NUMERICAL

If the area of the region $\{(x,y):x^{2}+1\le y\le3-x\}$ is divided by the line $x=-1$ in the ratio $m : n$, where $\gcd(m,n)=1$. Then the value of $m+n$ is .

NUMERICAL

If probability distribution is given by : $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline P(x) & k & 2k^{2} & 6k^{2} & k^{2}+k & 3k & k & k & k & k & k^{2} \\ \hline \end{array} $$ then $P(3

NUMERICAL

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

NUMERICAL

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

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 a 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:

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