1
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let a tangent to the curve $$\mathrm{y^2=24x}$$ meet the curve $$xy = 2$$ at the points A and B. Then the mid points of such line segments AB lie on a parabola with the :

A
length of latus rectum 2
B
directrix 4x = $$-$$3
C
directrix 4x = 3
D
length of latus rectum $$\frac{3}{2}$$
2
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{p,q\in\mathbb{R}}$$ and $${\left( {1 - \sqrt 3 i} \right)^{200}} = {2^{199}}(p + iq),i = \sqrt { - 1} $$ then $$\mathrm{p+q+q^2}$$ and $$\mathrm{p-q+q^2}$$ are roots of the equation.

A
$${x^2} + 4x - 1 = 0$$
B
$${x^2} - 4x + 1 = 0$$
C
$${x^2} + 4x + 1 = 0$$
D
$${x^2} - 4x - 1 = 0$$
3
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$$x + y + z = 1$$

$$2x + \mathrm{N}y + 2z = 2$$

$$3x + 3y + \mathrm{N}z = 3$$

has unique solution is $${k \over 6}$$, then the sum of value of k and all possible values of N is :

A
18
B
21
C
20
D
19
4
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The relation $$\mathrm{R = \{ (a,b):\gcd (a,b) = 1,2a \ne b,a,b \in \mathbb{Z}\}}$$ is :

A
reflexive but not symmetric
B
transitive but not reflexive
C
symmetric but not transitive
D
neither symmetric nor transitive
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