1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-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 :
A
continuous in [$$-$$2, 2] but not differentiable at more than
four points in ($$-$$2, 2)
B
not continuous at exactly three points in [$$-$$2, 2]
C
continuous in [$$-$$2, 2] but not differentiable at exactly
three points in ($$-$$2, 2)
D
not continuous at exactly four points in [$$-$$2, 2]
2
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :
A
$$\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )$$
B
$$\left[ { - {1 \over 2},0} \right) \cup [1,\infty )$$
C
$$\left( { - {1 \over 2},\infty } \right) - \{ 0\}$$
D
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\}$$
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-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 :
A
{80, 83, 86, 89}
B
{84, 86, 88, 90}
C
{79, 81, 83, 85}
D
{84, 87, 90, 93}
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-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 :
A
cosec2(21) cos(20) cos(2)
B
sec2(1) sec(21) cos(20)
C
cosec2(1) cosec(21) sin(20)
D
sec2(21) sin(20) sin(2)
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