$$ \text { Match the following : } $$
| (i) | $$ \int_0^{\pi / 2}(\sin x)^{\cos x}\left(\cos x \cot x-\log \left(\sin ^x\right)^{\sin } x\right) \mathrm{d} x $$ |
(A) | 1 |
|---|---|---|---|
| (ii) | $$ \text { Area bounded by }-4 y^2=x \text { and } x-1=-5 y^2 $$ |
(B) | 0 |
| (iii) | Cosine of the angle of intersection of $y=3^{x-1} \log x$ and $y=x^{x-1}$ is | (C) | 6 In 2 |
| (iv) | $$ \frac{d y}{d x}=\frac{2}{(x+y)} ; y\left(-\frac{2}{3}\right)=0 \text {, then value of constant }(\mathrm{k})= $$ |
(D) | 4/3 |
- A
$$ \begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(B); }\text { (iv)-(D) } \end{aligned} $$
- B
$$ \begin{aligned} & \text { (i)-(A); (ii)-(C); (iii)-(B); }\text { (iv)-(D) } \end{aligned} $$
- C
$$ \begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(A); }\text { (iv)-(D) } \end{aligned} $$
- D
$$ \begin{aligned} & \text { (i)-(A); (ii)-(B); (iii)-(C); }\text { (iv)-(D) } \end{aligned} $$
✓ Correct answer: C
Want the full step-by-step reasoning?