1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let $$\alpha$$ and $$\beta$$ be the roots of the quadratic equation x2 sin $$\theta$$ – x(sin $$\theta$$ cos $$\theta$$ + 1) + cos $$\theta$$ = 0 (0 < $$\theta$$ < 45o), and $$\alpha$$ < $$\beta$$. Then $$\sum\limits_{n = 0}^\infty {\left( {{\alpha ^n} + {{{{\left( { - 1} \right)}^n}} \over {{\beta ^n}}}} \right)}$$ is equal to :
A
$${1 \over {1 + \cos \theta }} + {1 \over {1 - \sin \theta }}$$
B
$${1 \over {1 - \cos \theta }} + {1 \over {1 + \sin \theta }}$$
C
$${1 \over {1 - \cos \theta }} - {1 \over {1 + \sin \theta }}$$
D
$${1 \over {1 + \cos \theta }} - {1 \over {1 - \sin \theta }}$$
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is
A
$$-$$ 81
B
$$-$$ 300
C
100
D
144
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The value of $$\lambda$$ such that sum of the squares of the roots of the quadratic equation, x2 + (3 – $$\lambda$$)x + 2 = $$\lambda$$ has the least value is -
A
1
B
2
C
$${{15} \over 8}$$
D
$${4 \over 9}$$
4
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
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