1
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then
A
$${\tan ^2}x = {2 \over 3}$$
B
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {1 \over {125}}$$
C
$${\tan ^2}x = {1 \over 3}$$
D
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {2 \over {125}}$$
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-0

Match the statements/expressions in Column I with the open intervals in Column II :

Column I Column II
(A) Interval contained in the domain of definition of non-zero solutions of the differential equation $${(x - 3)^2}y' + y = 0$$ (P) $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
(B) Interval containing the value of the integral $$\int\limits_1^5 {(x - 1)(x - 2)(x - 3)(x - 4)(x - 5)dx} $$ (Q) $$\left( {0,{\pi \over 2}} \right)$$
(C) Interval in which at least one of the points of local maximum of $${\cos ^2}x + \sin x$$ lies (R) $$\left( {{\pi \over 8},{{5\pi } \over 4}} \right)$$
(D) Interval in which $${\tan ^{ - 1}}(\sin x + \cos x)$$ is increasing (S) $$\left( {0,{\pi \over 8}} \right)$$
(T) $$( - \pi ,\pi )$$

A
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)
B
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (R); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(R)
C
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(S), (Q), (R), (T); (D)$$\to$$(S)
D
(A)$$\to$$(P), (T), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)
3
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If L is finite, then

A
$$a = 2$$
B
$$a = 1$$
C
$$L = {1 \over {64}}$$
D
$$L = {1 \over {32}}$$
4
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let A be the set of all 3 $$\times$$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices in A is

A
12
B
6
C
9
D
3
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