1
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let C be the set of all complex numbers. Let

$${S_1} = \{ z \in C||z - 3 - 2i{|^2} = 8\} $$

$${S_2} = \{ z \in C|{\mathop{\rm Re}\nolimits} (z) \ge 5\} $$ and

$${S_3} = \{ z \in C||z - \overline z | \ge 8\} $$.

Then the number of elements in $${S_1} \cap {S_2} \cap {S_3}$$ is equal to :
A
1
B
0
C
2
D
Infinite
2
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the area of the bounded region
$$R = \left\{ {(x,y):\max \{ 0,{{\log }_e}x\} \le y \le {2^x},{1 \over 2} \le x \le 2} \right\}$$ is ,
$$\alpha {({\log _e}2)^{ - 1}} + \beta ({\log _e}2) + \gamma $$, then the value of $${(\alpha + \beta - 2\lambda )^2}$$ is equal to :
A
8
B
2
C
4
D
1
3
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $${1 \over 3}$$ and the distance of the nearer focus from this directrix is $${8 \over {\sqrt {53} }}$$, then the equation of the other directrix can be :
A
11x + 7y + 8 = 0 or 11x + 7y $$-$$ 15 = 0
B
11x $$-$$ 7y $$-$$ 8 = 0 or 11x + 7y + 15 = 0
C
2x $$-$$ 7y + 29 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
D
2x $$-$$ 7y $$-$$ 39 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
4
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the coefficients of x7 in $${\left( {{x^2} + {1 \over {bx}}} \right)^{11}}$$ and x$$-$$7 in $${\left( {{x} - {1 \over {bx^2}}} \right)^{11}}$$, b $$\ne$$ 0, are equal, then the value of b is equal to :
A
2
B
$$-$$1
C
1
D
$$-$$2
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