MCQ
If $\sin (x+y) = log(x+y)$, then ${{dy} \over {dx}} =$
- A$2$
- B$-2$
- C$1$
- ✓$-1$
$\frac{{dy}}{{dx}} = - \frac{{\partial f/\partial x}}{{\partial f/\partial y}} $
$= - \frac{{\cos (x + y) - \frac{1}{{x + y}}}}{{\cos (x + y) - \frac{1}{{x + y}}}} = - 1$.
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$1.$ If $\mathrm{f}(-10 \sqrt{2})=2 \sqrt{2}$, then $\mathrm{f}^{\prime \prime}(-10 \sqrt{2})=$
$(A)$ $\frac{4 \sqrt{2}}{7^3 3^2}$ $(B)$ $-\frac{4 \sqrt{2}}{7^3 3^2}$ $(C)$ $\frac{4 \sqrt{2}}{7^3 3}$ $(D)$ $-\frac{4 \sqrt{2}}{7^3 3}$
$2.$ The area of the region bounded by the curves $y=f(x)$, the $x$-axis, and the lines $x=a$ and $x=b$, where $-\infty < \mathrm{a} < \mathrm{b} < -2$, is
$(A)$ $\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x+b f(b)-a f(a)$
$(B)$ $-\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x+b f(b)-a f(a)$
$(C)$ $\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x-b f(b)+a f(a)$
$(D)$ $-\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x-b f(b)+a f(a)$
$3.$ $\int_{-1}^1 g^{\prime}(x) d x=$
$(A)$ $2 g(-1)$ $(B)$ 0 $(C)$ $-2 g(1)$ $(D)$ $2 \mathrm{~g}(1)$
Give the answer question $1,2$ and $3.$
If A and B are events such that
$\text{P}(\text{A}|\text{B})=\text{P}(\text{B}|\text{A}),\ \text{then}:$$(A)$ $N ^{\top} M N$ is symmetric or skew symmetric, according as $M$ is symmetric or skew symmetric
$(B)$ $M N-N M$ is skew symmetric for all symmetric matrices $M$ and $N$
$(C)$ $M N$ is symetric for all symmetric matrices $M$ and $N$
$(D)$ $(\operatorname{adj} M)(\operatorname{adj} N)=\operatorname{adj}(M N)$ for all invertible matrices $M$ and $N$