NTA JEE Main 10th April 2023 Shift 2

Let $$S = \{z = x + iy: \frac{2z - 3i}{4z + 2i} \text{ is a real number}\}$$. Then which of the following is NOT correct?

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is

If $$S_n = 4 + 11 + 21 + 34 + 50 + \ldots$$ to $$n$$ terms, then $$\frac{1}{60}S_{29} - S_9$$ is equal to

Let the number $$(22)^{2022} + (2022)^{22}$$ leave the remainder $$\alpha$$ when divided by 3 and $$\beta$$ when divided by 7. Then $$(\alpha^2 + \beta^2)$$ is equal to

If the coefficients of $$x$$ and $$x^2$$ in $$(1 + x)^p(1 - x)^q$$ are 4 and -5 respectively, then $$2p + 3q$$ is equal to

Let $$S = \{x \in [-\frac{\pi}{2}, \frac{\pi}{2}]: 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10\}$$ and $$\beta = \sum_{x \in S} \tan^2 \frac{x}{3}$$, then $$\frac{1}{6}(\beta - 14)^2$$ is equal to

Let $$A$$ be the point (1, 2) and $$B$$ be any point on the curve $$x^2 + y^2 = 16$$. If the centre of the locus of the point $$P$$, which divides the line segment AB in the ratio 3:2 is the point $$C(\alpha, \beta)$$, then the length of the line segment $$AC$$ is

Let a circle of radius 4 be concentric to the ellipse $$15x^2 + 19y^2 = 285$$. Then the common tangents are inclined to the minor axis of the ellipse at the angle

The statement $$\sim p \vee \sim p \wedge q$$ is equivalent to

Let $$\mu$$ be the mean and $$\sigma$$ be the standard deviation of the distribution