1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c $$\ne$$ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is -
A
12
B
18
C
10
D
11
2
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
If both the roots of the quadratic equation x2 $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :
A
($$-$$5, $$-$$4)
B
(4, 5)
C
(5, 6)
D
(3, 4)
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
The number of all possible positive integral values of $$\alpha$$  for which the roots of the quadratic equation, 6x2 $$-$$ 11x + $$\alpha$$ = 0 are rational numbers is :
A
3
B
2
C
4
D
5
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let p, q and r be real numbers (p $$\ne$$ q, r $$\ne$$ 0), such that the roots of the equation $${1 \over {x + p}} + {1 \over {x + q}} = {1 \over r}$$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :
A
$${{{p^2} + {q^2}} \over 2}$$
B
p2 + q2
C
2(p2 + q2)
D
p2 + q2 + r2
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