Binomial Theorem, Sequences and Series

The value of 2 + 4 + 6 +…….+ 2n is
1. n(n-1)/2
2. n(n+1)/2
3. 2n(2n+1)/2
4. n(n+1)
The coefficient of x⁶ in (2 + 2x)¹⁰ is
1. 10C6
2. 2⁶
3. 10C6 2⁶
4. 10C6 2¹⁰
The coefficient of x⁸y¹² in the expansion of (2x + 3y)²⁰ is
1. 0
2. 2⁸3¹²
3. 2⁸3¹²+2¹²3⁸
4. 20C8 2⁸3¹²
If nC10 > nCr for all possible r, then a value of n is
1. 20
2. 19
3. 21
4. 10
If a is the arithmetic mean and g is the geometric mean of two numbers, then
1. a ≤ g
2. a ≥ g
3. a=g
4. a>g
If (1 + x²)² (1 + x)ⁿ = a₀ + a₁x + a₂x² +……..+ xⁿ⁺⁴ and if a₀, a₁, a₂ are in AP, then n is
1. 1
2. 2
3. 3
4. 4
If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is
1. 2
2. 1
3. 4
4. 16
1. AP
2. GP
3. HP
4. AGP
The HM of two positive numbers whose AM and GM are 16, 8 respectively is
1. 10
2. 5
3. 6
4. 4
If Sᵣ denotes the sum of r terms of an AP whose common difference is d, the value of Sᵣ−Sᵣ₋₁ + Sᵣ₋₂ is
1. 0
2. 2d
3. 4d
4. None
The remainder when 38¹⁵ is divided by 13 is
1. 12
2. 1
3. 11
4. 5
The nth term of the sequence 1, 2, 4, 7, 11,…….is
1. n³ + 3n² + 2n
2. n³ - 3n² + 2n
3. (n² - n+2)/2
4. None
1. [√(2n+1)]/2
2. [√(2n+1)−1]/2
3. √(2n+1)
4. √(2n+1)−1]
The nth term of the sequence 1/2 , 3/4 , 7/8 , 15/16 ,……….is
1. 2−2ⁿ+1
2. 2ⁿ-n-1
3. 1−2⁻ⁿ
4. 2ⁿ-1
The sum up to n terms of the series √2 + √8 + √18 + √32 +……….is
1. n(n-1) / 2
2. 2n(n+1)
3. n(n+1) / 2
4. 1
The value of the series 1/2 + 7/4 + 13/8 + 19/16 +…………. is
1. 14
2. 7
3. 4
4. 6
The sum of an infinite GP is 18. If the first term is 6, the common ratio is
1. 1/3
2. 2/3
3. 1/6
4. 3/4
The coefficient of x⁵ in the series e^-2x is
1. 2/3
2. 3/2
3. -4/15
4. 4/15
The value of 1/2! + 1/4! + 1/6! +……… is
1. (e-1)² / 2e
2. (e+1)² / 2e
3. (e-1)² / e
4. (e+1)² / e
1. log (5/3)
2. 3/2 log (5/3)
3. 5/3 log (5/3)
4. 2/3 log (5/3)

Binomial Theorem, Sequences and Series

Quiz