1
JEE Advanced 2016 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
Let $$S = \left\{ {x \in \left( { - \pi ,\pi } \right):x \ne 0, \pm {\pi \over 2}} \right\}.$$ The sum of all distinct solutions of the equation $$\sqrt 3 \,\sec x + \cos ec\,x + 2\left( {\tan x - \cot x} \right) = 0$$ in the set S is equal to
A
$$ - {{7\pi } \over 9}$$
B
$$ - {{2\pi } \over 9}$$
C
0
D
$${{5\pi } \over 9}$$
2
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Consider a pyramid $$OPQRS$$ located in the first octant $$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$ with $$O$$ as origin, and $$OP$$ and $$OR$$ along the $$x$$-axis and the $$y$$-axis, respectively. The base $$OPQR$$ of the pyramid is a square with $$OP=3.$$ The point $$S$$ is directly above the mid-point, $$T$$ of diagonal $$OQ$$ such that $$TS=3.$$ Then
A
the acute angle between $$OQ$$ and $$OS$$ is $${\pi \over 3}$$
B
the equation of the plane containing the triangle $$OQS$$ is $$x-y=0$$
C
the length of the perpendicular from $$P$$ to the plane containing the triangle $$OQS$$ is $${3 \over {\sqrt 2 }}$$
D
the perpendicular distance from $$O$$ to the straight line containing $$RS$$ is $$\sqrt {{{15} \over 2}} $$
3
JEE Advanced 2016 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
A computer producing factory has only two plants $${T_1}$$ and $${T_2}.$$ Plant $${T_1}$$ produces $$20$$% and plant $${T_2}$$ produces $$80$$% of the total computers produced. $$7$$% of computers produced in the factory turn out to be defective. It is known that $$P$$ (computer turns out to be defective given that it is produced in plant $${T_1}$$)
$$ = 10P$$ (computer turns out to be defective given that it is produced in plant $${T_2}$$),
where $$P(E)$$ denotes the probability of an event $$E$$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $${T_2}$$ is
A
$${{36} \over {73}}$$
B
$${{47} \over {79}}$$
C
$${{78} \over {93}}$$
D
$${{75} \over {83}}$$
4
JEE Advanced 2016 Paper 1 Offline
Numerical
+3
-0
Change Language
The total number of distinct $$x \in \left[ {0,1} \right]$$ for which

$$\int\limits_0^x {{{{t^2}} \over {1 + {t^4}}}} dt = 2x - 1$$
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