1
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$f:\left[ {0,2} \right] \to R$$ be a function which is continuous on $$\left[ {0,2} \right]$$ and is differentiable on $$(0,2)$$ with $$f(0)=1$$. Let
$$F\left( x \right) = \int\limits_0^{{x^2}} {f\left( {\sqrt t } \right)dt} $$ for $$x \in \left[ {0,2} \right]$$. If $$F'\left( x \right) = f'\left( x \right)$$ for all $$x \in \left[ {0,2} \right]$$, then $$F(2)$$ equals
A
$${e^2} - 1$$
B
$${e^4} - 1$$
C
$$e - 1$$
D
$${e^4}$$
2
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let f1 : R $$ \to $$ R, f2 : [0, $$\infty $$) $$ \to $$ R, f3 : R $$ \to $$ R, and f4 : R $$ \to $$ [0, $$\infty $$) be defined by

$${f_1}\left( x \right) = \left\{ {\matrix{ {\left| x \right|} & {if\,x < 0,} \cr {{e^x}} & {if\,x \ge 0;} \cr } } \right.$$

f2(x) = x2 ;

$${f_3}\left( x \right) = \left\{ {\matrix{ {\sin x} & {if\,x < 0,} \cr x & {if\,x \ge 0;} \cr } } \right.$$

and

$${f_4}\left( x \right) = \left\{ {\matrix{ {{f_2}\left( {{f_1}\left( x \right)} \right)} & {if\,x < 0,} \cr {{f_2}\left( {{f_1}\left( x \right)} \right) - 1} & {if\,x \ge 0;} \cr } } \right.$$

JEE Advanced 2014 Paper 2 Offline Mathematics - Functions Question 15 English
A
P - 3, Q - 1, R - 4, S - 2
B
P - 1, Q - 3, R - 4, S - 2
C
P - 3, Q - 1, R - 2, S - 4
D
P - 1, Q - 3, R - 2, S - 4
3
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then
JEE Advanced 2014 Paper 2 Offline Physics - Electrostatics Question 57 English 1
JEE Advanced 2014 Paper 2 Offline Physics - Electrostatics Question 57 English 2
A
$${E_1} > {E_2} > {E_3}$$
B
$${E_3} > {E_1} > {E_2}$$
C
$${E_2} > {E_1} > {E_3}$$
D
$${E_3} > {E_2} > {E_1}$$
4
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Parallel rays of light of intensity $$I$$ = 912 Wm–2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant $$\sigma $$ = 5.7 $$ \times $$ 10–8 Wm–2K–4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to
A
330 K
B
660 K
C
990 K
D
1550 K
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