Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 24

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Weekly Quiz Competition

Question 1
4 / -1

For every natural number n,n(n+1) is always

A
Even

B
Odd

C
Multiple of 3

D
Multiple of 4
Question 2
4 / -1

For every positive integer n.2ⁿ < n! when

A
n < 4

B
n ≥ 4

C
n < 3

D
None of these

Solution
Question 3
4 / -1

For every positive integral value of n, 3ⁿ > n³ when

A
n > 2

B
n ≥ 3

C
n ≥ 4

D
n < 4

Solution
Question 4
4 / -1

For natural number n, (n!)² > nⁿ , if

A
n > 3

B
n > 4

C
n ≥ 4

D
n ≥ 3

Solution
Question 5
4 / -1

If p is a prime number, then n^p - n is divisible by p when n is a

A
Natural number greater than 1

B
Irrational number

C
Complex number

D
Odd number
Question 6
4 / -1

A
n > 1

B
n > 2

C
All n ∈ N

D
None of these
Question 7
4 / -1

The remainder left out when 8²ⁿ - (62)^{2n + 1} is divided by 9 is

A
0

B
2

C
7

D
8
Question 8
4 / -1

7⁹ + 9⁷ is divisible by

A
128

B
24

C
64

D
72

Solution
Question 9
4 / -1

The coefficients of x^r in the expansion of (1 – x)^–2 is

A
r

B
r + 1

C
r + 3

D
r – 1

Solution
Question 10
4 / -1

if |x| < 1 then the coefficient of xⁿ in the expansion of (1 + x + x² + ...)² will be

A
1

B
n

C
n + 1

D
None of these

Solution