1
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
2
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
3
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R be a function. We say that f has

PROPERTY 1 if $$\mathop {\lim }\limits_{h \to 0} {{f(h) - f(0)} \over {\sqrt {|h|} }}$$ exists and is finite, and

PROPERTY 2 if $$\mathop {\lim }\limits_{h \to 0} {{f(h) - f(0)} \over {{h^2}}}$$ exists and is finite. Then which of the following options is/are correct?
A
f(x) = sin x has PROPERTY 2
B
f(x) = x2/3 has PROPERTY 1
C
f(x) = |x| has PROPERTY 1
D
f(x) = x|x| has PROPERTY 2
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R $$\to$$ R be given by

$$f(x) = \left\{ {\matrix{ {{x^5} + 5{x^4} + 10{x^3} + 10{x^2} + 3x + 1,} & {x < 0;} \cr {{x^2} - x + 1,} & {0 \le x < 1;} \cr {{2 \over 3}{x^3} - 4{x^2} + 7x - {8 \over 3},} & {1 \le x < 3;} \cr {(x - 2){{\log }_e}(x - 2) - x + {{10} \over 3},} & {x \ge 3;} \cr } } \right\}$$

Then which of the following options is/are correct?
A
f is increasing on ($$-$$$$\infty$$, 0)
B
f' is not differentiable at x = 1
C
f is onto
D
f' has a local maximum at x = 1
EXAM MAP
Medical
NEET