1
JEE Advanced 2024 Paper 1 Online
+3
-1

Let $\frac{\pi}{2} < x < \pi$ be such that $\cot x=\frac{-5}{\sqrt{11}}$. Then

$$\left(\sin \frac{11 x}{2}\right)(\sin 6 x-\cos 6 x)+\left(\cos \frac{11 x}{2}\right)(\sin 6 x+\cos 6 x)$$

is equal to :

A
$\frac{\sqrt{11}-1}{2 \sqrt{3}}$
B
$\frac{\sqrt{11}+1}{2 \sqrt{3}}$
C
$\frac{\sqrt{11}+1}{3 \sqrt{2}}$
D
$\frac{\sqrt{11}-1}{3 \sqrt{2}}$
2
JEE Advanced 2022 Paper 1 Online
+3
-1

Consider the following lists :

List-I List-II
(I) $$\left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos x+\sin x=1\right\}$$ (P) has two elements
(II) $$\left\{x \in\left[-\frac{5 \pi}{18}, \frac{5 \pi}{18}\right]: \sqrt{3} \tan 3 x=1\right\}$$ (Q) has three elements
(III) $$\left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}$$ (R) has four elements
(IV) $$\left\{x \in\left[-\frac{7 \pi}{4}, \frac{7 \pi}{4}\right]: \sin x-\cos x=1\right\}$$ (S) has five elements
(T) has six elements

The correct option is:

A
(I) $$\rightarrow(\mathrm{P})$$; (II) $$\rightarrow(\mathrm{S})$$; (III) $$\rightarrow(\mathrm{P})$$; (IV) $$\rightarrow(\mathrm{S})$$
B
(I) $$\rightarrow$$ (P); (II) $$\rightarrow$$ (P); (III) $$\rightarrow$$ (T); (IV) $$\rightarrow$$ (R)
C
(I) $$\rightarrow$$ (Q); (II) $$\rightarrow(\mathrm{P})$$; (III) $$\rightarrow$$ (T); (IV) $$\rightarrow$$ (S)
D
(I) $$\rightarrow(\mathrm{Q})$$; (II) $$\rightarrow(\mathrm{S}) ;$$ (III) $$\rightarrow(\mathrm{P})$$; (IV) $$\rightarrow(\mathrm{R})$$
3
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)
4
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 combinations is correct?
A
(II), (Q), (T)
B
(II), (R), (S)
C
(I), (P), (R)
D
(I), (Q), (U)
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