1
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 Let f : R $$\to$$ R be defined by $$f(x) = {{{x^2} - 3x - 6} \over {{x^2} + 2x + 4}}$$

Then which of the following statements is (are) TRUE?
A
f is decreasing in the interval ($$-$$2, $$-$$1)
B
f is increasing in the interval (1, 2)
C
f is onto
D
Range of f is $$\left[ { - {3 \over 2},2} \right]$$
2
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2 Let f : R $$\to$$ R and g : R $$\to$$ R be functions
satisfying f(x + y) = f(x) + f(y) + f(x)f(y)
and f(x) = xg(x) for all x, y$$\in$$R.
If $$\mathop {\lim }\limits_{x \to 0} g(x) = 1$$, then which of the following statements is/are TRUE?
A
f is differentiable at every x$$\in$$R
B
If g(0) = 1, then g is differentiable at every x$$\in$$R
C
The derivative f'(1) is equal to 1
D
The derivative f'(0) is equal to 1
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2 Let the function f : R $$\to$$ R be defined by f(x) = x3 $$-$$ x2 + (x $$-$$ 1)sin x and let g : R $$\to$$ R be an arbitrary function. Let fg : R $$\to$$ R be the product function defined by (fg)(x) = f(x)g(x). Then which of the following statements is/are TRUE?
A
If g is continuous at x = 1, then fg is differentiable at x = 1
B
If f g is differentiable at x = 1, then g is continuous at x = 1
C
If g is differentiable at x = 1, then fg is differentiable at x = 1
D
If f g is differentiable at x = 1, then g is differentiable at x = 1
4
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1 For $$a \in R,\,|a|\, > 1$$, let

$$\mathop {\lim }\limits_{n \to \infty } \left( {{{1 + \root 3 \of 2 + ...\root 3 \of n } \over {{n^{7/3}}\left( {{1 \over {{{(an + 1)}^2}}} + {1 \over {{{(an + 2)}^2}}} + ... + {1 \over {{{(an + n)}^2}}}} \right)}}} \right) = 54$$
A
$$-$$6
B
$$-$$7
C
8
D
$$-$$9
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