JEE Main 2021 (Online) 27th August Morning Shift | Limits, Continuity and Differentiability Question 44 | Mathematics

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

If $$\alpha$$, $$\beta$$ are the distinct roots of x² + bx + c = 0, then

$$\mathop {\lim }\limits_{x \to \beta } {{{e^{2({x^2} + bx + c)}} - 1 - 2({x^2} + bx + c)} \over {{{(x - \beta )}^2}}}$$ is equal to :

b² + 4c

2(b² + 4c)

2(b² $$-$$ 4c)

b² $$-$$ 4c

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-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 :

$${9 \over {44}}$$

$${5 \over {24}}$$

$${1 \over 5}$$

$${7 \over {36}}$$

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-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 :

$$-$$4

$$-$$1

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-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?

f is continuous everywhere but not differentiable exactly at one point in (0, $$\infty$$)

f is differentiable everywhere in (0, $$\infty$$)

f is not continuous exactly at two points in (0, $$\infty$$)

f is continuous everywhere but not differentiable exactly at two points in (0, $$\infty$$)

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