MCQ_SINGLE

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

MCQ_SINGLE

The area enclosed by $x^{2}+4y^{2}\le4$, $y\le|x|-1$, $y\ge1-|x|$ is equal to:

NUMERICAL

Let $A=\begin{bmatrix}2&3\\3&5\end{bmatrix}$ , then $|A^{2025}-3A^{2024}-A^{2023}|$ is equal to .

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 $\int(\cos x)^{-5/2}(\sin x)^{-11/2}dx=\frac{P_{1}}{q_{1}}(\cot x)^{9/2}+\frac{P_{2}}{q_{2}}(\cot x)^{5/2}+\frac{P_{3}}{q_{3}}(\cot x)^{1/2}-\frac{P_{4}}{q_{4}}(\cot x)^{-3/2}+C$, then $\frac{15P_{1}P_{2}P_{3}P_{4}}{q_{1}q_{2}q_{3}q_{4}}$ is equal to :

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