1
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

For every integer n, let an and bn be real numbers. Let function f : R $$\to$$ R be given by

$$f(x) = \left\{ {\matrix{ {{a_n} + \sin \pi x,} & {for\,x \in [2n,2n + 1]} \cr {{b_n} + \cos \pi x,} & {for\,x \in (2n - 1,2n)} \cr } } \right.$$, for all integers n. If f is continuous, then which of the following hold(s) for all n ?

A
an $$-$$ 1 $$-$$ bn $$-$$ 1 = 0
B
an $$-$$ bn = 1
C
an $$-$$ bn $$+$$ 1 = 1
D
an $$-$$ 1 $$-$$ bn = $$-$$1
2
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

If the ad joint of a 3 $$\times$$ 3 matrix P is $$\left[ {\matrix{ 1 & 4 & 4 \cr 2 & 1 & 7 \cr 1 & 1 & 3 \cr } } \right]$$, then the possible value(s) of the determinant of P is(are)

A
$$-$$2
B
$$-$$1
C
1
D
2
3
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

Let $$f:( - 1,1) \to R$$ be such that $$f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}$$ for $$\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)$$. Then the value(s) of $$f\left( {{1 \over 3}} \right)$$ is(are)

A
$$1 - \sqrt {{3 \over 2}}$$
B
$$1 + \sqrt {{3 \over 2}}$$
C
$$1 - \sqrt {{2 \over 3}}$$
D
$$1 + \sqrt {{2 \over 3}}$$
4
IIT-JEE 2012 Paper 2 Offline
+3
-0.75
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega$$. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by
A
B
C
D
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