Quant Questions

1

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

  1. 20 cm
  2. 25 cm
  3. 35 cm
  4. 50 cm
2

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is

  1. 8960
  2. 5120
  3. 4830
  4. 6420
3

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

  1. 2 : 1 : 3
  2. 3 : 2 : 1
  3. 1 : 2 : 3
  4. 1 : 3 : 1
4

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to

  1. 3
  2. 3.5
  3. 3
  4. 4.5
5

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

  1. 1 : 4
  2. 1 : 7
  3. 8 : 19
  4. 1 : 3
6

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

  1. 2 : 5
  2. √3 : 2
  3. 3 : 4
  4. 1 : √3
7

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

  1. 168 m2
  2. 84 m2
  3. 42 m2
  4. 22 m2
8

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

  1. 4 : 3
  2. 4 : 1
  3. 3 : 1
  4. 1 : 3
9

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

  1. 17.05
  2. 22.45
  3. 26.25
  4. 27.85
10

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

  1. 110
  2. 220
  3. 440
  4. 660
11

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

  1. 3√2
  2. 3
  3. 4
  4. √3
12

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

  1. 1300
  2. 1340
  3. 1480
  4. 1520
13

A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?

  1. 2 : 3
  2. 3 : 4
  3. 1 : 2
  4. 1 : 4
14

A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm) will be:

  1. 32 π
  2. 40.5 π
  3. 50 π
  4. 81 π
15

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer then how many such triangles exist?

  1. 5
  2. 10
  3. 15
  4. 21
16

If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10π, then the area of the sector XYZ is

  1. 10π
  2. 25π
  3. 100π
  4. None of the above
17

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

  1. 17 cm
  2. 18 cm
  3. 19 cm
  4. 20 cm
  5. 21 cm
18

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1 : d2 = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

  1. slightly less than 10 units
  2. 10 units
  3. slightly greater than 10 units
  4. slightly less than 20 units
  5. slightly greater than 20 units
19

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

  1. -5
  2. -6
  3. -7
  4. -8
20

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 - 1) is

  1. always divisible by 6, and may or may not be divisible by 12
  2. always divisible by 24
  3. never divisible by 6
  4. always divisible by 12, and may or may not be divisible by 24
21

If n is a positive integer, then (√3+1)2n - (√3−1)2n is

  1. An even positive integer
  2. A rational number other than positive integers
  3. An odd positive integer
  4. An irrational number
22

The last digit of the number 32015 is

  1. 1
  2. 3
  3. 5
  4. 7
23

When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits, we get 486. Find the number?

  1. 81
  2. 45
  3. 36
  4. 54
24

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

  1. 1
  2. 2
  3. 3
  4. 4
25

The number of integers n satisfying -–n+2 ≥ 0 and 2n ≥ 4 is

  1. 0
  2. 1
  3. 2
  4. 3
26

What is the right most non-zero digit of the number 302720?

  1. 1
  2. 3
  3. 7
  4. 9
27

The product of all integers from 1 to 100 will have the following numbers of zeros at the end?

  1. 19
  2. 20
  3. 22
  4. 24
28

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

  1. 21
  2. 25
  3. 41
  4. 67
29

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

  1. 55
  2. 57
  3. 58
  4. 59
30

What are the last two digits of 72008?

  1. 01
  2. 21
  3. 41
  4. 61
31

What is the digit in the unit’s place of 251?

  1. 1
  2. 2
  3. 4
  4. 8
32

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

  1. 5
  2. 6
  3. 7
  4. 8
33

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

  1. 16
  2. 15
  3. 14
  4. 13
34

What is the number of all possible positive integer values of n for which n2 + 96 is a perfect square?

  1. 2
  2. 4
  3. 5
  4. Infinite
35

If N = (11p + 7)(7q – 2)(5r + 1)(3s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

  1. 5
  2. 6
  3. 7
  4. 8
  5. 9
36

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

  1. 1777
  2. 1785
  3. 1875
  4. 1877
37

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

  1. 16
  2. 18
  3. 36
  4. 40
38

Largest value of min(2 + x2, 6 - 3x), when x > 0, is

  1. 1
  2. 2
  3. 3
  4. 4
39

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

  1. -180
  2. -159
  3. -110
  4. -119
40

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax2+ bx + 1 = 0 having real roots is

  1. 6
  2. 7
  3. 10
  4. 12
41

Let p and q be the roots of the quadratic equation x2 - (α - 2)x - α - 1 = 0. What is the minimum possible value of p2 + q2?

  1. 0
  2. 3
  3. 4
  4. 5
42

The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is

  1. 0
  2. 1
  3. 2
  4. 3
43

One root of x2 + kx - 8 = 0 is square of the other. Then the value of k is

  1. 2
  2. -2
  3. 8
  4. -8
44

What is the value of m which satisfies 3m2 - 21m + 30 < 0?

  1. m < 2 or m > 5; 2 < m < 5
  2. 2 < m < 5
  3. m < 2 or m > 5
  4. m > 2
45

Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all?

  1. 0 ≥ x ≥ –2
  2. 0 ≤ x ≤ 2
  3. –1 ≥ x ≥ –2
  4. 1 ≤ x ≤ 2
46

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

  1. 1
  2. 2
  3. 3
  4. 4
47

What is the sum of the following series?

- 64, - 66, - 68, …… , - 100

  1. - 1458
  2. - 1558
  3. - 1568
  4. - 1664
  5. None of the above
48

If three positive real numbers x, y and z satisfy y - x = z - y  and xyz = 4, then what is the minimum possible value of y?

  1. 2(1/4)
  2. 2(2/3)
  3. 2(1/3)
  4. 2(3/4)
49

If log3 2, log3 (2x - 5), log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to

  1. 2
  2. 3
  3. 4
  4. 5
50

Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

  1. 741
  2. 780
  3. 800
  4. 820