1
WB JEE 2021
+1
-0.25
Let f : R $$\to$$ R be given by f(x) = | x2 $$-$$ 1 |, x$$\in$$R. Then,
A
f has a local minimum at x = $$\pm$$ 1 but no local maximum.
B
f has a local minimum at x = 0 but no local minimum.
C
f has a local minima at x = $$\pm$$ 1 and a local maxima at x = 0.
D
f has neither a local maxima nor a local minima at any point.
2
WB JEE 2021
+1
-0.25
f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =
A
$$-$$15
B
22
C
11
D
0
3
WB JEE 2021
+1
-0.25
Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect
A
once in (0, 1) but never in (1, $$\infty$$)
B
once in (0, 1) and once in (e2, $$\infty$$)
C
once in (0, 1) and once in (e, e2)
D
more than twice in (0, $$\infty$$)
4
WB JEE 2021
+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, $$\infty$$)
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