1
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is

A
one-one and onto.
B
onto but not one-one.
C
one-one but not onto.
D
neither one-one nor onto.
2
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0

The value of $$6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}...} } } } \right)$$ is __________.

Your input ____
3
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A cubical region of side $$a$$ has its center at the origin. It encloses three fixed point charges, $$-q$$ at $$\left( {0, - a/4,0} \right), + 3q$$ at $$\left( {0,0,0} \right)$$ and $$-q$$ at $$\left( {0, + a/4,0} \right).$$ Choose the correct option(s)
IIT-JEE 2012 Paper 1 Offline Physics - Electrostatics Question 51 English
A
The net electric flux crossing the plane $$x=+a/2$$ is equal to the net electric flux crossing the plane $$x=-a/2$$
B
The net electric flux crossing the plane $$y=+a/2$$ is more than the net electric flux crossing the plane $$y=-a/2.$$
C
The net electric flux crossing the entire region is $${q \over {{\varepsilon _0}}}$$
D
The net electric flux crossing the plane $$z = + a/2$$ is equal to the net electric flux crossing the plane $$x=+a/2.$$
4
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Consider a thin spherical shell of radius $$R$$ with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $$\left| {\overrightarrow E \left( r \right)} \right|$$ and the electric potential $$V(r)$$ with the distance $$r$$ from the center, best represented by which graph?
A
IIT-JEE 2012 Paper 1 Offline Physics - Electrostatics Question 58 English Option 1
B
IIT-JEE 2012 Paper 1 Offline Physics - Electrostatics Question 58 English Option 2
C
IIT-JEE 2012 Paper 1 Offline Physics - Electrostatics Question 58 English Option 3
D
IIT-JEE 2012 Paper 1 Offline Physics - Electrostatics Question 58 English Option 4
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