1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{x \to 2} \left( {\sum\limits_{n = 1}^9 {{x \over {n(n + 1){x^2} + 2(2n + 1)x + 4}}} } \right)$$ is equal to :
A
$${9 \over {44}}$$
B
$${5 \over {24}}$$
C
$${1 \over 5}$$
D
$${7 \over {36}}$$
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
The value of

$$\mathop {\lim }\limits_{x \to 0} \left( {{x \over {\root 8 \of {1 - \sin x} - \root 8 \of {1 + \sin x} }}} \right)$$ is equal to :
A
0
B
4
C
$$-$$4
D
$$-$$1
4
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let $$f:[0,\infty ) \to [0,3]$$ be a function defined by

$$f(x) = \left\{ {\matrix{ {\max \{ \sin t:0 \le t \le x\} ,} & {0 \le x \le \pi } \cr {2 + \cos x,} & {x > \pi } \cr } } \right.$$

Then which of the following is true?
A
f is continuous everywhere but not differentiable exactly at one point in (0, $$\infty$$)
B
f is differentiable everywhere in (0, $$\infty$$)
C
f is not continuous exactly at two points in (0, $$\infty$$)
D
f is continuous everywhere but not differentiable exactly at two points in (0, $$\infty$$)
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