1
JEE Main 2019 (Online) 12th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then $$\int\limits_0^a \, $$f(x) g(x) dx is equal to :
A
4$$\int\limits_0^a \, $$f(x)dx
B
$$-$$ 3$$\int\limits_0^a \, $$f(x)dx
C
$$\int\limits_0^a \, $$f(x)dx
D
2$$\int\limits_0^a \, $$f(x)dx
2
JEE Main 2019 (Online) 12th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to \pi /4} {{{{\cot }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}$$ is :
A
$$8\sqrt 2 $$
B
4
C
$$4\sqrt 2 $$
D
8
3
JEE Main 2019 (Online) 12th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let S be the set of all points in (–$$\pi $$, $$\pi $$) at which the function, f(x) = min{sin x, cos x} is not differentiable. Then S is a subset of which of the following ?
A
$$\left\{ { - {\pi \over 2}, - {\pi \over 4},{\pi \over 4},{\pi \over 2}} \right\}$$
B
$$\left\{ { - {{3\pi } \over 4}, - {\pi \over 2},{\pi \over 2},{{3\pi } \over 4}} \right\}$$
C
$$\left\{ { - {\pi \over 4},0,{\pi \over 4}} \right\}$$
D
$$\left\{ { - {{3\pi } \over 4}, - {\pi \over 4},{{3\pi } \over 4},{\pi \over 4}} \right\}$$
4
JEE Main 2019 (Online) 11th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let K be the set of all real values of x where the function f(x) = sin |x| – |x| + 2(x – $$\pi $$) cos |x| is not differentiable. Then the set K is equal to :
A
{0, $$\pi $$}
B
$$\phi $$ (an empty set)
C
{ r }
D
{0}
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