1
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-0
Match the statements given in Column -$$I$$ with the values given in Column-$$II.$$

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column-$$I$$
(A) $$\,\,\,\,$$If $$\overrightarrow a = \widehat j + \sqrt 3 \widehat k,\overrightarrow b = - \widehat j + \sqrt 3 \widehat k$$ and $$\overrightarrow c = 2\sqrt 3 \widehat k$$ form a triangle, then the internal angle of the triangle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is
(B)$$\,\,\,\,$$ If $$\int\limits_a^b {\left( {f\left( x \right) - 3x} \right)dx = {a^2} - {b^2},}$$ then the value of $$f$$ $$\left( {{\pi \over 6}} \right)$$ is
(C)$$\,\,\,\,$$ The value of $${{{\pi ^2}} \over {\ell n3}}\int\limits_{7/6}^{5/6} {\sec \left( {\pi x} \right)dx}$$ is
(D)$$\,\,\,\,$$ The maximum value of $$\left| {Arg\left( {{1 \over {1 - z}}} \right)} \right|$$ for $$\left| z \right| = 1,\,z \ne 1$$ is given by

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column-$$II$$
(p)$$\,\,\,\,$$ $${{\pi \over 6}}$$
(q)$$\,\,\,\,$$ $${{2\pi \over 3}}$$
(r)$$\,\,\,\,$$ $${{\pi \over 3}}$$
(s)$$\,\,\,\,$$ $$\pi$$
(t) $$\,\,\,\,$$ $${{\pi \over 2}}$$

A
$$\left( A \right) \to q;\,\,\left( B \right) \to p;\,\,\left( C \right) \to s;\,\,\left( D \right) \to t$$
B
$$\left( A \right) \to q;\,\,\left( B \right) \to p;\,\,\left( C \right) \to t;\,\,\left( D \right) \to s$$
C
$$\left( A \right) \to p;\,\,\left( B \right) \to q;\,\,\left( C \right) \to s;\,\,\left( D \right) \to t$$
D
$$\left( A \right) \to q;\,\,\left( B \right) \to s;\,\,\left( C \right) \to p;\,\,\left( D \right) \to t$$
2
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$P,Q,R$$ and $$S$$ be the points on the plane with position vectors $${ - 2\widehat i - \widehat j,4\widehat i,3\widehat i + 3\widehat j}$$ and $${ - 3\widehat i + 2\widehat j}$$ respectively. The quadrilateral $$PQRS$$ must be a
A
parallelogram, which is neither a rhombus nor a rectangle
B
square
C
rectangle, but not a square
D
rhombus, but not a square
3
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Equation of the plane containing the straight line $${x \over 2} = {y \over 3} = {z \over 4}$$ and perpendicular to the plane containing the straight lines $${x \over 3} = {y \over 4} = {z \over 2}$$ and $${x \over 4} = {y \over 2} = {z \over 3}$$ is
A
$$x+2y-2z=0$$
B
$$3x+2y-2z=0$$
C
$$x-2y+z=0$$
D
$$5x+2y-4z=0$$
4
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Two adjacent sides of a parallelogram $$ABCD$$ are given by
$$\overrightarrow {AB} = 2\widehat i + 10\widehat j + 11\widehat k$$ and $$\,\overrightarrow {AD} = \widehat i + 2\widehat j + 2\widehat k$$
The side $$AD$$ is rotated by an acute angle $$\alpha$$ in the plane of the parallelogram so that $$AD$$ becomes $$AD'.$$ If $$AD'$$ makes a right angle with the side $$AB,$$ then the cosine of the angle $$\alpha$$ is given by
A
$${{8 \over 9}}$$
B
$${{{\sqrt {17} } \over 9}}$$
C
$${{1 \over 9}}$$
D
$${{{4\sqrt 5 } \over 9}}$$
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