NUMERICAL

The number of real solutions of equation $x|x+4|+3|x+2|+10=0$ is equal to .

NUMERICAL

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

MCQ_SINGLE

In the binomial expansion of $(ax^{2}+bx+c)(1-2x)^{26}$, the coefficients of $x$, $x^{2}$, $x^{3}$ are 56, 0 and 0 respectively. Then the value of $(a+b+c)$ is:

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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