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

Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}} \over {{x^2} - 1}}$$.

Then the function fog is :

A
one-one but not onto
B
onto but not one-one
C
both one-one and onto
D
neither one-one nor onto
2
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :

A
(1, $$-$$3)
B
($$-$$1, 3)
C
(1, 3)
D
($$-$$1, $$-$$3)
3
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If $$A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$ and $$B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$, then $${A \over B}$$ is equal to :

A
$${{11} \over 9}$$
B
1
C
$$-$$$${{11} \over 9}$$
D
$$-$$$${{11} \over 3}$$
4
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
$${1 \over 3}$$
B
$${1 \over 4}$$
C
$${1 \over 6}$$
D
$${1 \over 12}$$
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