1
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$I = \int\limits_{\pi /4}^{\pi /3} {{{\sin x} \over x}} dx$$. Then
A
$${1 \over 2} \le I \le 1$$
B
$$4 \le I \le 2\sqrt {30} $$
C
$${{\sqrt 3 } \over 8} \le I \le {{\sqrt 2 } \over 6}$$
D
$$1 \le I \le {{2\sqrt 3 } \over {\sqrt 2 }}$$
2
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of

$$I = \int_{\pi /2}^{5\pi /2} {{{{e^{{{\tan }^{ - 1}}(\sin x)}}} \over {{e^{{{\tan }^{ - 1}}(\sin x)}} + {e^{{{\tan }^{ - 1}}(\cos x)}}}}} dx$$, is
A
1
B
$$\pi$$
C
e
D
$${\pi \over 2}$$
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of

$$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left\{ {{{\sec }^2}{\pi \over {4n}} + {{\sec }^2}{{2\pi } \over {4n}} + ... + {{\sec }^2}{{n\pi } \over {4n}}} \right\}$$ is
A
$${\log _e}2$$
B
$${\pi \over 2}$$
C
$${4 \over \pi }$$
D
e
4
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $${I_1} = \int_0^n {[x]} \,dx$$ and $${I_2} = \int_0^n {\{ x\} } \,dx$$, where [x] and {x} are integral and fractional parts of x and n $$ \in $$ N $$-$$ {1}. Then I1 / I2 is equal to
A
$${1 \over {n - 1}}$$
B
$${1 \over n}$$
C
n
D
n $$-$$ 1
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Graduate Aptitude Test in Engineering
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Class 12