1
JEE Main 2019 (Online) 12th April Morning Slot
+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
$${{21} \over {346}}$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
If $$\mathop {\lim }\limits_{x \to 1} {{{x^2} - ax + b} \over {x - 1}} = 5$$, then a + b is equal to :
A
1
B
- 4
C
- 7
D
5
3
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If $$\mathop {\lim }\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \mathop {\lim }\limits_{x \to k} {{{x^3} - {k^3}} \over {{x^2} - {k^2}}}$$, then k is :
A
$${3 \over 2}$$
B
$${8 \over 3}$$
C
$${4 \over 3}$$
D
$${3 \over 8}$$
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Let f : R $$\to$$ R be differentiable at c $$\in$$ R and f(c) = 0. If g(x) = |f(x)| , then at x = c, g is :
A
differentiable if f '(c) = 0
B
differentiable if f '(c) $$\ne$$ 0
C
not differentiable
D
not differentiable if f '(c) = 0
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