1
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
If $$f(x) = \left\{ {\matrix{ {{1 \over {|x|}}} & {;\,|x|\, \ge 1} \cr {a{x^2} + b} & {;\,|x|\, < 1} \cr } } \right.$$ is differentiable at every point of the domain, then the values of a and b are respectively :
A
$${1 \over 2},{1 \over 2}$$
B
$${1 \over 2}, - {3 \over 2}$$
C
$${5 \over 2}, - {3 \over 2}$$
D
$$- {1 \over 2},{3 \over 2}$$
2
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
The value of the limit

$$\mathop {\lim }\limits_{\theta \to 0} {{\tan (\pi {{\cos }^2}\theta )} \over {\sin (2\pi {{\sin }^2}\theta )}}$$ is equal to :
A
0
B
$$-$$$${1 \over 2}$$
C
$${1 \over 4}$$
D
$$-$$$${1 \over 4}$$
3
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
The value of $$\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}$$, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :
A
r
B
$${r \over 2}$$
C
0
D
2r
4
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
The value of
$$\mathop {\lim }\limits_{x \to {0^ + }} {{{{\cos }^{ - 1}}(x - {{[x]}^2}).{{\sin }^{ - 1}}(x - {{[x]}^2})} \over {x - {x^3}}}$$, where [ x ] denotes the greatest integer $$\le$$ x is :
A
$$\pi$$
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
0
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