Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 14

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D
None of these

Solution
Question 2
4 / -1

If n is an integer with 0 ≤ n ≤ 11, then the minimum value of n!(11 - 1) ! is attained, when a value of n equals

A
11

B
5

C
7

D
9

Solution
Question 3
4 / -1

A

B

C

D
None of these

Solution
Question 4
4 / -1

A
5

B
10

C
15

D
20

Solution
Question 5
4 / -1

A

B

C

D

Solution
Question 6
4 / -1

A
4

B
8

C
16

D
32

Solution
Question 7
4 / -1

If the binomial coefficients of (3r)th and (r+2)th terms in the binomial expansion of (1 + χ )²ⁿ are equal, then

A
n = r

B
n = r + 1

C
n = 2r

D
n = 2r - 1

Solution
Question 8
4 / -1

If ⁿC₄, ⁿC₅, and ⁿC₆ are in AP, then n is

A
7 or 14

B
7

C
14

D
14 or 21

Solution
Question 9
4 / -1

¹⁵C₃ + ¹⁵C₅ + ...+¹⁵C₁₅ is equal to

A
2¹⁴

B
2¹⁴ - 15

C
2¹⁴ + 15

D
2¹⁴ - 1

Solution
Question 10
4 / -1

If C₀, C₁,...C_n denote the binomial coefficients in the expansion of (1 + χ)ⁿ. Then, the value of C₁ - 2C₂ + 3C₃ - 4C₄ + ....(up to n terms) is

A
2ⁿ

B
2^-n

C
0

D
1

Solution