1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-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 :
A
$$\left[ {0,{1 \over 4}} \right]$$
B
$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\}$$
D
$$\left[ {0,{1 \over 2}} \right]$$
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-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 :
A
6
B
54
C
18
D
36
3
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.
4
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]
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