1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The integral $$\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,$$ loge x dx is equal to :
A
$$- {1 \over 2} + {1 \over e} - {1 \over {2{e^2}}}$$
B
$${3 \over 2} - e - {1 \over {2{e^2}}}$$
C
$${1 \over 2} - e - {1 \over {{e^2}}}$$
D
$${3 \over 2} - {1 \over e} - {1 \over {2{x^2}}}$$
2
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
Out of Syllabus
$$\mathop {\lim }\limits_{x \to \infty } \left( {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + {n \over {{n^2} + {3^2}}} + ..... + {1 \over {5n}}} \right)$$ is equal to :
A
tan–1 (2)
B
tan–1 (3)
C
$${\pi \over 4}$$
D
$${\pi \over 2}$$
3
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then $$\int\limits_0^a \,$$f(x) g(x) dx is equal to :
A
4$$\int\limits_0^a \,$$f(x)dx
B
$$-$$ 3$$\int\limits_0^a \,$$f(x)dx
C
$$\int\limits_0^a \,$$f(x)dx
D
2$$\int\limits_0^a \,$$f(x)dx
4
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
The integral  $$\int\limits_{\pi /6}^{\pi /4} {{{dx} \over {\sin 2x\left( {{{\tan }^5}x + {{\cot }^5}x} \right)}}}$$  equals :
A
$${\pi \over {40}}$$
B
$${1 \over {20}}{\tan ^{ - 1}}\left( {{1 \over {9\sqrt 3 }}} \right)$$
C
$${1 \over {10}}\left( {{\pi \over 4} - {{\tan }^{ - 1}}\left( {{1 \over {9\sqrt 3 }}} \right)} \right)$$
D
$${1 \over 5}\left( {{\pi \over 4}{{-\tan }^{ - 1}}\left( {{1 \over {3\sqrt 3 }}} \right)} \right)$$
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