Number System (Part-5)​​​

1. What is the remainder when 4⁹⁹⁹ is divided by 7? [Matriculation Level 27/06/2023 (Shift-2)]

(a) 2
(b) 4
(c) 1
(d) 3

Correct Answer: (c) 1

Solution:

2. Which of the following numbers is divisible by 120? [Matriculation Level 28/06/2023 (Shift-4)]

(a) 170280
(b) 140240
(c) 156200
(d) 170360

Correct Answer: (a) 170280

Solution:

3. How many whole numbers lie between 11² and 12²? [SSC CHSL Tier II (26/06/2023)]

(a) 23
(b) 24
(c) 21
(d) 22

Correct Answer: (d) 22

Solution:

4. A number is divisible by 3 only when: [SSC CHSL Tier II (26/06/2023)]

(a) the difference of the sum of the odd and the even digits is divisible by 3
(b) the sum of its digits is divisible by 3
(c) the last digit is either 0 or an even number
(d) the last two digits are divisible by 3

Correct Answer: (b) the sum of its digits is divisible by 3

Solution:Divisibility of 3 :- sum of digits sould always be divisible by 3.

5. What is the smallest three digit number which when divided by 2, 3 and 4 leaves remainder 1 in each case? [SSC MTS 19/05/2023 (Evening)]

(a) 111
(b) 105
(c) 101
(d) 109

Correct Answer: (d) 109

Solution:

6. Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3 ? [SSC MTS 13/06/2023 (Morning)]

(a) 102
(b) 105
(c) 103
(d) 108

Correct Answer: (c) 103

Solution:In this type of question go through option (c) get satisfied (103 + 5) = 108, is divisble by 2 and 3

7. What is the value of the expression 1-2+3-4+5-6...... to 100 terms? [SSC CHSL 09/03/2023 (2nd Shift)]

(a) -50
(b) -55
(c) -49
(d) -60

Correct Answer: (a) -50

Solution:

1 - 2 + 3 - 4 + 5 - 6 .... to 100 terms
⇒ (1 - 2) = -1, (3 - 4) = -1 and so no
Total terms = 50
Therefore, 1 - 2 + 3 - 4 + 5 - 6 .... to 100
= 50 × - 1 = - 50

8. What is the sum of the first 200 terms of the given series? [SSC CHSL 10/03/2023 (1st Shift)]

1+5+6+10+11+15+16+20+........

(a) 49400
(b) 49600
(c) 50100
(d) 48300

Correct Answer: (c) 50100

Solution:Series = 1 + 5 + 6 + 10 + 11 + 15 + 16 + 20 + ........ = (1 + 6 + 11 + 16 + ...... ) + (5 + 10 + 15 + ...)
S₂₀₀ = 100/2 [2 + (99) × 5] + 100/2 [10 + (99) × 5] = 50[497 + 50 [505] = 50 × 1002 = 50100

9. How many prime numbers are there between 20 and 50? [SSC CHSL 10/03/2023 (2nd Shift)]

(a) 8
(b) 5
(c) 6
(d) 7

Correct Answer: (d) 7

Solution:Prime numbers between 20 and 50 = (23, 29, 31, 37, 41, 43, 47) = 7 prime numbers

10. The sum of three consecutive even numbers is 126. What is the product of the smallest and the largest numbers? [SSC CHSL 10/03/2023 (3rd Shift)]

(a) 1840
(b) 1950
(c) 1760
(d) 1620

Correct Answer: (c) 1760

Solution:

Number System (Part-5)​​​

1. What is the remainder when 4⁹⁹⁹ is divided by 7? [Matriculation Level 27/06/2023 (Shift-2)]

2. Which of the following numbers is divisible by 120? [Matriculation Level 28/06/2023 (Shift-4)]

3. How many whole numbers lie between 11² and 12²? [SSC CHSL Tier II (26/06/2023)]

4. A number is divisible by 3 only when: [SSC CHSL Tier II (26/06/2023)]

5. What is the smallest three digit number which when divided by 2, 3 and 4 leaves remainder 1 in each case? [SSC MTS 19/05/2023 (Evening)]

6. Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3 ? [SSC MTS 13/06/2023 (Morning)]

7. What is the value of the expression 1-2+3-4+5-6...... to 100 terms? [SSC CHSL 09/03/2023 (2nd Shift)]

8. What is the sum of the first 200 terms of the given series? [SSC CHSL 10/03/2023 (1st Shift)]

9. How many prime numbers are there between 20 and 50? [SSC CHSL 10/03/2023 (2nd Shift)]

10. The sum of three consecutive even numbers is 126. What is the product of the smallest and the largest numbers? [SSC CHSL 10/03/2023 (3rd Shift)]

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Number System (Part-5)