1
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
$${3 \over 8}$$
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If$$f(x) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}}}} & {,x > 0} \cr } } \right.$$
is continuous at x = 0, then the ordered pair (p, q) is equal to
A
$$\left( { - {3 \over 2}, - {1 \over 2}} \right)$$
B
$$\left( { - {1 \over 2},{3 \over 2}} \right)$$
C
$$\left( { - {3 \over 2}, {1 \over 2}} \right)$$
D
$$\left( { {5 \over 2}, {1 \over 2}} \right)$$
3
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
4
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If $$f(x) = [x] - \left[ {{x \over 4}} \right]$$ ,x $$\in$$ 4 , where [x] denotes the greatest integer function, then
A
Both $$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ and $$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ exist but are not equal
B
f is continuous at x = 4
C
$$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ exists but $$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ does not exist
D
$$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ exists but $$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ does not exist
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