Column IColumn 2Column 3(I)f(x)=tan(2tan−1√√1+√x−1√1+√x+

1.	Column IColumn 2Column 3(I)f(x)=tan(2tan−1√√1+√x−1√1+√x+1)(i)∫f(x)dx=43x34+C(P)∫10f(x)dx=43(II)f(x)=cot(2tan−1√√1+√x−4√x√1+√x+4√x)(ii)∫f(x)dx=45x54+C(Q)∫10f(x)dx=45(III)f(x)⎛⎜⎝1−tan(12sin−1(1−√x1+√x))1+tan(12sin−1(1−√x1+√x))⎞⎟⎠(iii)∫f(x)dx=23x34+C(R)∫10f(x)dx=23(IV)f(x)=√xtan(2tan−1(√√1+√x+1−√√1+√x−1√√1+√x+1+√√1+√x−1))(iv)∫f(x)dx=25x54+C(S)∫10f(x)dx=25 Which of the following options is only correct combination?
Answer» $\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & f (x) = t a n (2 t a n^{- 1} \sqrt{\frac{\sqrt{1 + \sqrt{x}} - 1}{\sqrt{1 + \sqrt{x}} + 1}}) & (i) & \int f (x) d x = \frac{4}{3} x^{\frac{3}{4}} + C & (P) & \int_{0}^{1} f (x) d x = \frac{4}{3} (I I) & f (x) = c o t (2 t a n^{- 1} \sqrt{\frac{\sqrt{1 + \sqrt{x}} - \sqrt[4]{x}}{\sqrt{1 + \sqrt{x}} + \sqrt[4]{x}}}) & (i i) & \int f (x) d x = \frac{4}{5} x^{\frac{5}{4}} + C & (Q) & \int_{0}^{1} f (x) d x = \frac{4}{5} (I I I) & f (x) ⎛ ⎜ ⎝ \frac{1 - t a n (\frac{1}{2} s i n^{- 1} (\frac{1 - \sqrt{x}}{1 + \sqrt{x}}))}{1 + t a n (\frac{1}{2} s i n^{- 1} (\frac{1 - \sqrt{x}}{1 + \sqrt{x}}))} ⎞ ⎟ ⎠ & (i i i) & \int f (x) d x = \frac{2}{3} x^{\frac{3}{4}} + C & (R) & \int_{0}^{1} f (x) d x = \frac{2}{3} (I V) & f (x) = \sqrt{x} t a n (2 t a n^{- 1} (\frac{\sqrt{\sqrt{1 + \sqrt{x} + 1}} - \sqrt{\sqrt{1 + \sqrt{x} - 1}}}{\sqrt{\sqrt{1 + \sqrt{x} + 1}} + \sqrt{\sqrt{1 + \sqrt{x} - 1}}})) & (i v) & \int f (x) d x = \frac{2}{5} x^{\frac{5}{4}} + C & (S) & \int_{0}^{1} f (x) d x = \frac{2}{5} \end{matrix}$ Which of the following options is only correct combination?

Column IColumn 2Column 3(I)f(x)=tan(2tan−1√√1+√x−1√1+√x+1)(i)∫f(x)dx=43x34+C(P)∫10f(x)dx=43(II)f(x)=cot(2tan−1√√1+√x−4√x√1+√x+4√x)(ii)∫f(x)dx=45x54+C(Q)∫10f(x)dx=45(III)f(x)⎛⎜⎝1−tan(12sin−1(1−√x1+√x))1+tan(12sin−1(1−√x1+√x))⎞⎟⎠(iii)∫f(x)dx=23x34+C(R)∫10f(x)dx=23(IV)f(x)=√xtan(2tan−1(√√1+√x+1−√√1+√x−1√√1+√x+1+√√1+√x−1))(iv)∫f(x)dx=25x54+C(S)∫10f(x)dx=25 Which of the following options is only correct combination?

Answer»

$\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & f (x) = t a n (2 t a n^{- 1} \sqrt{\frac{\sqrt{1 + \sqrt{x}} - 1}{\sqrt{1 + \sqrt{x}} + 1}}) & (i) & \int f (x) d x = \frac{4}{3} x^{\frac{3}{4}} + C & (P) & \int_{0}^{1} f (x) d x = \frac{4}{3} (I I) & f (x) = c o t (2 t a n^{- 1} \sqrt{\frac{\sqrt{1 + \sqrt{x}} - \sqrt[4]{x}}{\sqrt{1 + \sqrt{x}} + \sqrt[4]{x}}}) & (i i) & \int f (x) d x = \frac{4}{5} x^{\frac{5}{4}} + C & (Q) & \int_{0}^{1} f (x) d x = \frac{4}{5} (I I I) & f (x) ⎛ ⎜ ⎝ \frac{1 - t a n (\frac{1}{2} s i n^{- 1} (\frac{1 - \sqrt{x}}{1 + \sqrt{x}}))}{1 + t a n (\frac{1}{2} s i n^{- 1} (\frac{1 - \sqrt{x}}{1 + \sqrt{x}}))} ⎞ ⎟ ⎠ & (i i i) & \int f (x) d x = \frac{2}{3} x^{\frac{3}{4}} + C & (R) & \int_{0}^{1} f (x) d x = \frac{2}{3} (I V) & f (x) = \sqrt{x} t a n (2 t a n^{- 1} (\frac{\sqrt{\sqrt{1 + \sqrt{x} + 1}} - \sqrt{\sqrt{1 + \sqrt{x} - 1}}}{\sqrt{\sqrt{1 + \sqrt{x} + 1}} + \sqrt{\sqrt{1 + \sqrt{x} - 1}}})) & (i v) & \int f (x) d x = \frac{2}{5} x^{\frac{5}{4}} + C & (S) & \int_{0}^{1} f (x) d x = \frac{2}{5} \end{matrix}$

Which of the following options is only correct combination?

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