## Binomial Theorem Questions and Answers Part-7

1. Coeffient of $x^{8}$ in the expansion of $\left(1+2x-x^{3}\right)^{6}$   is
a) 528
b) -428
c) 238
d) -238

Explanation:

2. If the 3rd term in the expansion of $\left(\frac{1}{x}+x^{\log_{2}x}\right)^{5}$     is 40 then x equals
a) $1/\sqrt{2},2$
b) $\sqrt{2},4$
c) $1/\sqrt{2},4$
d) $\sqrt{2},1/\sqrt{2}$

Explanation:

3. If the term independent of x in the expansion of $\left(\sqrt{x}-\frac{k}{x^{2}}\right)^{10}$    is 405, then k equals
a) 2,-2
b) 3,-3
c) 4,-4
d) 1,-1

Explanation:

4. If the third term in the expansion $\left(x+x^{\log_{5} x}\right)^{5}$     is 2, then x equals
a) 1/5,5
b) $1/5,1/\sqrt{5}$
c) $\sqrt{5},5$
d) $1/\sqrt{5},5$

Explanation:

5. If the fifth term in the expansion $\left(x^{1/3}+\frac{1}{x}\right)^{n}$     does not depend upon x, then $^{n}C_{2}+^{n}C_{14}$   equals
a) 240
b) 480
c) 360
d) 120

Explanation:

6. If the coefficients of three consecutive terms of $\left(1+x\right)^{n+5}$    are in the ratio 5:10:14, then n is equal to
a) 5
b) 6
c) 7
d) 8

Explanation:

7. Cofficients of the terms independent of x in the expansion of $\left(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\right)^{10}$
is
a) 105
b) 210
c) 310
d) 180

Explanation:

8. Value(s) of x for which the fourth term in the expansion of $\left(\sqrt{x}^{1/\left(\log_{2}x+1\right)}+x^{1/12}\right)^{6}$
is 40 is (are)
a) 1/8
b) 2
c) 1/16,2
d) 1/8,4

Explanation:

9. If $n\epsilon N$, n ≥ 3, then value of $S=\left(1\right)n-\frac{1}{1!}\left(n-1\right)^{2}+\frac{1}{2!}\left(n-1\right)\left(n-2\right)^{2}-\frac{1}{3!}\left(n-1\right)\left(n-2\right)\left(n-3\right)^{2}+....$                 upto n terms is
a) 1
b) $\left(-1\right)^{n}$
c) -1
d) 0

10. If $x^{2r}$ occurs in $\left(x+\frac{2}{x^{2}}\right)^{n}$   , then n – 2r must be of the form
d) $4k\pm1$