1
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let the function, ƒ:[-7, 0]$$ \to $$R be continuous on [-7,0] and differentiable on (-7, 0). If ƒ(-7) = - 3 and ƒ'(x) $$ \le $$ 2, for all x $$ \in $$ (-7,0), then for all such functions ƒ, ƒ(-1) + ƒ(0) lies in the interval:
A
$$\left[ { - 6,20} \right]$$
B
$$\left( { - \infty ,\left. {20} \right]} \right.$$
C
$$\left[ { - 3,11} \right]$$
D
$$\left( { - \infty ,\left. {11} \right]} \right.$$
2
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{x + 2\sin x} \over {\sqrt {{x^2} + 2\sin x + 1} - \sqrt {{{\sin }^2}x - x + 1} }}$$ is :
A
6
B
1
C
3
D
2
3
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let f(x) = 5 – |x – 2| and g(x) = |x + 1|, x $$ \in $$ R. If f(x) attains maximum value at $$\alpha $$ and g(x) attains minimum value at $$\beta $$, then $$\mathop {\lim }\limits_{x \to -\alpha \beta } {{\left( {x - 1} \right)\left( {{x^2} - 5x + 6} \right)} \over {{x^2} - 6x + 8}}$$ is equal to :
A
$${1 \over 2}$$
B
$$-{1 \over 2}$$
C
$${3 \over 2}$$
D
$$-{3 \over 2}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If $$\alpha $$ and $$\beta $$ are the roots of the equation 375x2 – 25x – 2 = 0, then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\alpha ^r}} + \mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\beta ^r}} $$ is equal to :
A
$${7 \over {116}}$$
B
$${{29} \over {348}}$$
C
$${1 \over {12}}$$
D
$${{21} \over {346}}$$
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