NTA JEE Main 27th June 2022 Shift 2
For the following questions answer them individually
NTA JEE Main 27th June 2022 Shift 2 - Question 61
The number of points of intersection $$|z - (4+3i)| = 2$$ and $$|z| + |z-4| = 6, z \in C$$ is
NTA JEE Main 27th June 2022 Shift 2 - Question 62
Let for some real numbers $$\alpha$$ and $$\beta$$, $$a = \alpha - i\beta$$. If the system of equations $$4ix + (1+i)y = 0$$ and $$8\left(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3}\right)x + \bar{a}y = 0$$ has more than one solution then $$\frac{\alpha}{\beta}$$ is equal to
NTA JEE Main 27th June 2022 Shift 2 - Question 63
Let $$S = 2 + \frac{6}{7} + \frac{12}{7^2} + \frac{20}{7^3} + \frac{30}{7^4} + \ldots$$ then $$4S$$ is equal to
NTA JEE Main 27th June 2022 Shift 2 - Question 64
If $$a_1, a_2, a_3 \ldots$$ and $$b_1, b_2, b_3 \ldots$$ are A.P. and $$a_1 = 2, a_{10} = 3, a_1b_1 = 1 = a_{10}b_{10}$$ then $$a_4b_4$$ is equal to
NTA JEE Main 27th June 2022 Shift 2 - Question 65
$$\alpha = \sin 36°$$ is a root of which of the following equation
NTA JEE Main 27th June 2022 Shift 2 - Question 66
The set of values of $$k$$ for which the circle $$C : 4x^2 + 4y^2 - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$(1, -\frac{1}{3})$$ lies on or inside the circle $$C$$ is
NTA JEE Main 27th June 2022 Shift 2 - Question 67
If the equation of the parabola, whose vertex is at $$(5, 4)$$ and the directrix is $$3x + y - 29 = 0$$, is $$x^2 + ay^2 + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to
NTA JEE Main 27th June 2022 Shift 2 - Question 68
Which of the following statement is a tautology?
NTA JEE Main 27th June 2022 Shift 2 - Question 69
The mean and variance of the data $$4, 5, 6, 6, 7, 8, x, y$$ where $$x < y$$ are $$6$$ and $$\frac{9}{4}$$ respectively. Then $$x^4 + y^2$$ is equal to
NTA JEE Main 27th June 2022 Shift 2 - Question 70
Let $$A$$ and $$B$$ be two $$3 \times 3$$ matrices such that $$AB = I$$ and $$|A| = \frac{1}{8}$$ then $$|adj(B \cdot adj(2A))|$$ is equal to
