1
JEE Advanced 2019 Paper 2 Offline
+3
-1 Let f(x) = sin($$\pi$$ cos x) and g(x) = cos(2$$\pi$$ sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:

X = {x : f(x) = 0}, Y = {x : f'(x) = 0}

Z = {x : g(x) = 0}, W = {x : g'(x) = 0}

List - I contains the sets X, Y, Z and W. List - II contains some information regarding these sets. Which of the following is the only CORRECT combination?
A
(IV), (P), (R), (S)
B
(III), (P), (Q), (U)
C
(III), (R), (U)
D
(IV), (Q), (T)
2
JEE Advanced 2019 Paper 2 Offline
+3
-1 Let f(x) = sin($$\pi$$ cos x) and g(x) = cos(2$$\pi$$ sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order :

X = {x : f(x) = 0}, Y = {x : f'(x) = 0}

Z = {x : g(x) = 0}, W = {x : g'(x) = 0}

List - I contains the sets X, Y, Z and W. List - II contains some information regarding these sets. A
(II), (Q), (T)
B
(II), (R), (S)
C
(I), (P), (R)
D
(I), (Q), (U)
3
JEE Advanced 2016 Paper 2 Offline
+3
-1
The value of

$$\sum\limits_{k = 1}^{13} {{1 \over {\sin \left( {{\pi \over 4} + {{\left( {k - 1} \right)\pi } \over 6}} \right)\sin \left( {{\pi \over 4} + {{k\pi } \over 6}} \right)}}}$$ is equal to
A
$$3 - \sqrt 3$$
B
$$2\left( {3 - \sqrt 3 } \right)$$
C
$$2\left( {\sqrt 3 - 1} \right)\,\,\,$$
D
$$2\left( {2 - \sqrt 3 } \right)$$
4
JEE Advanced 2016 Paper 1 Offline
+3
-1
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
$${{5\pi } \over 9}$$
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