Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 30

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

The greatest term in the expansion of (1 + 3χ)⁵⁴ , where χ = 1/3 is

A
T₂₈

B
T₂₅

C
T₂₆

D
T₂₄

Solution
Question 2
4 / -1

The expression ⁿC₀ + 2ⁿC₁ + 3ⁿC₂ + (n + 1)ⁿC_n is equal to

A
(n + 1)2ⁿ

B
2ⁿ(n + 2)

C
(n + 2)2^n-1

D
(n + 2)2ⁿ⁺¹

Solution
Question 3
4 / -1

The sum of series ²⁰C₀ – ²⁰C₁ + ²⁰C₂ – ²⁰C₃ + ...+²⁰C₁₀ is

A
^–20C₁₀

B
(1/2) ²⁰C₁₀

C
0

D
²⁰C₁₀

Solution
Question 4
4 / -1

If the coefficient of rth, (r + 1)th and (r + 2)th term in the binomial expansion of (1 + y)^m are in AP, then m and r satisfy the equation

A
m² – m(4r – 1) + 4r² + 2 = 0

B
m² - m(4r–1) + 4r² – 2 = 0

C
m²– m(4r + 1) + 4r² + 2 = 0

D
m² – n(4r – 1) + 4r²– 2 = 0

Solution
Question 5
4 / -1

The sum of the last ten co-efficients in the expansion of (1 + x)¹⁹ when expanded in ascending powers of x is

A

B

C

D

Solution
Question 6
4 / -1

A

B

C

D

Solution
Question 7
4 / -1

A
1260

B
126

C
630

D
210

Solution
Question 8
4 / -1

A
249

B
501

C
251

D
250

Solution
Question 9
4 / -1

A
56

B
57

C
30

D
59

Solution
Question 10
4 / -1

A

B

C

D
none of these

Solution