1
JEE Advanced 2016 Paper 1 Offline
+3
-1
Let $$- {\pi \over 6} < \theta < - {\pi \over {12}}.$$ Suppose $${\alpha _1}$$ and $${\beta_1}$$ are the roots of the equation $${x^2} - 2x\sec \theta + 1 = 0$$ and $${\alpha _2}$$ and $${\beta _2}$$ are the roots of the equation $${x^2} + 2x\,\tan \theta - 1 = 0.$$ $$If\,{\alpha _1} > {\beta _1}$$ and $${\alpha _2} > {\beta _2},$$ then $${\alpha _1} + {\beta _2}$$ equals
A
$$2\left( {\sec \theta - \tan \theta } \right)$$
B
$$2\,\sec \,\theta$$
C
$$- 2\tan \theta$$
D
$$0$$
2
JEE Advanced 2014 Paper 2 Offline
+3
-1
The quadratic equation $$p(x)$$ $$= 0$$ with real coefficients has purely imaginary roots. Then the equation $$p(p(x))=0$$ has
A
one purely imaginary root
B
all real roots
C
two real and two purely imaginary roots
D
neither real nor purely imaginary roots
3
IIT-JEE 2012 Paper 2 Offline
+3
-1

Let $$\alpha$$(a) and $$\beta$$(a) be the roots of the equation $$(\root 3 \of {1 + a} - 1){x^2} + (\sqrt {1 + a} - 1)x + (\root 6 \of {1 + a} - 1) = 0$$ where $$a > - 1$$. Then $$\mathop {\lim }\limits_{a \to {0^ + }} \alpha (a)$$ and $$\mathop {\lim }\limits_{a \to {0^ + }} \beta (a)$$ are

A
$$- {5 \over 2}$$
B
$$- {1 \over 2}$$
C
$$- {7 \over 2}$$
D
$$- {9 \over 2}$$
4
IIT-JEE 2011 Paper 1 Offline
+4
-1
Let $$\alpha$$ and $$\beta$$ be the roots of $${x^2} - 6x - 2 = 0,$$ with $$\alpha > \beta .$$ If $${a_n} = {\alpha ^n} - {\beta ^n}$$ for $$\,n \ge 1$$ then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is
A
1
B
2
C
3
D
4
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