1
WB JEE 2021
MCQ (Single Correct Answer)
+2
-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
A
f has no fixed point in [1, $$\infty$$)
B
f has unique fixed point in [1, $$\infty$$)
C
f has to fixed points in [1, $$\infty$$)
D
f has infinitely many fixed points in [1, $$\infty$$)
2
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Let $$f(x) = 1 - \sqrt {({x^2})}$$, where the square root is to be taken positive, then
A
f has no extrema at x = 0
B
f has minima at x = 0
C
f has maxima at x = 0
D
f' exists at 0
3
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)}$$ is
A
$$x > - 1$$
B
$$( - 1,\infty )\backslash \{ 0\}$$
C
$$\left( {0,{{\sqrt 5 - 1} \over 2}} \right]$$
D
$$\left[ {{{1 - \sqrt 5 } \over 2},0} \right)$$
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Let $$A = \{ x \in R: - 1 \le x \le 1\}$$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then f is
A
injective but not surjective
B
surjective but not injective
C
neither injective nor surjective
D
bijective
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