1
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+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
$${1 \over 12}$$
2
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+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)
3
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+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
$$- {1 \over {\sqrt 2 }}$$
4
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let f, g : R $$\to$$ R be two real valued functions defined as $$f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$$ and $$g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$$, where k1 and k2 are real constants. If (gof) is differentiable at x = 0, then (gof) ($$-$$ 4) + (gof) (4) is equal to :

A
$$4({e^4} + 1)$$
B
$$2(2{e^4} + 1)$$
C
$$4{e^4}$$
D
$$2(2{e^4} - 1)$$
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