Binomial Theorem and Mathematical lnduction Test

Result

Binomial Theorem and Mathematical lnduction Test - 7

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Weekly Quiz Competition

Question 1
4 / -1

Given positive integers r > 1, n >2 and that the coefficient of (3r)th and (r + 2)th terms in the binomial expansion of (1+ x)²ⁿ are equal . Then

A
n = 2r

B
n = 2r + 1

C
n = 3r

D
none of these

Solution
Question 2
4 / -1

If 21st and 22nd terms in the expansion of (1 + χ)⁴⁴ are equal, then χ is equal to

A
8/7

B
21/22

C
7/8

D
23/24

Solution
Question 3
4 / -1

If the coefficient of χ⁸ in (aχ² + 1/bχ )¹³ is equal to the coefficient of χ^–8 in(aχ – 1/bχ² )¹³, then a and b will satisfy the relation

A
ab + 1 = 0

B
ab = 1

C
a = 1 – b

D
a+b = – 1

Solution
Question 4
4 / -1

The coefficient of χ³ in the infinite series expansion of 2/(1– χ) (2 – χ), for |χ| < 1 is

A
– (1/16)

B
15/8

C
– (1/8)

D
15/16

Solution
Question 5
4 / -1

If (a + bχ)^–3 = 1/27 + (1/3)χ + ..., the the ordered pair (a, b) equals

A
(3, – 27)

B
(1, 1/3)

C
(3, 9)

D
(3, – 9)

Solution
Question 6
4 / -1

The coefficient of three consecutive of (1 + χ)ⁿ⁺⁵ are in the ratio 5 : 10 : 14. Then, n is equal to (answer lies between 0 to 9 )

A
1

B
3

C
4

D
6

Solution
Question 7
4 / -1

A
0

B
1

C
- 2

D
3

Solution
Question 8
4 / -1

A
1/2 , 6

B
6, 1/2

C
2, 6

D
None of these

Solution
Question 9
4 / -1

If e^χ / 1 – χ = B₀ + B₁χ + B₂χ² +....+ B_nχⁿ + ..., then B_n– B_n–1 equals

A
1/n!

B
1/(n – 1)!

C
1/n! - (1/(n – 1)!)

D
1

Solution
Question 10
4 / -1

A
5

B
6

C
7

D
8

Solution