Class 11 Mathematics

1. The nth term of an Arithmetic Progression (A.P.) is given by:

• A. a + (n - 1)d
• B. a + nd
• C. a rⁿ⁻¹
• D. a + (n + 1)d

2. If a, b, c are in A.P., then:

• A. 2b = a + c
• B. b² = ac
• C. b = a + c
• D. a + b = c

3. The sum of first n natural numbers is equal to:

• A. n(n + 1) / 2
• B. n(n - 1) / 2
• C. n²
• D. (n + 1) / 2

4. The nth term of a Geometric Progression (G.P.) is given by:

• A. a rⁿ⁻¹
• B. a rⁿ
• C. a + (n - 1)r
• D. a rⁿ⁺¹

5. If a, b, c are in G.P., then:

• A. b² = ac
• B. 2b = a + c
• C. b = ac
• D. a² = bc

6. What is the 10th term of the G.P. 5, 25, 125, ...?

• A. 5¹⁰
• B. 5⁹
• C. 5¹¹
• D. 10⁵

7. Sum of first n terms of a G.P. when r ≠ 1 is:

• A. a(rⁿ - 1) / (r - 1)
• B. a(1 - r) / (1 - rⁿ)
• C. a rⁿ / (r - 1)
• D. n a rⁿ⁻¹

8. The Geometric Mean (G.M.) between two positive numbers a and b is:

• A. √(ab)
• B. (a + b) / 2
• C. ab / 2
• D. √(a + b)

9. The Arithmetic Mean (A.M.) between two numbers a and b is:

• A. (a + b) / 2
• B. √(ab)
• C. 2ab / (a + b)
• D. a + b

10. Relation between Arithmetic Mean (A) and Geometric Mean (G) of two distinct positive numbers is:

• A. A > G
• B. A < G
• C. A = G
• D. A G = 1

11. Find the sum of an infinite G.P. 1, 1/2, 1/4, 1/8, ... :

• A. 2
• B. 1
• C. 3/2
• D. Infinity

12. Formula for sum of an infinite G.P. when |r| < 1 is:

• A. a / (1 - r)
• B. a / (r - 1)
• C. a (1 - r)
• D. 1 / (1 - r)

13. The 7th term of the sequence defined by a = (-1)ⁿ⁻¹ n³ is:

• A. 343
• B. -343
• C. 243
• D. -243

14. Which term of the G.P. 2, 8, 32, ... is 131072?

• A. 9th term
• B. 8th term
• C. 10th term
• D. 7th term

15. If the 3rd term of a G.P. is 4, then the product of its first 5 terms is:

• A. 4⁵
• B. 4³
• C. 4⁴
• D. 1024

16. The Geometric Mean of 3 and 27 is:

• A. 9
• B. 15
• C. 81
• D. 12

17. Arithmetic Mean of two numbers is 10 and their Geometric Mean is 8. The numbers are:

• A. 16 and 4
• B. 12 and 8
• C. 18 and 2
• D. 20 and 5

18. The common ratio of the G.P. 5/2, 5/4, 5/8, ... is:

• A. 1/2
• B. 2
• C. 5/2
• D. 1/4

19. If Sₙ = n² p and Sₘ = m² p for an A.P., then Sₚ is equal to:

• A. p³
• B. p²
• C. p
• D. 0

20. The 4th term of a G.P. is 2/3 and the 7th term is 16/81. Find the first term:

• A. 9/4
• B. 4/9
• C. 2/9
• D. 3/2

21. Find the sum of the series 3 + 33 + 333 + ... to n terms:

• A. (1/3) [10(10ⁿ - 1)/9 - n]
• B. (1/3) [10ⁿ - 1]
• C. (3/9) [10ⁿ⁺¹ - 10 - n]
• D. (1/9) [10ⁿ - 1 - n]

22. What is the sum of odd integers from 1 to 2001?

• A. 1002001
• B. 1000000
• C. 2002000
• D. 1001000

23. Sum of the infinite G.P. 6, 1.2, 0.24, ... is:

• A. 7.5
• B. 7.2
• C. 8
• D. 6.5

24. If x, 2y, 3z are in A.P. and x, y, z are in G.P., then common ratio r of G.P. is:

• A. 1/3
• B. 3
• C. 1/2
• D. 2

25. Number of terms in sequence 2, 4, 8, 16, ... 1024 is:

• A. 10
• B. 9
• C. 11
• D. 8

26. Insert 2 geometric means between 3 and 81:

• A. 9, 27
• B. 6, 18
• C. 12, 36
• D. 9, 18

27. If -2/7, x, -7/2 are in G.P., then x is equal to:

• A. ±1
• B. 1
• C. -1
• D. 0

28. Sum of first n terms of a G.P. with a = 1, r = 2 is:

• A. 2ⁿ - 1
• B. 2ⁿ⁺¹ - 1
• C. 2ⁿ
• D. 2ⁿ⁻¹

29. The value of 0.999... in fractional form using infinite G.P. is:

• A. 1
• B. 9/10
• C. 99/100
• D. 0.9

30. If A and G be A.M. and G.M. of two positive numbers, the quadratic equation having these numbers as roots is:

• A. x² - 2Ax + G² = 0
• B. x² - Ax + G = 0
• C. x² + 2Ax + G² = 0
• D. x² - 2Ax - G² = 0