1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The integral

$$\int {{{{{\sin }^2}x{{\cos }^2}x} \over {{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}} dx$$

is equal to
A
$${{ - 1} \over {1 + {{\cot }^3}x}} + C$$
B
$${1 \over {3\left( {1 + {{\tan }^3}x} \right)}} + C$$
C
$${{ - 1} \over {3\left( {1 + {{\tan }^3}x} \right)}} + C$$
D
$${1 \over {1 + {{\cot }^3}x}} + C$$
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If    $$\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C$$
(where C is a constant of integration), then the ordered pair (A, B) is equal to :
A
(2,  1)
B
($$-$$ 2,   $$-$$1)
C
($$-$$ 2,  1)
D
(2,   $$-$$1)
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$$ (x $$ \in $$ R $$-$${1, $$-$$ 2}), then $$\int f \left( x \right)dx$$ is equal to :
(where C is a constant of integration)
A
12 loge | 1 $$-$$ x | + 3x + C
B
$$-$$ 12 loge | 1 $$-$$ x | $$-$$ 3x + C
C
12 loge | 1 $$-$$ x | $$-$$ 3x + C
D
$$-$$ 12 loge | 1 $$-$$ x | + 3x + C
4
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$\left( { {8 \over 3}, - {2 \over 3}} \right)$$
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