1
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
$$\sqrt 2 $$
B
$$ - \sqrt 2 $$
C
$${1 \over {\sqrt 2 }}$$
D
$$ - {1 \over {\sqrt 2 }}$$
2
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$2(2{e^4} - 1)$$
3
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of the absolute minimum and the absolute maximum values of the

function f(x) = |3x $$-$$ x2 + 2| $$-$$ x in the interval [$$-$$1, 2] is :

A
$${{\sqrt {17} + 3} \over 2}$$
B
$${{\sqrt {17} + 5} \over 2}$$
C
5
D
$${{9 - \sqrt {17} } \over 2}$$
4
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let S be the set of all the natural numbers, for which the line $${x \over a} + {y \over b} = 2$$ is a tangent to the curve $${\left( {{x \over a}} \right)^n} + {\left( {{y \over b}} \right)^n} = 2$$ at the point (a, b), ab $$\ne$$ 0. Then :

A
S = $$\phi$$
B
n(S) = 1
C
S = {2k : k $$\in$$ N}
D
S = N
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