Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 29

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Weekly Quiz Competition

Question 1
4 / -1

In the polynomial (x – 1) (x – 2) (x – 3) ... (x – 100), the coefficient of x⁹⁹ is

A
5050

B
–5050

C
100

D
99

Solution
Question 2
4 / -1

The coefficient of (2r + 4)^th and (r – 2)^th terms in the expansion of (1 + x)¹⁸ are equal, then r =

A
12

B
10

C
8

D
6

Solution
Question 3
4 / -1

Middle term in the expansion of (1 + 3x + 3x² + x³)⁶ is

A
4^th

B
3^rd

C
10^th

D
None of these

Solution
Question 4
4 / -1

The term independent of y in the expansion of (y^–1/6 – y^1/3)⁹ is

A
84

B
8.4

C
0.84

D
–84

Solution
Question 5
4 / -1

The sum of the coefficients in the expansion of (1 + x – 3x²)²¹⁶³ will be

A
0

B
1

C
–1

D
2²¹⁶³

Solution
Question 6
4 / -1

The sum of the coefficients in the expansion of (x + y)ⁿ is 4096. The greatest coefficient in the expansion is

A
1024

B
924

C
824

D
724

Solution
Question 7
4 / -1

For every natural number n,3²ⁿ⁺² – 8n – 9 is divisible by

A
16

B
128

C
256

D
None of these

Solution
Question 8
4 / -1

The least remainder when 17³⁰ is divided by 5 is

A
1

B
2

C
3

D
4

Solution
Question 9
4 / -1

The value of the natural numbers n such that the inequal 2ⁿ > 2n + 1 is valid is

A
For n ≥ 3

B
For n < 3

C
For mn

D
For any n
Question 10
4 / -1

The sum of the coefficients in the expansion of (5χ - 4y)ⁿ , where n is a positive integer is

A
0

B
n

C
1

D
- 1

Solution