JEE Main 2021 (Online) 31st August Evening Shift | Functions Question 60 | Mathematics

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)

-1

The domain of the function

$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$$ is :

$$\left[ {0,{1 \over 4}} \right]$$

$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$

$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\} $$

$$\left[ {0,{1 \over 2}} \right]$$

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)

-1

Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3) is equal to :

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

Which of the following is not correct for relation R on the set of real numbers ?

(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

Let [t] denote the greatest integer less than or equal to t. Let
f(x) = x $$-$$ [x], g(x) = 1 $$-$$ x + [x], and h(x) = min{f(x), g(x)}, x $$\in$$ [$$-$$2, 2]. Then h is :

continuous in [$$-$$2, 2] but not differentiable at more than
four points in ($$-$$2, 2)

not continuous at exactly three points in [$$-$$2, 2]

continuous in [$$-$$2, 2] but not differentiable at exactly
three points in ($$-$$2, 2)

not continuous at exactly four points in [$$-$$2, 2]

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