1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I Column II
(A) The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is (P) 0
(B) Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are (Q) 1
(C) Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than (R) 2
(D) If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are (S) 3

A
A - iii; B - ii, iv; C - iii, iv; D - i, iii
B
A - iii; B - ii; C - iii, iv; D - i, iii
C
A - ii; B - ii, iv; C - iii, iv; D - i
D
A - ii; B - ii, iv; C - iii, iv; D - i, iii
2
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+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
3
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

Consider a system of three charges $${q \over 3},{q \over 3}$$ and $$ - {{2q} \over 3}$$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60$$^\circ$$

IIT-JEE 2008 Paper 2 Offline Physics - Electrostatics Question 10 English

A
The electric field at point O is $${q \over {8\pi {\varepsilon _0}{R^2}}}$$ directed along the negative x-axis
B
The potential energy of the system is zero
C
The magnitude of the force between the charges at C and B is $${{{q^2}} \over {54\pi {\varepsilon _0}{R^2}}}$$
D
The potential at point O is $${q \over {12\pi {\varepsilon _0}R}}$$
4
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

A radioactive sample S1 having activity of 5 $$\mu$$Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $$\mu$$Ci. The half lives of S1 and S2 can be :

A
20 years and 5 years, respectively
B
20 years and 10 years, respectively
C
10 years each
D
5 years each
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