k is
A
B
CD
O
(a) 3 (b) 2
(c) 1 (d) 4
7. As shown in the figure, PQ and PR are tangents
to the circle from an external point P. If ∠QPR
= 60°, find out ∠QOR and QSR.
60°
Q
S
R
PO
(a) 130° and 65° (b) 140° and 70°
(c) 150° and 75° (d) 120° and 60°
8. The perimeter of an isosceles right-angled
triangle is 2p. Find out the area of the same
triangle.
(a) ( )+ 2
2 2 p (b) ( )− 2
2 2 p
(c) ( ) 2
3 – 2 p (d) ( )− 2
3 2 2 p
9. ABCD is a square in which P and Q are mid-
points of AD and DC respectively. The area of
∆BPQ constitutes what part of the whole area?
A B
CD
P
Q
x
x
x
2
x
2
x
2
x
2
(a) 50% (b) 37.5%
(c) 66.66% (d) 40%
10. In the square ABCD, E and F are the two points
on its diagonals. If O is the intersection point of
the two diagonals and OF = 1, OE = 2, then what
is the length of the line segment EF?
I. 3 cm
II. 1 cm
III. 5 cm
(a) I or II only (b) II or III only
(c) III only (d) I, II or III
11. Four discs of diameter 10 cm each are cut from
the bigger circular disc of radius 20 cm. Find out
the percentage of the left-out area with respect
to the total area.
(a) 75% (b) 66.66%
(c) 33.33% (d) 50%
12. The interior angles of a convex polygon form an
arithmetic progression with a common difference
of 5 degrees. If the smallest interior angle is 120º,
then the number of sides of the polygon could
be
(a) 8 (b) 9
(c) 12 (d) 16

3. Page 3LPU Set - 3
13. It is given that AB and AC are the equal sides of
an isosceles ∆ABC, in which an equilateral
∆DEF is inscribed. As shown in the figure, ∠BFD
= a and ∠ADE = b, and ∠FEC = c. Then
A
B C
D E
F
a
b
c
(a) a =
+b c
2
(b) b =
+a c
2
(c) c = 2a + 2b (d)
+
=
b c
a
3
14. In the figure, where AB is tangent to the circle
with centre O, find the ratio of the area of shaded
region to the area of unshaded region of triangle
AOB.
O
A
C
B
260°
(a)
−
π
2 3 2
(b)
−
π
3 3 2
(c)
−
π
2 3
(d) −
π
3 3
1
15. The coordinates of an equilateral triangle are as
shown in the figure below. What is the length of
the median?
A (x, y)
B
D
C
(0, 0) (4 3, 0)
(a) 4 3 (b) 4.5
(c) 6 (d) 6.5
16. In the given figure, BO and CO are the bisectors
of ∠MBC and ∠NCB respectively. Find the
value of ∠COB.
A
M N
B C
O
50°
(a) 75° (b) 65°
(c) 90° (d) 80°
17. A wheel with a rubber tyre has an outside
diameter of 25 inches. When the radius has been
decreased by a quarter of an inch, the number of
revolutions of the wheel in one mile will be
(a) increased by about 2%
(b) increased by about 30%
(c) increased by about 20%
(d) increased by about 0.2%

4. Page 4 LPU Set - 3
Directionsforquestions18and19:Answerthequestions
based on the information given below.
A cube is divided into eight equal small cubes. Each of
these small cube is further sub-divided into eight equal
smaller cubes.
18. What is the surface area of the smallest cube as a
fraction of the surface area of the original cube?
(a) 0.625 (b) 0.0625
(c) 0.0156 (d) 0.0039
19. If the original cube’s sides were painted blue,
then what is the probability that exactly two
sides of any randomly selected small cube is
painted blue?
(a)
3
8
(b)
1
16
(c)
1
4
(d)
3
4
20. Three sides of an isosceles triangle are variably
represented as (x + 1), (9 – x) and (5x – 3). How
many such triangles are possible?
(a) 0 (b) 1
(c) 2 (d) 3
21. Two vertices of a rectangle lie on the line
Y = 2x + λ and coordinate of the rest two vertices
opposite to each other are (1, 3) and
( 5, 1). Find the value of λ .
(a) 4 (b) 5
(c) –4 (d) – 3
22. A ladder rests against a wall with its lower end at
a distance x from the wall and its upper end at a
height of 2x above the floor. If the lower end
slides through a distance y away from the wall,
from its earlier position then by how much
distance does the upper end slide?
D
A
E
B Cx
2x
y
(a) − − +2 2
x 5 5x (x y)
(b) − − −2 2
x 5 5x (x y)
(c) − − +2 2
2x 5x (x y)
(d) − − −2 2
2x 5x (x y)
23. A circle of radius
R
2
is cut out of another circle
of radius R. How much paint is needed to paint
this circle (with a hole in it) if the original circle
needed 20 L for the painting?
(a) 16.66 L (b) 18 L
(c) 12 L (d) 15 L
24. The interior angle of the regular polygon
exceeds the exterior angle by 132°. The number
of sides in the polygon will be
(a) 10 (b) 16
(c) 12 (d) 15
25. The length of the circumference of a circle equals
the perimeter of a triangle of equal sides, and
also the perimeter of a square. The areas covered
by the circle, triangle, and square are c, t and s,
respectively. Then,
(a) s > t > c (b) c > t > s
(c) c > s > t (d) s > c > t

