1
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
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face occurs with probability $${1 \over 6} + x$$. All other faces occur with probability $${1 \over 6}$$. Note that opposite faces sum to 7 in any die. If 0 < x < $${1 \over 6}$$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is $${13 \over 96}$$, then the value of x is :
A
$${1 \over 16}$$
B
$${1 \over 8}$$
C
$${1 \over 9}$$
D
$${1 \over 12}$$
3
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
If x2 + 9y2 $$-$$ 4x + 3 = 0, x, y $$\in$$ R, then x and y respectively lie in the intervals :
A
$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$
B
$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and [1, 3]
C
[1, 3] and [1, 3]
D
[1, 3] and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$
4
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
$$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx} $$ is equal to :
A
6
B
8
C
5
D
10
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