Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 45

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

If for positive integers r > 1, n > 2 the coefficient of the (3r)^th and (r + 2)^th powers of x in the expansion of (1 + x)²ⁿ are equal , then

A
n = 2r

B
n = 3r

C
n = 2r + 1

D
None of these

Solution
Question 2
4 / -1

If the coefficient of the second, third and fourth terms in the expansion of (1 + x)ⁿ are in A.P., then n is equal to

A
7

B
2

C
6

D
None of these

Solution
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

A

B

C

D
None of these

Solution
Question 5
4 / -1

A
1

B
2

C
3

D
4

Solution
Question 6
4 / -1

Let S(k) = 1 + 3 + 5 + ...+ (2k - 1) = 3 + k². Then which of the following is true.

A
Principle of mathematical induction can be used to prove the formula

B
S(k) ⇒ S(k + 1)

C
S(k) ⇏ S(k + 1)

D
S(1) is correct

Solution
Question 7
4 / -1

A
1/256

B
1/562

C
1/265

D
-1/256

Solution
Question 8
4 / -1

A
2

B
1

C
3

D
5
Question 9
4 / -1

A
18

B
16

C
12

D
-10
Question 10
4 / -1

If the coefficients of r^th term and (r + 4)^th th term are equal in the expansion of (1 + x)²⁰, then the value of r will be

A
7

B
8

C
9

D
10