SOLVED PAPER 2021 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

81. Consider the production of each company separately. In how many instances was the percentage increase in production of cars over the previous year's production greater than 20% ?

Correct Answer: (a) 5
Solution:

82. In which year was the percentage increase in production of cars minimum as compared to its previous year?

Correct Answer: (d) 2018
Solution:

We can see that the percentage increase in production of cars is minimum in 2018 as compared to its previous year.

83. In one of the years the percentage increase in production of cars was minimum as compared to its previous year. What was the minimum percentage ?

Correct Answer: (a)
Solution:

84. (Questions 84 and 85) Consider the following for the next two questions that follow.

Collect all the sequences of five consecutive integers such that their product is equal to one of these integers. Let X be the collection of all possible such sequences. Let P be the smallest integer and Q be the largest integer occuring in these sequences.

How many such sequences of five consecutive integers are possible ?

Correct Answer: (d) Five
Solution:


85. What is the arithmetic mean of P and Q ?

Correct Answer: (d) Cannot be determined due to insufficient data
Solution:



86. If one of the roots of the equation ax² - 4ax + 15 = 0 is (³⁄₂) then what is the sum of the squares of the roots?

Correct Answer: (b)
Solution:




87. A two-digit number is such that the product of the digits is 8. If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number?

Correct Answer: (d) 9
Solution:Let the digits at units and tens place of the given number be x and y respectively.

Thus, the number is 10y + x.
The product of the digits is 8.
∴ xy = 8 … (i)

After interchanging the digits, the number becomes 10x + y.
If 63 is added to the number, the digits interchange their places.

Thus,
(10y + x) + 63 = 10x + y
⇒ 10x + y - 10y - x = 63
⇒ 9x - 9y = 63
⇒ x - y = 7 … (ii)

From Eq. (ii), put y = x - 7 into Eq. (i), we get
x(x - 7) = 8
⇒ x² - 7x - 8 = 0
⇒ x² - 8x + x - 8 = 0
⇒  x(x - 8) + 1(x - 8) = 0
⇒  (x - 8) (x + 1) = 0 ⇒ x = 8 or -1

From Equation (ii),
when x = 8
⇒ y = 8 - 7 = 1
When x = - 1
⇒ y = - 1 - 7 = - 8

We get (x, y) = (8, 1) and (x, y) = (- 1, - 8) Since, the digits of the number can't be negative.
So, we must remove second pair. Therefore, the number is 10 × 1 + 8 = 18 Hence, sum of the digits in the number is 1 + 8 = 9.

88. A motor boat has speed 30 km/h in still water. It goes 60 km down stream and comes back in (⁹⁄₂)h. What is the speed of the stream?

Correct Answer: (c) 10 km/h
Solution:



89. The present age of a father is equal to sum of the ages of his 4 children. After ten years the sum of the ages of the children will be 1.6 times the age of their father. What is the present age of father?

Correct Answer: (b) 40 year
Solution:


90. The sum of nummerator and denominator of a fraction is 10. If the numerator is increased by 3 and denominator is decreased by 1, the fraction becomes 1. What is the difference between numerator and denominator of the fraction?

Correct Answer: (c) 4
Solution: