Binomial Theorem (Algebra, Teaching Exam)

Total Questions: 75

61. Sum of all the coefficients of expansion (x+1)ⁿ is: [PGT 2002]

Correct Answer: (d) 2ⁿ
Solution:

62. The number of permutations of n distinct things taken r together, in which 3 particular things must occur, is: [PGT 2002]

Correct Answer: (b) ⁿ⁻³Pᵣ₋₃
Solution:

The number of permutations of n distinct things taken r together, in which 3 particular things must occur is = ⁿ⁻³Pᵣ₋₃

63. Number of terms in the expansion of (a+b+c)²⁵ is [Rajasthan TGT 2016, 2013, UP PGT 2019,16]

Correct Answer: (a) 351
Solution:

64. In the expansion of (1+px)ⁿ,n,p ∈ N the coefficients of x and x² are 8 and 24 respectively, then [Rajasthan TGT 2015]

Correct Answer: (b) n =4,p = 2
Solution:


65. The middle term in the expansion of (x+a)²ⁿ; is [Rajasthan TGT 2015]

Correct Answer: (d)
Solution:

66. The binomial expansion of (1+x)⁻¹ is valid only when [(GIC) 2015]

Correct Answer: (c) -1<x <1
Solution:

Binomial expansion of (1+x)⁻¹ is valid only when -1<x<1

67. Solve the following equation? [Rajasthan TGT 2013]


Correct Answer: (c)
Solution:

68. In the expansion of (x+a)ⁿ, P is the sum of odd terms and Q is even the sum of the terms. Then what is the value of (x+a)²ⁿ-(x-a)²ⁿ. [TGT 2013]

Correct Answer: (d) 4PQ
Solution:



69. Solve the following equtaion? [TGT 2011]

Correct Answer: (a)
Solution:

70. Solve the following equation? [TGT 2010]

Correct Answer: (b) -252
Solution: