NUMERICAL

If $A=\{1,2,3,4,5,6\}$ and $B=\{1,2,3,...,9\}$, then the number of strictly increasing functions $f:A\rightarrow B$ such that $f(i)\ne i$ for all $i$ is:

NUMERICAL

Chord joining at two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ on the parabola $y^{2}=12x$ intersect at right angle at the vertex, then $x_{1}x_{2}-y_{1}y_{2}=$ .

MCQ_SINGLE

If O is the vertex of the parabola $x^{2}=4y,$ Q is a point on the parabola. If C is the locus of the point which divides OQ in the ratio $2:3,$ then the equation of the chord of C which is bisected at the point (1,2) is: (Duplicate Question)

NUMERICAL

If $a_{1}=1$ and for all $n\ge1$, $a_{n+1}=\frac{1}{2}a_{n}+\frac{n^{2}-2n-1}{n^{2}(n+1)^{2}}$, then the value of $\sum_{n=1}^{\infty}(a_{n}-\frac{2}{n^{2}})$ is equal to:

NUMERICAL

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

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