1
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
Let f : R $$\to$$ R and g : R $$\to$$ R be respectively given by f(x) = | x | + 1 and g(x) = x2 + 1. Define h : R $$\to$$ R by $$h(x) = \left\{ {\matrix{ {\max \{ f(x),g(x)\} ,} & {if\,x \le 0.} \cr {\min \{ f(x),g(x)\} ,} & {if\,x > 0.} \cr } } \right.$$

The number of points at which h(x) is not differentiable is
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2
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
Airplanes A and B are flying with constant velocity in the same vertical plane at angles $$30^\circ $$ and $$60^\circ $$ with respect to the horizontal respectively as shown in the figure. The speed of A is $$100\sqrt 3 $$ m/s. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t0, A just escapes being hit by B, t0 in seconds is

JEE Advanced 2014 Paper 1 Offline Physics - Motion Question 10 English
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3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
A parallel plate capacitor has a dielectric slab of dielectric constant $$K$$ between its plates that covers $$1/3$$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $$C$$ while that of the portion with dielectric in between is $${C_1}.$$ When the capacitor is charged, the plate area covered by the dielectric gets charge $${Q_1}$$ and the rest of the area gets charge $${Q_2}.$$ The electric field in the dielectric is $${E_1}$$ and that in the other portion is $${E_2}.$$ Choose the correct option/ options, ignoring edge effects.

JEE Advanced 2014 Paper 1 Offline Physics - Capacitor Question 14 English
A
$${{{E_1}} \over {{E_2}}} = 1$$
B
$${{{E_1}} \over {{E_2}}} = {1 \over K}$$
C
$${{{Q_1}} \over {{Q_2}}} = {3 \over K}$$
D
$${C \over {{C_1}}} = {{2 + K} \over K}$$
4
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
Let $${E_1}\left( r \right),{E_2}\left( r \right)$$ and $${E_3}\left( r \right)$$ be the respective electric field at a distance $$r$$ from a point charge $$Q,$$ an infinitely long wire with constant linear charge density $$\lambda ,$$ and an infinite plane with uniform surface charge density $$\sigma .$$ If $$E{}_1\left( {{r_0}} \right) = {E_2}\left( {{r_0}} \right) = {E_3}\left( {{r_0}} \right)$$ at a given distance $${r_0}.$$ then
A
$$Q = 4\sigma \pi r_0^2$$
B
$${r_0} = {\lambda \over {2\pi \sigma }}$$
C
$${E_1}\left( {{r_0}/2} \right) = 2{E_2}\left( {{r_0}/2} \right)$$
D
$${E_2}\left( {{r_0}/2} \right) = 4{E_3}\left( {{r_0}/2} \right)$$
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