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