1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x $$\in$$ R, is always positive, is :
A
7
B
8
C
3
D
6
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
If $$\lambda$$ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m – 4)x + 2 = 0, then the least value of m for which $$\lambda + {1 \over \lambda } = 1,$$ is
A
$$- 2 + \sqrt 2$$
B
4$$-$$3$$\sqrt 2$$
C
2 $$-$$ $$\sqrt 3$$
D
4 $$-$$ 2$$\sqrt 3$$
3
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
$${1 \over {1 + \cos \theta }} - {1 \over {1 - \sin \theta }}$$
4
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
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