Binomial Theorem (Algebra, Teaching Exam)

Total Questions: 75

1. The greatest positive integer k, for which 49ᵏ +1 is a factor of the sum 49¹²⁵+49¹²⁴+.......+49²+1 is : [EMRS PGT-2023]

Correct Answer: (b) 63
Solution:

2. If three consecutive coefficients in the binomial expansion of (x+1)ⁿ in power of x are in the ratio 2:15:70, then the average of these three coefficients is : [EMRS PGT-2023]

Correct Answer: (b) 232
Solution:

3. The coefficient of x⁷ in the expansion (1+x)¹⁰+x(1+x)⁹+x²(1+x)⁸+...+x¹⁰ is: [EMRS PGT-2023]

Correct Answer: (a) 330
Solution:

4. The coefficient of xⁿ in the expansion of (1+x) (1-x)ⁿ is: [EMRS PGT-2023]

Correct Answer: (a) (-1)ⁿ (1-n)
Solution:

5. The two successive terms in the expansion of (1+x)²⁴ whose coefficients are in the ratio 1:4 are: [EMRS PGT-2023]

Correct Answer: (c) 5ᵗʰ and 6ᵗʰ
Solution:

6. Solve the following question? [Bihar (TRE 2.0)-2023]

Correct Answer: (e) None of the above
Solution:

7. The value of (99)⁵ is [Bihar (TRE 2.0)-2023]

Correct Answer: (b) 9509900499
Solution:


8. Solve the following equation? [EMRS TGT-2023]

Correct Answer: (a)
Solution:

9. Solve the following equation? [EMRS TGT-2023]

Correct Answer: (b)
Solution:

10. Solve the following equation? [KVS PGT 2023]

Correct Answer: (b) 8
Solution: