1
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
If $$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} - x + 1} - ax} \right) = b$$, then the ordered pair (a, b) is :
A
$$\left( {1,{1 \over 2}} \right)$$
B
$$\left( {1, - {1 \over 2}} \right)$$
C
$$\left( { - 1,{1 \over 2}} \right)$$
D
$$\left( { - 1, - {1 \over 2}} \right)$$
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-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 :
A
b2 + 4c
B
2(b2 + 4c)
C
2(b2 $$-$$ 4c)
D
b2 $$-$$ 4c
3
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
$${7 \over {36}}$$
4
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
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