JEE Main 2019 (Online) 12th January Morning Slot | Limits, Continuity and Differentiability Question 138 | Mathematics

JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)

-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 :

4$$\int\limits_0^a \, $$f(x)dx

$$-$$ 3$$\int\limits_0^a \, $$f(x)dx

$$\int\limits_0^a \, $$f(x)dx

2$$\int\limits_0^a \, $$f(x)dx

JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to \pi /4} {{{{\cot }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}$$ is :

$$8\sqrt 2 $$

$$4\sqrt 2 $$

JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)

-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 ?

$$\left\{ { - {\pi \over 2}, - {\pi \over 4},{\pi \over 4},{\pi \over 2}} \right\}$$

$$\left\{ { - {{3\pi } \over 4}, - {\pi \over 2},{\pi \over 2},{{3\pi } \over 4}} \right\}$$

$$\left\{ { - {\pi \over 4},0,{\pi \over 4}} \right\}$$

$$\left\{ { - {{3\pi } \over 4}, - {\pi \over 4},{{3\pi } \over 4},{\pi \over 4}} \right\}$$

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)

-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 :

{0, $$\pi $$}

$$\phi $$ (an empty set)

{ r }

{0}

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