1
JEE Advanced 2017 Paper 2 Offline
+3
-0.75
Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $$\rho$$ remains uniform throughout the volume. The rate of fractional change in density $$\left( {{1 \over \rho } {{d\rho } \over {dt}}} \right)$$ is constant. The velocity $$v$$ of any point on the surface of the expanding sphere is proportional to
A
$$R$$
B
$${R^3}$$
C
$${1 \over R}$$
D
$${R^{2/3}}$$
2
JEE Advanced 2017 Paper 2 Offline
+3
-0.75
Three vectors $$\overrightarrow P ,\overrightarrow Q$$ and $$\overrightarrow R$$ are shown in the figure. Let $$S$$ be any point on the vector $$\overrightarrow R .$$ The distance between the points $$P$$ and $$S$$ is $$b\left| {\overrightarrow R } \right|.$$ The general relation among vectors $$\overrightarrow P ,\overrightarrow Q$$ and $$\overrightarrow S$$ is

A
$$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + b\overrightarrow Q$$
B
$$\overrightarrow S = \left( {b - 1} \right)\overrightarrow P + b\overrightarrow Q$$
C
$$\overrightarrow S = \left( {1 - {b^2}} \right)\overrightarrow P + b\overrightarrow Q$$
D
$$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + {b^2}\overrightarrow Q$$
3
IIT-JEE 2008 Paper 2 Offline
+3
-1
STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2: If the observer and the object are moving at velocities $${\overrightarrow v _1}$$ and $${\overrightarrow v _2}$$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $${\overrightarrow v _2}$$ - $${\overrightarrow v _1}$$.

A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT ,- 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True
4
IIT-JEE 2004 Screening
+2
-0.5
A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio Sn / Sn+1 is
A
$${{2n - 1} \over {2n + 1}}$$
B
$${{2n + 1} \over {2n}}$$
C
$${{2n} \over {2n + 1}}$$
D
$${{2n + 1} \over {2n - 1}}$$
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