NUMBER SYSTEM (CDS)

Total Questions: 101

81. If A, G and H are the arithmetic, geometric and harmonic means between a and b respectively, then which one of the following relations is correct? [2015 (I) Morning Shift ]

Correct Answer: (a) G is the geometric mean between A and H
Solution:Given, A, G and H are the arithmetic, geometric and harmonic means between a and b, respectively.

82. The geometric mean of three positive numbers a, b, c is 3 and the geometric mean of another three positive numbers d, e, f is 4. [2015 (I) Morning Shift ]

Also, atleast three elements in the set {a, b, c, d, e, f} are distinct. Which one of the following inequalities gives the best information about M, the arithmetic mean of the six numbers?

Correct Answer: (a) M > 2√3
Solution:

83. Out of 532 savings accounts held in a post office, 218 accounts have deposits over ₹10000 each. Further, in 302 accounts, the first or sole depositors are men, of which the deposits exceed ₹10000 in 102 accounts. In how many accounts the first or sole depositors are women and the deposits are upto ₹10000 only? [2015 (I) Morning Shift ]

Correct Answer: (b) 114
Solution:Total savings accounts = 532

84. Solve the following equation [2015 (I) Morning Shift ]

Correct Answer: (c)
Solution:

85. How many right angled triangles can be formed by joining the vertices of a cuboid? [2015 (I) Morning Shift ]

Correct Answer: (d) None of these
Solution:A cuboid has 8 vertices, 12 edges and 6 faces. By selectively choosing and 3 vertices of the cuboid, we can form 2 types of right angled triangles.

86. 7¹⁰ − 5¹⁰ is divisible by [2014 (II) Evening Shift ]

Correct Answer: (d) 11
Solution:

87. What is the number of divisors of 360? [2014 (II) Evening Shift ]

Correct Answer: (c) 24
Solution:∴ 360 = 2³ × 3² × 5
∴ Number of divisors
= (3 + 1) (2 + 1) (1 + 1)
= 4 × 3 × 2 = 24

88. The multiplication of a three-digits number XY 5 with digit Z yields X215. What is X +Y+ Z equal to ? [2014 (II) Evening Shift ]

Correct Answer: (a) 13
Solution:Given, three-digits number = XY 5

89. If N² − 33, N² − 31 and N² − 29 are prime numbers, then what is the number of possible values of N, where N is an integer ? [2014 (II) Evening Shift ]

Correct Answer: (c) 6
Solution:Let us consider the integer, N = 6

90. Consider all those two-digits positive integers less than 50, which when divided by 4 yield unity as remainder. What is their sum? [2014 (II) Evening Shift ]

Correct Answer: (a) 310
Solution:Let the two-digits numbers less than, 50 which when divided by 4 yield unity as remainder be 13, 17, ..., 49.