5. Page 5LPU Set - 3
26. The sum of the squares of first ten natural
numbers is
(a) 281 (b) 385
(c) 402 (d) 502
27. The largest number among the following is
(a) (2 + 2 × 2)3 (b)
3 1/ 2
[(2 2) ]+
(c) 25 (d) (2 × 2 – 2)7
28. The smallest number among the following is
(a) (7)3 (b) (8.5)3
(c) (4)4 (d) (34/5)5
29. Find the sum of the first 50 even numbers.
(a) 1275 (b) 2650
(c) 5100 (d) 2550
30. Evaluate: 112 + 114 ÷ 113 – 11 + (0.5) 112
(a) 302.5 (b) 181.5
(c) 484.0 (d) 121
31. Which one of the following is incorrect?
(a) Square root of 5184 is 72.
(b) Square root of 15625 is 125.
(c) Square root of 1444 is 38.
(d) Square root of 1296 is 34.
32. The sum of first 45 natural numbers is
(a) 2070 (b) 975
(c) 1280 (d) 1035
33. The greatest fraction among
2 3 1 7 4
, , , and
5 5 5 15 5
is
(a) 4
5
(b) 3
5
(c) 2
5
(d) 7
15
34. The lowest four-digit number which is exactly
divisible by 2, 3, 4, 5, 6 and 7 is
(a) 1400 (b) 1300
(c) 1250 (d) 1260
35. The sum of the two numbers is twice their
difference. If their product is 27, then the numbers
are
(a) 5, 15 (b) 10, 30
(c) 9, 6 (d) 9, 3
36. The largest fraction among the following is
(a)
17
21
(b)
11
14
(c)
12
15
(d)
5
6
37. If the product of three consecutive integers is
720, then their sum is
(a) 54 (b) 45
(c) 18 (d) 27
38. How many numbers between 200 and 600 are
divisible by 4, 5 and 6?
(a) 5 (b) 6
(c) 7 (d) 8
39. The number (10n – 1) is divisible by 11 for
(a) even values of n (b) odd values of n
(c) all values of n (d) n = multiples of 11
40. Solve:
3
3
1
3
1
3
3
+
+
+
(a) 1 (b) 3
(c) 43
11
(d)
63
19
41. How many numbers are there between 500 and
600 in which 9 occurs only once?
(a) 19 (b) 20
(c) 21 (d) 18
42. How many zeros are there at the end of the
product × × × × × ×33 175 180 12 44 80 66 ?
(a) 2 (b) 4
(c) 5 (d) 6

6. Page 6 LPU Set - 3
43. N = 5656
+ 56. What would be the remainder
when N is divided by 57?
(a) 0 (b) 56
(c) 55 (d) 1
44. The largest number that always divides the
product of 3 consecutive multiples of 2 is
(a) 8 (b) 16
(c) 24 (d) 48
45. The sum of two natural numbers is 85 and their
LCM is 102. Find the numbers.
(a) 51 and 34 (b) 50 and 35
(c) 60 and 25 (d) 45 and 40
46. By what smallest number, 21600 must be
multiplied or divided in order to make it a perfect
square?
(a) 6 (b) 5
(c) 8 (d) 10
47. If we write down all the natural numbers from
259 to 492 side by side we shall get a very large
natural number 259260261262 L 490491492.
How many 8’s will be used to write this large
natural number?
(a) 52 (b) 53
(c) 32 (d) 43
48. n3 + 2n for any natural number n is always a
multiple of
(a) 3 (b) 4
(c) 5 (d) 6
49. A number when divided by 238 leaves a
remainder 79. What will be the remainder when
that number is divided by 17?
(a) 8 (b) 9
(c) 10 (d) 11
50. What is the remainder when 17 23 is divided by
16?
(a) 0 (b) 1
(c) 2 (d) 3
51. 96
+ 1 when divided by 8, would leave a
remainder
(a) 0 (b) 1
(c) 2 (d) 3
52. N = 2 × 4 × 6 × 8 × 10 × L 100. How many zeros
are there at the end of N?
(a) 24 (b) 13
(c) 12 (d) 15
53. It is given that 232 + 1 is exactly divisible by a
certain number. Which one of the following is
also divisible by the same number?
(a) 296
+ 1 (b) 216
– 1
(c) 216 + 1 (d) 7 × 233
54. 461
+ 462
+ 463
+ 464
+ 465
is divisible by
(a) 3 (b) 5
(c) 11 (d) 17
55. What is the smallest perfect square that is
divisible by 8, 9 and 10?
(a) 4000 (b) 6400
(c) 3600 (d) 14641
56. In a group of 500 students, selected for admission
in a business school, 64% opted for finance and
56% for operations as specialisations. If dual
specialisation is allowed, how many have opted
for both? Each student opts for at least one of
the two specialisations.
(a) 200 (b) 100
(c) 150 (d) 125
Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59: Read the passage
given below and answer the questions.
In a locality, 30% of the residents read The Times of
India and 75% read The Hindustan Times.
3 people read neither of the papers and 6 read both.
Only The Times of India and The Hindustan Times
newspapers are available.
57. How many people are there in the locality?
(a) 60 (b) 120
(c) 126 (d) 130

7. Page 7LPU Set - 3
58. What is the percentage of people who read only
The Times of India?
(a) 15% (b) 20%
(c) 25% (d) 30%
59. What percentage of residents read only one
newspaper?
(a) 11% (b) 43%
(c) 85% (d) 20%
60. Each student in a class of 40, studies at least one
of the subjects namely English, Mathematics and
Economics. 16 study English, 22 study
Economics and 26 study Mathematics, 5 study
English and Economics, 14 study Mathematics
and Economics and 2 study English, Economics
and Mathematics. Find the number of students
who study English and Mathematics.
(a) 10 (b) 7
(c) 17 (d) 27