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Question Bank No: 3

1. The greatest term in the expansion of $\sqrt{3} {(1 + \frac{1}{\sqrt{3}})}^{20} is$

a)		$(\begin{matrix} 20 \\ 7 \end{matrix}) \frac{1}{27}$
b)		$(\begin{matrix} 20 \\ 6 \end{matrix}) \frac{1}{81}$
c)		$\frac{1}{9} (\begin{matrix} 20 \\ 9 \end{matrix})$
d)		none of these

2. If the coefficients of ${(2 r + 4)}^{th}$ term and ${(r - 2)}^{th}$ term in the expansion of ${(1 + x)}^{18} are$ equal, then r=

a)		5
b)		6
c)		7
d)		8

3. Correct to four places of decimals, ${(0.99)}^{15} =$

a)		0.8101
b)		0.8200
c)		0.8501
d)		0.8600

4. The term independent of x in the expansion of (1+x+2 $x^{3}) {(\frac{3 x^{2}}{2} - \frac{1}{3 x})}^{9}$ is

a)		$\frac{17}{27}$
b)		$\frac{17}{54}$
c)		$\frac{19}{27}$
d)		$\frac{19}{54}$

5. $C_{r} = (\begin{matrix} 15 \\ r \end{matrix}),$ then $\sum_{r = 1}^{15} r \cdot \frac{C_{r}}{C_{r - 1}} =$

a)		80
b)		100
c)		120
d)		150

6. The greatest positive integer which divides (n + 1) (n + 2) (n + 3)----(n + r) for all n e N is

a)		r
b)		r !
c)		n + r
d)		r + 1 !

7. The inequality n ! > $2^{n - 1}$ is true

a)		for all n e N
b)		for all n > 1
c)		for all n > 2
d)		for no n e N

8. If n is a +ve integer, the $n^{3}$ + 2 n is divisible by

a)		3
b)		2
c)		6
d)		5

9. $49^{n}$ + 16n - 1 divisible by

a)		3
b)		64
c)		9
d)		29

10. If n is a positive integer, then the number of terms in the expansion of ${(x + a)}^{n}$ is

a)		n
b)		n + 1
c)		n - 1
d)		none of these

11. ${(\sqrt{3} + 1)}^{4}$ + ${(\sqrt{3} - 1)}^{4}$ is equal to

a)		rational number
b)		an irrational number
c)		negative number
d)		none of these

12. The co-efficient of $X^{4}$ in ( $\frac{X}{2}$ - $\frac{3}{x^{2}})^{10}$ is

a)		$\frac{405}{256}$
b)		$\frac{504}{259}$
c)		$\frac{450}{263}$
d)		None of these

13. Binomial co-efficient of the 4th term in the expansion of ${(x - q)}^{5}$ is

a)		5
b)		20
c)		10
d)		15

14. The terms containing $x^{3}$ in the expansion of ${(x - 2 y)}^{7}$ is

a)		3rd
b)		4th
c)		5th
d)		6th

15. The co-efficient of xn in the expansion of ${(1 + x)}^{2 n}$ and ${(1 + x)}^{2 n - 1}$ are in the ratio

a)		1 : 2
b)		1 : 3
c)		3 : 1
d)		2 : 1

16. In pascal's triangle, each row is bounded by

a)		2
b)		1
c)		-1
d)		none of these

17. If the co-efficient of rth term in the expansion of ${(1 + x)}^{20}$ = co-efficient of(r + 2)th term, then r equals

a)		12
b)		8
c)		10
d)		9

18. In the binomial expansion of ${(1 + x)}^{n}$ where n is a natural number, the co-efficient of 5th, 6th, 7th terms are in A.P., then n is equal to

a)		7 and 13
b)		7 and 14
c)		7 and 17
d)		none of these

19. If n is a +ve integer, then the binomial co-efficient equidistant from the beginning and the end in the expansion of ${(x + a)}^{n}$ are

a)		equal
b)		additive inverse of each other
c)		multiplicative inverse of each other
d)		none of these

20. Given positive integers r > 1, n > 2 and the coefficient of (3r)th and (r + 2)th terms in the expansion of ${(1 + x)}^{2 n}$ are equal, then

a)		n = 2r
b)		n = 3r
c)		n = 2r + 1
d)		none of these

21. When the number of terms in the expansion of binomial (x + a)n. Where n is a +ve integer, is even, then there is/are only

a)		one middle term
b)		two middle terms
c)		no middle term
d)		none of the above

22. In the expansion of ${(3 x + 2)}^{4}$ the coefficient of the middle term is,

a)		81
b)		54
c)		216
d)		36

23. The total number of terms in the expansion of ${(x + y)}^{100}$ + ${(x - y)}^{100}$ after simplification is

a)		50
b)		51
c)		202
d)		none of these

24. If the sum of the coefficients in the expansion of ${(a}^{2} + x^{2} - 2 ax + 1)^{51}$ vanishes, then a is equal to

a)		2
b)		-1
c)		1
d)		-2

25. The number of dissimilar terms in the expansion of ${(x + y)}^{n}$ is n + 1. Therefore number of dissimilar terms in the expansion of ${(x + y + z)}^{12}$ is

a)		13
b)		39
c)		78
d)		91