MCQ
Match the integrals in Column $I$ with the values in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$ Column $II$
$(A)$ $\int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}$ $(p)$ $\frac{1}{2} \log \left(\frac{2}{3}\right)$
$(B)$ $\int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}$ $(q)$ $2 \log \left(\frac{2}{3}\right)$
$(C)$ $\int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}$ $(r)$ $\frac{\pi}{3}$
$(D)$ $\int_1^2 \frac{d x}{x \sqrt{x^2-1}}$ $(s)$ $\frac{\pi}{2}$
  • A
    $A-p\ \ B-r\ \ C-p\ \ D-s$
  • B
    $A-r\ \ B-s\ \ C-p\ \ D-q$
  • $A-s\ \ B-s\ \ C-p\ \ D-r$
  • D
    $A-q\ \ B-r\ \ C-q\ \ D-s$

Answer

Correct option: C.
$A-s\ \ B-s\ \ C-p\ \ D-r$
c
$(A)$. $\quad \int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}=\frac{\pi}{2}$

$(B)$. $\quad \int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}=\frac{\pi}{2}$

$(C)$. $\quad \int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}=\frac{1}{2} \ln \frac{2}{3}$

$(D)$. $\quad \int_1^2 \frac{d x}{x \sqrt{x^2-1}}=\frac{\pi}{3}$

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