1
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0.75
Let $$P(6, 3)$$ be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at the point $$P$$ intersects the $$x$$-axis at $$(9, 0)$$, then the eccentricity of the hyperbola is
A
$$\sqrt {{5 \over 2}} $$
B
$$\sqrt {{3 \over 2}} $$
C
$${\sqrt 2 }$$
D
$${\sqrt 3 }$$
2
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let f $$:$$$$\left[ { - 1,2} \right] \to \left[ {0,\infty } \right]$$ be a continuous function such that
$$f\left( x \right) = f\left( {1 - x} \right)$$ for all $$x \in \left[ { - 1,2} \right]$$

Let $${R_1} = \int\limits_{ - 1}^2 {xf\left( x \right)dx,} $$ and $${R_2}$$ be the area of the region bounded by $$y=f(x),$$ $$x=-1,$$ $$x=2,$$ and the $$x$$-axis. Then

A
$${R_1} = 2{R_2}$$
B
$${R_1} = 3{R_2}$$
C
$${2R_1} = {R_2}$$
D
$${3R_1} = {R_2}$$
3
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$E$$ and $$F$$ be two independent events. The probability that exactly one of them occurs is $$\,{{11} \over {25}}$$ and the probability of none of them occurring is $$\,{{2} \over {25}}$$. If $$P(T)$$ denotes the probability of occurrence of the event $$T,$$ then
A
$$P\left( E \right) = {4 \over 5},P\left( F \right) = {3 \over 5}$$
B
$$P\left( E \right) = {1 \over 5},P\left( F \right) = {2 \over 5}$$
C
$$P\left( E \right) = {2 \over 5},P\left( F \right) = {1 \over 5}$$
D
$$P\left( E \right) = {3 \over 5},P\left( F \right) = {4 \over 5}$$
4
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
$$\left( A \right) \to q;\,\,\left( B \right) \to s;\,\,\left( C \right) \to p;\,\,\left( D \right) \to t$$
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