1
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Which of the following is not correct for relation R on the set of real numbers ?
A
(x, y) $$\in$$ R $$\Leftrightarrow$$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.
B
(x, y) $$\in$$ R $$\Leftrightarrow$$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.
C
(x, y) $$\in$$ R $$\Leftrightarrow$$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.
D
(x, y) $$\in$$ R $$\Leftrightarrow$$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.
2
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]
3
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
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\}$$
4
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}
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