1
IIT-JEE 2008 Paper 2 Offline
+3
-1

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :

A
2, 4 or 8
B
3, 6 or 9
C
4 or 8
D
5 or 10
2
IIT-JEE 2008 Paper 2 Offline
+4
-1

Consider the lines given by:

$${L_1}:x + 3y - 5 = 0$$

$${L_2}:3x - ky - 1 = 0$$

$${L_3}:5x + 2y - 12 = 0$$

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

Column I Column II
(A) L$$_1$$, L$$_2$$, L$$_3$$ are concurrent, if (P) $$K = - 9$$
(B) One of L$$_1$$, L$$_2$$, L$$_3$$ is parallel to atleast one of the other two, if (Q) $$K = - {6 \over 5}$$
(C) L$$_1$$, L$$_2$$, L$$_3$$ form a triangle, if (R) $$K = {5 \over 6}$$
(D) L$$_1$$, L$$_2$$, L$$_3$$ do not form a triangle, if (S) $$K = 5$$

A
A - iv; B - ii; C - iii; D - i, ii
B
A - iv; B - i, ii; C - iii; D - i, ii, iv
C
A - iv; B - i; C - iii; D - i, ii
D
A - ii; B - i, iii; C - iii; D - i, ii, iv
3
IIT-JEE 2008 Paper 2 Offline
+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
4
IIT-JEE 2008 Paper 2 Offline
+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
EXAM MAP
Medical
NEET