WB JEE 2021 | Functions Question 28 | Mathematics

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WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Consider the functions f₁(x) = x, f₂(x) = 2 + log_e x, x > 0. The graphs of the functions intersect

once in (0, 1) but never in (1, $$\infty$$)

once in (0, 1) and once in (e², $$\infty$$)

once in (0, 1) and once in (e, e²)

more than twice in (0, $$\infty$$)

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be defined by f(x) = 1 + $$\sqrt x $$. Then

f has no fixed point in [1, $$\infty$$)

f has unique fixed point in [1, $$\infty$$)

f has to fixed points in [1, $$\infty$$)

f has infinitely many fixed points in [1, $$\infty$$)

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then

f has no extrema at x = 0

f has minima at x = 0

f has maxima at x = 0

f' exists at 0

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is

$$x > - 1$$

$$( - 1,\infty )\backslash \{ 0\} $$

$$\left( {0,{{\sqrt 5 - 1} \over 2}} \right]$$

$$\left[ {{{1 - \sqrt 5 } \over 2},0} \right)$$

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