MCQ_SINGLE

If a line $ax+y=1$ does not intersect the hyperbola $x^{2}-9y^{2}=9$, then possible value of $a$ is :

MCQ_SINGLE

Coefficient of $x^{48}$ in $1.(1+x)+2.(1+x)^{2}+3.(1+x)^{3}+...+100(1+x)^{100}$ is :

NUMERICAL

If $x^{2}+x+1=0$ then evaluate $(x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4}$

MCQ_SINGLE

The locus of the point of intersection of tangents drawn to the circle $(x-2)^{2}+(y-3)^{2}=16$ which subtends an angle of $120^{\circ}$ is:

MCQ_SINGLE

If $y=y(x)$ and $(1+x^{2})dy+(1-\tan^{-1}x)dx=0$ and $y(0)=1$ then $y(1)$ is equal to:

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