Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 20

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D
None of these

Solution
Question 2
4 / -1

A
2

B
0

C
1/2

D
1

Solution
Question 3
4 / -1

The sum of the last eight coefficients in the expansion of (1 + χ)^{15^is}

A
2¹⁶

B
2¹⁵

C
2¹⁴

D
None of these

Solution
Question 4
4 / -1

If ⁿC₁₂ = ⁿC₆, then ⁿC₂ is equal to

A
172

B
153

C
306

D
2556

Solution
Question 5
4 / -1

The value of

A
⁵⁶C₄

B
⁵⁶C₃

C
⁵⁵C₃

D
⁵⁵C₄

Solution
Question 6
4 / -1

A
³⁰C₁₁

B
⁶⁰C₁₀

C
³⁰C₁₀

D
⁶⁵C₅₅

Solution
Question 7
4 / -1

If a_k is the coefficient of χ^k in the expansion of (1 + χ + χ²) for k = 0,1,2,...2n then the value of

A
- a₀

B
3ⁿ

C
n . 3ⁿ⁺¹

D
n . 3ⁿ

Solution
Question 8
4 / -1

If 49ⁿ + 16n + p is divisible by 64 for all n ∈ N, then the least negative integral value of P is

A
- 2

B
- 3

C
- 4

D
- 1

Solution
Question 9
4 / -1

Statement I For each number n, (n + 1)⁷ - n⁷ - 1 is divisible by 7
Statement II For each natural number n, n⁷ - n is divisible by 7.

A
Statement I is incorrect, Statement II is correct

B
Statement I correct, Statement II is correct; Statement II is correct explanation for Statement I

C
Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I

D
Statement I is correct; Statement II is incorrect

Solution
Question 10
4 / -1

A
Aⁿ = 2^n-1 A + (n - 1)I

B
Aⁿ = nA + (n - 1)I

C
Aⁿ = 2^n-1 A - (n - 1) I

D
Aⁿ = nA - (n - 1)I

Solution