1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta$$)
y(t) = B sin (bt)

Identify the correct match below.
A
Parameters   A $$\ne$$ B, a = b; $$\delta$$ = 0;
Curve    Parabola
B
Parameters    A = B, a = b; $$\delta$$ = $${\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
Curve    Line
C
Parameters    A $$\ne$$ B, a = b; $$\delta$$ = $${\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
Curve    Ellipse
D
Parameters    A = B, a = 2b; $$\delta$$ = $${\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
Curve    Circle
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta$$ between the radius vector passing through the common interface and the vertical is :
A
$$\theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$
B
$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$
C
$$\theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)$$
D
$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)$$
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium of damping constant 10−2 kg s−1 . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :
A
2 s
B
3.5 s
C
5 s
D
7 s
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :
A
$${1 \over 4}Hz$$
B
$${1 \over {2\sqrt 2 }}Hz$$
C
$${1 \over 2}Hz$$
D
$$2$$ $$Hz$$
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