1
JEE Advanced 2020 Paper 1 Offline
+3
-1 Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x $$-$$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 $$-$$ 20x + 2020. Then the value of

ac(a $$-$$ c) + ad(a $$-$$ d) + bc(b $$-$$ c) + bd(b $$-$$ d) is
A
0
B
8000
C
8080
D
16000
2
JEE Advanced 2017 Paper 2 Offline
+3
-0
Let p, q be integers and let $$\alpha$$, $$\beta$$ be the roots of the equation, x2 $$-$$ x $$-$$ 1 = 0 where $$\alpha$$ $$\ne$$ $$\beta$$. For n = 0, 1, 2, ........, let an = p$$\alpha$$n + q$$\beta$$n.

FACT : If a and b are rational numbers and a + b$$\sqrt 5$$ = 0, then a = 0 = b.
a12 = ?
A
a11 + 2a10
B
2a11 + a10
C
a11 $$-$$ a10
D
a11 + a10
3
JEE Advanced 2017 Paper 2 Offline
+3
-0
Let p, q be integers and let $$\alpha$$, $$\beta$$ be the roots of the equation, x2 $$-$$ x $$-$$ 1 = 0 where $$\alpha$$ $$\ne$$ $$\beta$$. For n = 0, 1, 2, ........, let an = p$$\alpha$$n + q$$\beta$$n.

FACT : If a and b are rational numbers and a + b$$\sqrt 5$$ = 0, then a = 0 = b.
If a4 = 28, then p + 2q =
A
14
B
7
C
21
D
12
4
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
$$0$$
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