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Syllabus

^{6}, correct upto four place of decimals.Ans: 2^19-1/2 20 C 10

How?

I got only 2^19.

13. If $\alpha ,\beta and\gamma $ are the roots of the equation ${x}^{3}-x-1=0$ then, $\frac{1+\alpha}{1-\alpha}+\frac{1+\beta}{1-\beta}+\frac{1+\gamma}{1-\gamma}$ has the value equal to

(a) zero

(b) -1

(c) -7

(d) 1

Q. The term independent of x is (2x

^{1/2}– 3x^{–1/3})^{20}is :(a)

^{20}C_{12}.2^{9}.3^{12}(a)^{20}C_{12}. 2^{8}. 3^{11}(c)

^{20}C_{12}. 2^{8}. 3^{12}(d) ^{20}C_{12}. 2^{9}.3^{11}5. Let 'a' be a real number satisfying ${a}^{3}+\frac{1}{{a}^{3}}=18$. Find the value of ${a}^{4}+\frac{1}{{a}^{4}}$?

(a) 100 (b) 269 (c) 225 (d) 0

Ans: B.

Please show once.

Ans: BD.

How?

$7.Thenumber{5}^{25}-{3}^{25}isdivisibleby\phantom{\rule{0ex}{0ex}}\left(a\right)2\left(b\right)3\left(c\right)5\left(d\right)7\phantom{\rule{0ex}{0ex}}8.Ifthesumofthebinomialcoefficentintheexpansionof{\left(x+\frac{1}{x}\right)}^{n}is\phantom{\rule{0ex}{0ex}}64,thenthetermindependentofxequalto\phantom{\rule{0ex}{0ex}}\left(a\right)10\left(b\right)20\left(c\right)40\left(d\right)60\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

........

n, (x–^{n}y) is divisible by^{n}(A)

x^{2}+y^{2}^{ }(B)x^{2}–y^{2}(C)x+y(D)x–yProve.

Asap

Please help in 7th question......

Help asap!

Q. If O$\le \mathrm{r},\le \mathrm{n}$ , then the coefficient of x' in the expansion of P = 1 + (1 + x) + (1 + x)

^{2}+ ........ + (1 + x)^{n}is(a)

^{n}C_{r} (b)^{n +1}C_{r +1}(c)

^{n}C_{r}_{ +1} (d) none of theseHow to do?