Find the nth term of the following sequence: 2 + 22 + 222 + ……….. Tn

\(\frac{2}{9}\left( {{{10}^n} - 1} \right)\)

\({\left( {\frac{2}{9}} \right)^n}\left( {{{10}^n} - 1} \right)\)

Number system SSC MCQ Questions With Answers Quiz

30.

What is the sum of the given series: \(2\left( {1 - \frac{1}{{n + 1}}} \right) + 2\left( {1 - \frac{2}{{n + 1}}} \right) + 2\left( {1 - \frac{3}{{n + 1}}} \right) + \ldots 2\left( {1 - \frac{n}{{n + 1}}} \right)\)

n

\(\frac{1}{2}n\)

(n + 1)

\(\frac{1}{2}\left( {n + 1} \right)\)

1.

Find the sum of the following: \(\frac{1}{{10}} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}}\)

2.

What largest number of four digits is exactly divisible by 89?

3.

Which one of the numbers is divisible by 15?

4.

What will be largest number which divides 37, 59 and 74 leaving remainder 2, 3 and 4 respectively?

5.

Ram distributes his pens among 5 people A, B, C, D and E in the ratio 1/2 : 1/3 : 1/4 : 1/5 : 1/6, then what will be the minimum number of pens Ram has?

6.

[13 + 23 + 33 + ……. + 93 + 103] is equal to

7.

How many of the following numbers are divisible by 31? 186, 226, 832, 656, 1264, 527

8.

The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is

9.

\({\rm{S}} = \frac{1}{{1 \times 3 \times 5}} + \frac{1}{{1 \times 4}} + \frac{1}{{3 \times 5 \times 7}} + \frac{1}{{4 \times 7}} + \frac{1}{{5 \times 7 \times 9}} + \frac{1}{{7 \times 10}} + \ldots \) upto 20 terms. Find the value of S.

10.

Which of the following statement (s) is/are true? I. 2 is a prime number II. 4 is a composite number.

11.

The number of times 2 is used while writing the numbers from 1 to 100 is:

12.

Sukhiram plants 12544 mango trees in his garden and arranges them so that there are as many rows as there are mango trees in each row. Find the number of rows.

13.

What is the value of 21 + 24 + 27 + ...... + 51?

14.

When n is divided by 4, the remainder is 3. The remainder when 2n is divided by 4 is:

15.

What is the value of \(\frac{1}{{3\; \times \;7}} + \frac{1}{{7\; \times \;11}} + \frac{1}{{11\; \times \;15}} + \ldots + \frac{1}{{899\; \times \;903}}\) ?

16.

Find the nth term of the following sequence: 2 + 22 + 222 + ……….. Tn

17.

If (1 + 1/2)(1 + 1/4)(1 + 1/6)(1 + 1/8)(1 - 1/3)(1 - 1/5)(1 - 1/7) = 1 + 1/x , then what is value of x?

18.

If the product of two numbers is 192 and the HCF is 8, then the ratio of HCF and LCM is

19.

Three men step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is

20.

The HCF of three numbers is 9. If they are in the ratio 1 :3 : 5, then the numbers are

21.

If A = 232, B = 231 + 230 + 229 + … + 20 and C = 315 + 314 + 313 + … + 30, then which of the following option is TRUE?

22.

How many times 4 is written in numbers from 1 to 60?

23.

A, B, C start running at the same time and at the same point in the same direction in a circular stadium. A completes a round in 252 s, B in 300 s and C in 198 s. After what time will they meet again at the starting point?

24.

The sum of two numbers is 20 and their product is 80. What will be the sum of their reciprocals?

25.

If the L.C.M. and H.C.F. of two expressions are (x2 + 6x + 8) (x + 1) and (x + 1) respectively and one of the expressions is x2 + 3x+ 2, find the other.

26.

The largest two digit prime number is ________.

27.

If 13 + 23 + 33 +…... + 103 = 3025, then find the value of 23 + 43 + 63 + ….. + 203

28.

