1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
If $$\,\,\,$$ f$$\left( {{{3x - 4} \over {3x + 4}}} \right)$$ = x + 2, x $$\ne$$ $$-$$ $${4 \over 3}$$, and

$$\int {}$$f(x) dx = A log$$\left| {} \right.$$1 $$-$$ x $$\left| {} \right.$$ + Bx + C,

then the ordered pair (A, B) is equal to :

(where C is a constant of integration)
A
$$\left( {{8 \over 3},{2 \over 3}} \right)$$
B
$$\left( { - {8 \over 3},{2 \over 3}} \right)$$
C
$$\left( { - {8 \over 3}, - {2 \over 3}} \right)$$
D
$$\left( { {8 \over 3}, - {2 \over 3}} \right)$$
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
The integral

$$\int {\sqrt {1 + 2\cot x(\cos ecx + \cot x)\,} \,\,dx}$$

$$\left( {0 < x < {\pi \over 2}} \right)$$ is equal to :

(where C is a constant of integration)
A
4 log(sin $${x \over 2}$$ ) + C
B
2 log(sin $${x \over 2}$$ ) + C
C
2 log(cos $${x \over 2}$$ ) + C
D
4 log(cos $${x \over 2}$$) + C
3
JEE Main 2017 (Offline)
+4
-1
Let $${I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).$$

If $${I_4} + {I_6}$$ = $$a{\tan ^5}x + b{x^5} + C$$, where C is a constant of integration,

then the ordered pair $$\left( {a,b} \right)$$ is equal to
A
$$\left( {{1 \over 5},0} \right)$$
B
$$\left( {{1 \over 5}, - 1} \right)$$
C
$$\left( { - {1 \over 5},0} \right)$$
D
$$\left( { - {1 \over 5},1} \right)$$
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
The integral $$\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}}$$ is equal to :

(where C is a constant of integration.)
A
$$- 2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C$$
B
$$- 2\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C$$
C
$$- \sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C$$
D
$$2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C$$
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