1
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
Suppose that the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ are $$\left( {{f_1},0} \right)$$ and $$\left( {{f_2},0} \right)$$ where $${{f_1} > 0}$$ and $${{f_2} < 0}$$. Let $${P_1}$$ and $${P_2}$$ be two parabolas with a common vertex at $$(0,0)$$ and with foci at $$\left( {{f_1},0} \right)$$ and $$\left( 2{{f_2},0} \right)$$, respectively. Let $${T_1}$$ be a tangent to $${P_1}$$ which passes through $$\left( 2{{f_2},0} \right)$$ and $${T_2}$$ be a tangent to $${P_2}$$ which passes through $$\left( {{f_1},0} \right)$$. If $${m_1}$$ is the slope of $${T_1}$$ and $${m_2}$$ is the slope of $${T_2}$$, then the value of $$\left( {{1 \over {m_1^2}} + m_2^2} \right)$$ is
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2
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
If $$\alpha $$ $$ = 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)$$ and $$\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} \right),$$ where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are)
A
$$cos\beta > 0$$
B
$$\sin \beta < 0$$
C
$$\cos \left( {\alpha + \beta } \right) > 0$$
D
$$\cos \alpha < 0$$
3
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$f\left( x \right) = 7{\tan ^8}x + 7{\tan ^6}x - 3{\tan ^4}x - 3{\tan ^2}x$$ for all $$x \in \left( { - {\pi \over 2},{\pi \over 2}} \right).$$
Then the correct expression(s) is (are)
A
$$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {12}}} $$
B
$$\int\limits_0^{\pi /4} {f\left( x \right)dx = 0} $$
C
$$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {6}}} $$
D
$$\int\limits_0^{\pi /4} {f\left( x \right)dx = 1} $$
4
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
The option(s) with the values of a and $$L$$ that satisfy the following equation is (are) $$${{\int\limits_0^{4\pi } {{e^t}\left( {{{\sin }^6}at + {{\cos }^4}at} \right)dt} } \over {\int\limits_0^\pi {{e^t}\left( {{{\sin }^6}at + {{\cos }^4}at} \right)dt} }} = L?$$$
A
$$a = 2,L = {{{e^{4\pi }} - 1} \over {{e^\pi } - 1}}$$
B
$$a = 2,L = {{{e^{4\pi }} + 1} \over {{e^\pi } + 1}}$$
C
$$a = 4,L = {{{e^{4\pi }} - 1} \over {{e^\pi } - 1}}$$
D
$$a = 4,L = {{{e^{4\pi }} + 1} \over {{e^\pi } + 1}}$$
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