1
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of tan-1 $$\left[ {{{\sqrt {1 + {x^2}} + \sqrt {1 - {x^2}} } \over {\sqrt {1 + {x^2}} - \sqrt {1 - {x^2}} }}} \right],$$ $$\left| x \right| < {1 \over 2},x \ne 0,$$ is equal to :
A
$${\pi \over 4} + {1 \over 2}{\cos ^{ - 1}}\,{x^2}$$
B
$${\pi \over 4} + {\cos ^{ - 1}}\,{x^2}$$
C
$${\pi \over 4} - {1 \over 2}{\cos ^{ - 1}}\,{x^2}$$
D
$${\pi \over 4} - {\cos ^{ - 1}}\,{x^2}$$
2
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If

$$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},$$

then $$\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $$ is equal to :
A
$$4 + 2\sqrt 3 $$
B
$$ - 2 + \sqrt 3 $$
C
$$ - 2 - \sqrt 3 $$
D
$$-\,\,4 - 2\sqrt 3 $$
3
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
A
$${{255} \over {256}}$$
B
$${{127} \over {128}}$$
C
$${{63} \over {64}}$$
D
$${{1} \over {2}}$$
4
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $${3 \over 4},{1 \over 2}$$ and $${5 \over 8}$$ respectively, then the probability that the target is hit by P or Q but not by R is :
A
$${{21} \over {64}}$$
B
$${{9} \over {64}}$$
C
$${{15} \over {64}}$$
D
$${{39} \over {64}}$$
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