MCQ
For which of the following element in the determinant $\triangle=\begin{bmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{bmatrix},$ the minor and the cofactor both are zero.
- A$-5$
- ✓$2$
- C$-6$
- D$8$
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| List $I$ | List $II$ |
| $P.$ The number of polynomials $f(x)$ with non-negative integer coefficients of degree $\leq 2$, satisfying $f(0)=0$ and $\int_0^1 f(x) d x=1$, is | $1.$ $8$ |
| $Q.$ The number of points in the interval $\mid-\sqrt{13}, \sqrt{13})$ at which $f(x)=\sin \left(x^2\right)+\cos \left(x^2\right)$ attains its maximum value, is | $2.$ $2$ |
| $R.$ $\int_{-2}^2 \frac{3 x^2}{\left(1+e^x\right)} d x$ equals | $3.$ $4$ |
| $S.$ $\frac{\left(\int_{-1 / 2}^{1 / 2} \cos 2 x \log \left(\frac{1+x}{1-x}\right) d x\right)}{\left(\int_0^{1 / 2} \cos 2 x \log \left(\frac{1+x}{1-x}\right) d x\right)}$ equals | $4.$ $0$ |
Codes: $ \quad P \quad Q \quad R \quad S$