1
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
For $$0 < \theta < {\pi \over 2},$$ the solution (s) of
$$$\sum\limits_{m = 1}^6 {\cos ec\,\left( {\theta + {{\left( {m - 1} \right)\pi } \over 4}} \right)\,\cos ec\,\left( {\theta + {{m\pi } \over 4}} \right) = 4\sqrt 2 } $$$ is (are)
2
IIT-JEE 2009 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0
Match the statements/expressions in Column I with the values given in Column II:
Column I | Column II | ||
---|---|---|---|
(A) | The number of solutions of the equation $$x{e^{\sin x}} - \cos x = 0$$ in the interval $$\left( {0,{\pi \over 2}} \right)$$ | (P) | 1 |
(B) | Value(s) of $$k$$ for which the planes $$kx + 4y + z = 0,4x + ky + 2z = 0$$ and $$2x + 2y + z = 0$$ intersect in a straight line | (Q) | 2 |
(C) | Value(s) of $$k$$ for which $$|x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k$$ has integer solution(s) | (R) | 3 |
(D) | If $$y' = y + 1$$ and $$y(0) = 1$$ then value(s) of $$y(\ln 2)$$ | (S) | 4 |
(T) | 5 |
3
IIT-JEE 2009 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0
Match the statements/expressions in Column I with the values given in Column II:
Column I | Column II | ||
---|---|---|---|
(A) | Root(s) of the expression $$2{\sin ^2}\theta + {\sin ^2}2\theta = 2$$ | (P) | $${\pi \over 6}$$ |
(B) | Points of discontinuity of the function $$f(x) = \left[ {{{6x} \over \pi }} \right]\cos \left[ {{{3x} \over \pi }} \right]$$, where $$[y]$$ denotes the largest integer less than or equal to y | (Q) | $${\pi \over 4}$$ |
(C) | Volume of the parallelopiped with its edges represented by the vectors $$\widehat i + \widehat j + \widehat i + 2\widehat j$$ and $$\widehat i + \widehat j + \pi \widehat k$$ | (R) | $${\pi \over 3}$$ |
(D) | Angle between vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ where $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying $$\overrightarrow a + \overrightarrow b + \sqrt 3 \overrightarrow c = \overrightarrow 0 $$ | (S) | $${\pi \over 2}$$ |
(T) | $$\pi $$ |
4
IIT-JEE 2009 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angles with the coordinate axes. The line meets the plane $$2x + y + z = 9$$ at point Q. The length of the line segment PQ equals
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