1
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

A
f(x) = 0 has at least one real root
B
f(x) = 0 has no real root
C
f(x) = 0 has at least one positive root
D
f(x) = 0 has at least one negative root
2
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then

A
p(x) has at least two real roots
B
p(x) has only one positive real root
C
p(x) may have negative real root
D
p(x) has infinitely many real roots
3
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is
A
periodic with period T1 + T2
B
non periodic
C
periodic with the period T1
D
periodic when T1 = T2
4
WB JEE 2018
MCQ (More than One Correct Answer)
+2
-0
Consider the function $$y = {\log _a}(x + \sqrt {{x^2} + 1} ),a > 0,a \ne 1$$. The inverse of the function
A
does not exist
B
is $$x = {\log _{1/a}}(y + \sqrt {{y^2} + 1} )$$
C
is $$x = \sinh (y\log a)$$
D
is $$x = \cosh \left( { - y\log {1 \over a}} \right)$$
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