1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Out of Syllabus
The number of solutions of sin3x = cos 2x, in the interval $$\left( {{\pi \over 2},\pi } \right)$$ is :
A
1
B
2
C
3
D
4
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Out of Syllabus
Consider the following two statements :

Statement p :
The value of sin 120o can be derived by taking $$\theta = {240^o}$$ in the equation
2sin$${\theta \over 2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta }$$

Statement q :
The angles A, B, C and D of any quadrilateral ABCD satisfy the equation
cos$$\left( {{1 \over 2}\left( {A + C} \right)} \right) + \cos \left( {{1 \over 2}\left( {B + D} \right)} \right) = 0$$

Then the truth values of p and q are respectively :
A
F, T
B
T, F
C
T, T
D
F, F
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $${30^o}$$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)
A
14 N
B
20 N
C
6 N
D
4 N
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c.

Which of the following correctly gives the Planck length ?
A
G $$\hbar$$2 c3
B
G2 $$\hbar$$ c
C
$${G^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}{\hbar ^2}c$$
D
$${\left( {{{G\hbar } \over {{c^3}}}} \right)^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}$$
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