Trigonometry
Inverse Trigonometric Functions
MCQ (Single Correct Answer)Subjective
1
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

The function $$f(x) = \log \left( {{{1 + x} \over {1 - x}}} \right)$$ satisfies the equation

A
$$f(x + 2) - 2f(x + 1) + f(x) = 0$$
B
$$f(x) + f(x + 1) = f(x(x + 1))$$
C
$$f(x) + f(y) = f\left( {{{x + y} \over {1 + xy}}} \right)$$
D
$$f(x + y) = f(x)f(y)$$
2
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

The equation ex + x $$-$$ 1 = 0 has, apart from x = 0

A
One other real root
B
Two real roots
C
No other real root
D
Infinite number of real roots
3
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

A mapping from IN to IN is defined as follows:

$$f:IN \to IN$$

$$f(n) = {(n + 5)^2},\,n \in IN$$

(IN is the set of natural numbers). Then

A
f is not one-to-one
B
f is onto
C
f is both one-to-one and onto
D
f is one-to-one but not onto
4
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

The domain of definition of the function $$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$ is

A
$$ - \infty < x \le 0$$
B
$$ - \infty < x \le {{e - 1} \over e}$$
C
$$ - \infty < x \le 1$$
D
$$x \ge 1 - e$$
WB JEE Subjects