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1.

For a positive integer n, if the quadratic equation, $x(x+1)+(x+1)(x+2)+.....+(x+\overline{n-1}) (x+n)=10n$  has two consecutive integral solutions, then n is equal to


A) 12

B) 9

C) 10

D) 11



2.

The radius of a circle having minimum area, which touches the curve y=4-x2 and the line y=|x| , is


A) $2(\sqrt{2}+1)$

B) $2(\sqrt{2}-1)$

C) $4(\sqrt{2}-1)$

D) $4(\sqrt{2}+1)$



3.

The value of $(^{21}C_{1}-^{10}C_{1})+(^{21}C_{2}-^{10}C_{2})+(^{21}C_{3}-^{10}C_{3})+.....+(^{21}C_{10}-^{10}C_{10})$ is


A) $2^{21}-2^{11}$

B) $2^{21}-2^{10}$

C) $2^{20}-2^{9}$

D) $2^{20}-2^{10}$



4.

The normal to the curve y(x-2) (x-3)=x+6  at the point, where the curve intersects the Y-axis passes through the point


A) $(-\frac{1}{2},-\frac{1}{2})$

B) $(\frac{1}{2},\frac{1}{2})$

C) $(\frac{1}{2},-\frac{1}{3})$

D) $(\frac{1}{2},\frac{1}{3})$



5.

$\lim_{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2x)^{3}}$ equals


A) $\frac{1}{24}$

B) $\frac{1}{16}$

C) $\frac{1}{8}$

D) $\frac{1}{4}$



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