Consider those numbers between 100 and 1000 such that when each number is divided by 6, 7 and 11 it leaves 5 as remainder in each case. What is the sum of the numbers?

29.

The product of two positive fractions is 21/40 and their quotient is 56/15. The greater fraction is?

30.

What is the sum of the given series: \(2\left( {1 - \frac{1}{{n + 1}}} \right) + 2\left( {1 - \frac{2}{{n + 1}}} \right) + 2\left( {1 - \frac{3}{{n + 1}}} \right) + \ldots 2\left( {1 - \frac{n}{{n + 1}}} \right)\)

Time

1. Find the sum of the following: \(\frac{1}{{10}} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}}\)

2. What largest number of four digits is exactly divisible by 89?

3. Which one of the numbers is divisible by 15?

4. What will be largest number which divides 37, 59 and 74 leaving remainder 2, 3 and 4 respectively?

5. Ram distributes his pens among 5 people A, B, C, D and E in the ratio 1/2 : 1/3 : 1/4 : 1/5 : 1/6, then what will be the minimum number of pens Ram has?

6. [13 + 23 + 33 + ……. + 93 + 103] is equal to

7. How many of the following numbers are divisible by 31? 186, 226, 832, 656, 1264, 527

8. The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is

9. \({\rm{S}} = \frac{1}{{1 \times 3 \times 5}} + \frac{1}{{1 \times 4}} + \frac{1}{{3 \times 5 \times 7}} + \frac{1}{{4 \times 7}} + \frac{1}{{5 \times 7 \times 9}} + \frac{1}{{7 \times 10}} + \ldots \) upto 20 terms. Find the value of S.

10. Which of the following statement (s) is/are true? I. 2 is a prime number II. 4 is a composite number.

11. The number of times 2 is used while writing the numbers from 1 to 100 is:

12. Sukhiram plants 12544 mango trees in his garden and arranges them so that there are as many rows as there are mango trees in each row. Find the number of rows.

13. What is the value of 21 + 24 + 27 + ...... + 51?

14. When n is divided by 4, the remainder is 3. The remainder when 2n is divided by 4 is:

15. What is the value of \(\frac{1}{{3\; \times \;7}} + \frac{1}{{7\; \times \;11}} + \frac{1}{{11\; \times \;15}} + \ldots + \frac{1}{{899\; \times \;903}}\) ?

16. Find the nth term of the following sequence: 2 + 22 + 222 + ……….. Tn

17. If (1 + 1/2)(1 + 1/4)(1 + 1/6)(1 + 1/8)(1 - 1/3)(1 - 1/5)(1 - 1/7) = 1 + 1/x , then what is value of x?

18. If the product of two numbers is 192 and the HCF is 8, then the ratio of HCF and LCM is

19. Three men step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is

20. The HCF of three numbers is 9. If they are in the ratio 1 :3 : 5, then the numbers are

21. If A = 232, B = 231 + 230 + 229 + … + 20 and C = 315 + 314 + 313 + … + 30, then which of the following option is TRUE?

22. How many times 4 is written in numbers from 1 to 60?

23. A, B, C start running at the same time and at the same point in the same direction in a circular stadium. A completes a round in 252 s, B in 300 s and C in 198 s. After what time will they meet again at the starting point?

24. The sum of two numbers is 20 and their product is 80. What will be the sum of their reciprocals?

25. If the L.C.M. and H.C.F. of two expressions are (x2 + 6x + 8) (x + 1) and (x + 1) respectively and one of the expressions is x2 + 3x+ 2, find the other.

26. The largest two digit prime number is ________.

27. If 13 + 23 + 33 +…... + 103 = 3025, then find the value of 23 + 43 + 63 + ….. + 203

28. Consider those numbers between 100 and 1000 such that when each number is divided by 6, 7 and 11 it leaves 5 as remainder in each case. What is the sum of the numbers?

