1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Which of the following inequalities is/are TRUE?
A
$$\int_0^1 {x\cos xdx\, \ge \,{3 \over 8}} $$
B
$$\int_0^1 {x\sin xdx\, \ge \,{3 \over {10}}} $$
C
$$\int_0^1 {{x^2}\cos xdx\, \ge \,{1 \over 2}} $$
D
$$\int_0^1 {{x^2}\sin xdx\, \ge \,{2 \over 9}} $$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
If $$I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx} $$, then
A
$$I > {\log _e}99$$
B
$$I < {\log _e}99$$
C
$$I < {{49} \over {50}}$$
D
$$I > {{49} \over {50}}$$
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let
$$f\left( x \right) = \mathop {\lim }\limits_{n \to \infty } {\left( {{{{n^n}\left( {x + n} \right)\left( {x + {n \over 2}} \right)...\left( {x + {n \over n}} \right)} \over {n!\left( {{x^2} + {n^2}} \right)\left( {{x^2} + {{{n^2}} \over 4}} \right)....\left( {{x^2} + {{{n^2}} \over {{n^2}}}} \right)}}} \right)^{{x \over n}}},$$ for

all $$x>0.$$ Then
A
$$f\left( {{1 \over 2}} \right) \ge f\left( 1 \right)$$
B
$$f\left( {{1 \over 3}} \right) \le f\left( {{2 \over 3}} \right)$$
C
$$\,f'\left( 2 \right) \le 0$$
D
$$\,{{f'\left( 3 \right)} \over {f\left( 3 \right)}} \ge {{f'\left( 2 \right)} \over {f\left( 2 \right)}}$$
4
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$f\left( x \right) = 7{\tan ^8}x + 7{\tan ^6}x - 3{\tan ^4}x - 3{\tan ^2}x$$ for all $$x \in \left( { - {\pi \over 2},{\pi \over 2}} \right).$$
Then the correct expression(s) is (are)
A
$$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {12}}} $$
B
$$\int\limits_0^{\pi /4} {f\left( x \right)dx = 0} $$
C
$$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {6}}} $$
D
$$\int\limits_0^{\pi /4} {f\left( x \right)dx = 1} $$
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