JEE Main 2021 (Online) 26th August Evening Shift | Functions Question 65 | Mathematics

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]

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :

$$\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )$$

$$\left[ { - {1 \over 2},0} \right) \cup [1,\infty )$$

$$\left( { - {1 \over 2},\infty } \right) - \{ 0\} $$

$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\} $$

JEE Main 2021 (Online) 26th August Morning Shift

MCQ (Single Correct Answer)

-1

Out of all patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

{80, 83, 86, 89}

{84, 86, 88, 90}

{79, 81, 83, 85}

{84, 87, 90, 93}

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the value of $$\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}} $$ is equal to :

cosec²(21) cos(20) cos(2)

sec²(1) sec(21) cos(20)

cosec²(1) cosec(21) sin(20)

sec²(21) sin(20) sin(2)

PREVIOUS NEXT