NTA JEE Main 25th June 2022 Shift 2
For the following questions answer them individually
NTA JEE Main 25th June 2022 Shift 2 - Question 61
Let $$A = \{x \in R : |x + 1| < 2\}$$ and $$B = \{x \in R : |x - 1| \geq 2\}$$. Then which one the following statements is NOT true?
NTA JEE Main 25th June 2022 Shift 2 - Question 62
Let $$a, b \in R$$ be such that the equation $$ax^2 - 2bx + 15 = 0$$ has repeated root $$\alpha$$ and if $$\alpha$$ and $$\beta$$ are the roots of the equation $$x^2 - 2bx + 21 = 0$$, then $$\alpha^2 + \beta^2$$ is equal to:
NTA JEE Main 25th June 2022 Shift 2 - Question 63
Let $$z_1$$ and $$z_2$$ be two complex numbers such that $$\bar{z}_1 = iz_2$$ and $$\arg\frac{z_1}{z_2} = \pi$$, then the argument of $$z_1$$ is
NTA JEE Main 25th June 2022 Shift 2 - Question 64
The sum $$1 + 2 \cdot 3 + 3 \cdot 3^2 + \ldots + 10 \cdot 3^9$$ is equal to
NTA JEE Main 25th June 2022 Shift 2 - Question 65
The coefficient of $$x^{101}$$ in the expression
$$5 + x^{500} + x5 + x^{499} + x^2(5 + x)^{498} + \ldots + x^{500}, x > 0$$ is
NTA JEE Main 25th June 2022 Shift 2 - Question 66
The value of $$2\sin 12° - \sin 72°$$ is
NTA JEE Main 25th June 2022 Shift 2 - Question 67
A circle touches both the $$y$$-axis and the line $$x + y = 0$$. Then the locus of its center is
NTA JEE Main 25th June 2022 Shift 2 - Question 68
The line $$y = x + 1$$ meets the ellipse $$\frac{x^2}{4} + \frac{y^2}{2} = 1$$ at two points $$P$$ and $$Q$$. If $$r$$ is the radius of the circle with $$PQ$$ as diameter then $$(3r)^2$$ is equal to
NTA JEE Main 25th June 2022 Shift 2 - Question 69
$$\lim_{x \to \frac{\pi}{2}} {\tan^2 x(2\sin^2 x + 3\sin x + 4)^{\frac{1}{2}} - (\sin^2 x + 6\sin x + 2)^{\frac{1}{2}}}{2}$$ is equal to
NTA JEE Main 25th June 2022 Shift 2 - Question 70
The negation of the Boolean expression $$\sim q \wedge p \Rightarrow \sim p \vee q$$ is logically equivalent to
