1
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$f, g :$$ $$\left[ { - 1,2} \right] \to R$$ be continuous functions which are twice differentiable on the interval $$(-1, 2)$$. Let the values of f and g at the points $$-1, 0$$ and $$2$$ be as given in the following table:
X = -1 X = 0 X = 2
f(x) 3 6 0
g(x) 0 1 -1

In each of the intervals $$(-1, 0)$$ and $$(0, 2)$$ the function $$(f-3g)''$$ never vanishes. Then the correct statement(s) is (are)

A
$$f'\left( x \right) - 3g'\left( x \right) = 0$$ has exactly three solutions in $$\left( { - 1,0} \right) \cup \left( {0,2} \right)$$
B
$$f'\left( x \right) - 3g'\left( x \right) = 0$$ has exactly one solution in $$(-1, 0)$$
C
$$f'\left( x \right) - 3g'\left( x \right) = 0$$ has exactly one solution in $$(0, 2)$$
D
$$f'\left( x \right) - 3g'\left( x \right) = 0$$ has exactly two solutions in $$(-1, 0)$$ and exactly two solutions in $$(0, 2)$$
2
JEE Advanced 2015 Paper 2 Offline
Numerical
+3
-1
Let m and n be two positive integers greater than 1. If $$$\mathop {\lim }\limits_{\alpha \to 0} \left( {{{{e^{\cos \left( {{\alpha ^n}} \right)}} - e} \over {{\alpha ^m}}}} \right) = - \left( {{e \over 2}} \right)$$$ then the value of $${m \over n}$$ is _________.
Your input ____
3
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Consider a uniform spherical charge distribution of radius $${R_1}$$ centred at the origin $$O.$$ In this distribution, a spherical cavity of radius $${R_2},$$ centred at $$P$$ with distance $$OP=a$$ $$ = {R_1} - {R_2}$$ (see figure) is made. If the electric field inside the cavity at position $$\overrightarrow r $$ is $$\overrightarrow E \overrightarrow {\left( r \right)} ,$$ then the correct statement(s) is (are)

JEE Advanced 2015 Paper 2 Offline Physics - Electrostatics Question 47 English
A
$$\overrightarrow E $$ is uniform, its magnitude is independent of $${R_2}$$ but its direction depends on $$\overrightarrow r .$$
B
$$\overrightarrow E $$ is uniform, its magnitude depends on $${R_2}$$ and its direction depends on $$\overrightarrow r .$$
C
$$\overrightarrow E $$ is uniform, its magnitude is independent of a but its direction depends on $$\overrightarrow a $$
D
$$\overrightarrow E $$ is uniform and both its magnitude and direction depend on $$\overrightarrow a $$
4
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)
A
$$P(r = 0) = 0$$
B
$${{P(r = 3R/4)} \over {P(r = 2R/3)}} = {{63} \over {80}}$$
C
$${{P(r = 3R/5)} \over {P(r = 2R/5)}} = {{16} \over {21}}$$
D
$${{P(r = R/2)} \over {P(r = R/3)}} = {{20} \over {27}}$$
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