NUMBER SYSTEM (CDS)

Total Questions: 101

1. Simplify the question [2019 (II) Evening Shift ]

Correct Answer: (a) 5
Solution:



2. Consider the following statements [2019 (II) Evening Shift ]

1. Unit digit in 17¹⁷⁴ is 7.
2. Difference of the squares of any two odd numbers is always divisible by 8.
3. Adding 1 to the product of two consecutive odd numbers makes it a perfect square.

Which of the above statements are correct?

Correct Answer: (c) Only 2 and 3
Solution:


3. When N is divided by 17, the quotient is equal to 182. The difference between the quotient and the remainder is 175. What is the value of N? [2019 (II) Evening Shift ]

Correct Answer: (c) 3101
Solution:Let the remainder be x.
According to the question,
182 - x = 175
⇒ x = 7
∴ Number = Divisor × Quotient + Remainder
= 17 × 182 +  7
= 3094 + 7 = 3101

4. Consider the following statements : [2019 (II) Evening Shift ]

1. If p is relatively prime to each of q and r, then p is relatively prime to the product qr.
2. If p divides the product qr and if p divides q, then p must divide r.

Which of the above statements is/are correct?

Correct Answer: (a) Only 1
Solution:

5. Let x be the smallest positive integer such that when 14 divides x, the remainder is 7; and when 15 divides x, the remainder is 5. Which one of the following is correct? [2019 (II) Evening Shift ]

Correct Answer: (b) 30 < x < 40
Solution:Dividend

6. Consider the following statements : [2019 (II) Evening Shift ]

Correct Answer: (d) 2 and 4
Solution:

7. What is the digit in the unit’s place of the number represented by 3⁹⁸ - 3⁸⁹ ? [2019 (II) Evening Shift ]

Correct Answer: (b) 6
Solution:


8. Which one of the following is not correct ? [2019 (II) Evening Shift ]

Correct Answer: (c) If p × q is even, then p and q are always even
Solution:If p × q is even, then p and q can or cannot be even,

9. What is the remainder when (17²⁹ + 10²⁹) is divided by 18 ? [2019 (I) Morning Shift ]

Correct Answer: (d) 0
Solution:


10. How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd? [2019 (I) Morning Shift ]

Correct Answer: (a) 5
Solution:Divisible rule of 9
Sum of digit of the numbers is divisible by 9.
The number = 479865AB
Sum of the digit = 4 + 7 + 9 + 8 + 6 + 5 + A + B = 39 + A + B
Pairs (A, B) also the number is odd. 45 and 54 are two numbers divisible by 9.
Pairs [(1, 5), (5, 1), (3, 3), (6, 9), (8, 7)]
Option (a) is correct.