1
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of   $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {\left[ x \right] + \left[ {\sin x} \right] + 4}}} ,$$  where [t] denotes the greatest integer less than or equal to t, is
A
$${1 \over {12}}\left( {7\pi - 5} \right)$$
B
$${1 \over {12}}\left( {7\pi + 5} \right)$$
C
$${3 \over {10}}\left( {4\pi - 3} \right)$$
D
$${3 \over {20}}\left( {4\pi - 3} \right)$$
2
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant :
A
third
B
fourth
C
second
D
first
3
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a1, a2, a3, ..... a10 be in G.P. with ai > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k $$ \in $$ N (the set of natural numbers) for which

$$\left| {\matrix{ {{{\log }_e}\,{a_1}^r{a_2}^k} & {{{\log }_e}\,{a_2}^r{a_3}^k} & {{{\log }_e}\,{a_3}^r{a_4}^k} \cr {{{\log }_e}\,{a_4}^r{a_5}^k} & {{{\log }_e}\,{a_5}^r{a_6}^k} & {{{\log }_e}\,{a_6}^r{a_7}^k} \cr {{{\log }_e}\,{a_7}^r{a_8}^k} & {{{\log }_e}\,{a_8}^r{a_9}^k} & {{{\log }_e}\,{a_9}^r{a_{10}}^k} \cr } } \right|$$ $$=$$ 0.

Then the number of elements in S, is -
A
10
B
4
C
2
D
infinitely many
4
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If  $$\sum\limits_{r = 0}^{25} {\left\{ {{}^{50}{C_r}.{}^{50 - r}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} ,\,\,$$ then K is equal to :
A
224
B
225$$-$$ 1
C
225
D
(25)2
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