1
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
A tangent and a normal are drawn at the point P(2, $$-$$4) on the parabola y2 = 8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that AQBP is a square, then 2a + b is equal to :
A
$$-$$16
B
$$-$$18
C
$$-$$12
D
$$-$$20
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let $${{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}$$, where A, B, C are angles of triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :
A
b2 $$-$$ a2 = a2 + c2
B
b2, c2, a2 are in A.P.
C
c2, a2, b2 are in A.P.
D
a2, b2, c2 are in A.P.
3
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
4
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
$${1 \over 12}$$
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