1
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$S$$ be the set of all non-zero real numbers $$\alpha$$ such that the quadratic equation $$\alpha {x^2} - x + \alpha = 0$$ has two distinct real roots $${x_1}$$ and $${x_2}$$ satisfying the inequality $$\left| {{x_1} - {x_2}} \right| < 1.$$ Which of the following intervals is (are) $$a$$ subset(s) os $$S$$?
A
$$\left( { - {1 \over 2} - {1 \over {\sqrt 5 }}} \right)$$
B
$$\left( { - {1 \over {\sqrt 5 }},0} \right)$$
C
$$\left( {0,{1 \over {\sqrt 5 }}} \right)$$
D
$$\left( {{1 \over {\sqrt 5 }},{1 \over 2}} \right)$$
2
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is
3
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
The coefficient of $${x^9}$$ in the expansion of (1 + x) (1 + $${x^2)}$$ (1 + $${x^3}$$) ....$$(1 + {x^{100}})$$ is
4
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $${E_1}$$ and $${E_2}$$ be two ellipses whose centres are at the origin. The major axes of $${E_1}$$ and $${E_2}$$ lie along the $$x$$-axis and the $$y$$-axis, respectively. Let $$S$$ be the circle $${x^2} + {\left( {y - 1} \right)^2} = 2$$. The straight line $$x+y=3$$ touches the curves $$S$$, $${E_1}$$ and $${E_2}$$ at $$P, Q$$ and $$R$$ respectively. Suppose that $$PQ = PR = {{2\sqrt 2 } \over 3}$$. If $${e_1}$$ and $${e_2}$$ are the eccentricities of $${E_1}$$ and $${E_2}$$, respectively, then the correct expression(s) is (are)
A
$$\mathop e\nolimits_1^2 + \mathop e\nolimits_2^2 = {{43} \over {40}}$$
B
$${e_1}{e_2} = {{\sqrt 7 } \over {2\sqrt {10} }}$$
C
$$\left| {\mathop e\nolimits_1^2 + \mathop e\nolimits_2^2 } \right| = {5 \over 8}$$
D
$${e_1}{e_2} = {{\sqrt 3 } \over 4}$$
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