29. The product of two positive fractions is 21/40 and their quotient is 56/15. The greater fraction is?

30. What is the sum of the given series: \(2\left( {1 - \frac{1}{{n + 1}}} \right) + 2\left( {1 - \frac{2}{{n + 1}}} \right) + 2\left( {1 - \frac{3}{{n + 1}}} \right) + \ldots 2\left( {1 - \frac{n}{{n + 1}}} \right)\)

Time

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1.

Find the sum of the following: \(\frac{1}{{10}} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}}\)

2.

What largest number of four digits is exactly divisible by 89?

3.

Which one of the numbers is divisible by 15?

4.

What will be largest number which divides 37, 59 and 74 leaving remainder 2, 3 and 4 respectively?

5.

Ram distributes his pens among 5 people A, B, C, D and E in the ratio 1/2 : 1/3 : 1/4 : 1/5 : 1/6, then what will be the minimum number of pens Ram has?

6.

[13 + 23 + 33 + ……. + 93 + 103] is equal to

7.

How many of the following numbers are divisible by 31? 186, 226, 832, 656, 1264, 527

8.

The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is

9.

\({\rm{S}} = \frac{1}{{1 \times 3 \times 5}} + \frac{1}{{1 \times 4}} + \frac{1}{{3 \times 5 \times 7}} + \frac{1}{{4 \times 7}} + \frac{1}{{5 \times 7 \times 9}} + \frac{1}{{7 \times 10}} + \ldots \) upto 20 terms. Find the value of S.

10.

Which of the following statement (s) is/are true? I. 2 is a prime number II. 4 is a composite number.

11.

The number of times 2 is used while writing the numbers from 1 to 100 is:

12.

Sukhiram plants 12544 mango trees in his garden and arranges them so that there are as many rows as there are mango trees in each row. Find the number of rows.

13.

What is the value of 21 + 24 + 27 + ...... + 51?

14.

When n is divided by 4, the remainder is 3. The remainder when 2n is divided by 4 is:

15.

What is the value of \(\frac{1}{{3\; \times \;7}} + \frac{1}{{7\; \times \;11}} + \frac{1}{{11\; \times \;15}} + \ldots + \frac{1}{{899\; \times \;903}}\) ?

16.

Find the nth term of the following sequence: 2 + 22 + 222 + ……….. Tn

17.

If (1 + 1/2)(1 + 1/4)(1 + 1/6)(1 + 1/8)(1 - 1/3)(1 - 1/5)(1 - 1/7) = 1 + 1/x , then what is value of x?

18.

If the product of two numbers is 192 and the HCF is 8, then the ratio of HCF and LCM is

19.

Three men step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is

20.

The HCF of three numbers is 9. If they are in the ratio 1 :3 : 5, then the numbers are

21.

If A = 232, B = 231 + 230 + 229 + … + 20 and C = 315 + 314 + 313 + … + 30, then which of the following option is TRUE?

22.

How many times 4 is written in numbers from 1 to 60?

23.

A, B, C start running at the same time and at the same point in the same direction in a circular stadium. A completes a round in 252 s, B in 300 s and C in 198 s. After what time will they meet again at the starting point?

24.

The sum of two numbers is 20 and their product is 80. What will be the sum of their reciprocals?

25.

If the L.C.M. and H.C.F. of two expressions are (x2 + 6x + 8) (x + 1) and (x + 1) respectively and one of the expressions is x2 + 3x+ 2, find the other.

26.

The largest two digit prime number is ________.

27.

If 13 + 23 + 33 +…... + 103 = 3025, then find the value of 23 + 43 + 63 + ….. + 203

28.

Consider those numbers between 100 and 1000 such that when each number is divided by 6, 7 and 11 it leaves 5 as remainder in each case. What is the sum of the numbers?

29.

The product of two positive fractions is 21/40 and their quotient is 56/15. The greater fraction is?

30.

What is the sum of the given series: \(2\left( {1 - \frac{1}{{n + 1}}} \right) + 2\left( {1 - \frac{2}{{n + 1}}} \right) + 2\left( {1 - \frac{3}{{n + 1}}} \right) + \ldots 2\left( {1 - \frac{n}{{n + 1}}} \right)\)