1
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

Let a be an integer such that $$\mathop {\lim }\limits_{x \to 7} {{18 - [1 - x]} \over {[x - 3a]}}$$ exists, where [t] is greatest integer $$\le$$ t. Then a is equal to :

A
$$-$$6
B
$$-$$2
C
2
D
6
2
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

$$\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}$$ is equal to :

A
$${1 \over 3}$$
B
$${1 \over 4}$$
C
$${1 \over 6}$$
D
$${1 \over 12}$$
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

Let f(x) = min {1, 1 + x sin x}, 0 $$\le$$ x $$\le$$ 2$$\pi$$. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

A
(2, 0)
B
(1, 0)
C
(1, 1)
D
(2, 1)
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

$$\mathop {\lim }\limits_{x \to {1 \over {\sqrt 2 }}} {{\sin ({{\cos }^{ - 1}}x) - x} \over {1 - \tan ({{\cos }^{ - 1}}x)}}$$ is equal to :

A
$$\sqrt 2$$
B
$$- \sqrt 2$$
C
$${1 \over {\sqrt 2 }}$$
D
$$- {1 \over {\sqrt 2 }}$$
EXAM MAP
Medical
NEET