SOLVED PAPER 2020 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

41. The number of three digit numbers (all digits are different) which are divisible by 7 and also divisible by 7 on reversing the order of the digits, is

Correct Answer: (c) Four
Solution:Let the three digits number = xyz and the reverse of it will be = zyx

42. How many integral values of x and y satisfy the equation 5x + 9y = 7, where - 500 < x < 500 and-500<y< 500 ?

Correct Answer: (b) 111
Solution:Given equation 5x + 9y = 7,


43. Let XYZ be a 3-digit number. Let S = XYZ + YZX + ZXY Which of the following statements is/are correct ?

1. S is always divisible by 3 and (X + Y + Z)
2. S is always divisible by 9.
3. S is always divisible by 37.

Select the correct answer using the code given below:

Correct Answer: (d) 1 and 3
Solution:Given, S = XYZ + YZX + ZXY

44. In covering certain distance, the average speeds of X and Y are in the ratio 4 : 5. If X takes 45 min more than Y to reach the destination, then what is the time taken by Y to reach the destination?

Correct Answer: (c) 180 min
Solution:When the speed is same, then speed is inversely proportional to time.

45. For two observations, the sum is S and product is P. What is the harmonic mean of these two observations ?

Correct Answer: (c)
Solution:

Given that, S = x + y, P = xy

46. If the annual income of X is 20% more than that of Y, then the income of Y is less than that of X by p%. What is the value of p?

Correct Answer: (b) 16⅔
Solution:Let annual income of Y = ₹100

47. What is the least perfect square which is divisible by 3, 4, 5, 6 and 7?

Correct Answer: (c) 44100
Solution:A number which is divisible by 3, 4, 5, 6 and 7 should be a multiple of 3, 4, 5, 6 and 7.
i.e. 22 × 3 × 5 × 7
For least perfect square, then it should be a perfect square i.e.
22 × 32 × 52 × 72 = 44100

48. In a water tank there are two outlets. It takes 20 min to empty the tank if both the outlets are opened. If the first outlet is opened, the tank is emptied in 30 min. What is the time taken to empty the tank by second outlet?

Correct Answer: (d) 60 min
Solution:Let x is the time taken when both outlets are open and y is the time taken by 1st outlet then time taken by IInd outlet

49. If (x² - 1) is a factor of ax⁴ + bx³ + cx² + dx + e, then which one of the following is correct?

Correct Answer: (d) a + c + e = b + d
Solution:Given, (x² – 1) is a factor of ax⁴ + bx³ + cx² + dx + e

50. Simplify the question

Correct Answer: (c) 18
Solution: