NTA JEE Main 9th January 2020 Shift 2

If $$A = \{x \in R : |x| < 2\}$$ and $$B = \{x \in R : |x - 2| \ge 3\}$$; then:

Let $$a, b \in R, a \ne 0$$ be such that the equation, $$ax^2 - 2bx + 5 = 0$$ has a repeated root $$\alpha$$, which is also a root of the equation, $$x^2 - 2bx - 10 = 0$$. If $$\beta$$ is the other root of this equation, then $$\alpha^2 + \beta^2$$ is equal to:

If $$z$$ is a complex number satisfying $$|Re(z)| + |Im(z)| = 4$$, then $$|z|$$ cannot be:

Let $$a_n$$ be the $$n^{th}$$ term of a G.P. of positive terms. If $$\sum_{n=1}^{100} a_{2n+1} = 200$$ and $$\sum_{n=1}^{100} a_{2n} = 100$$, then $$\sum_{n=1}^{200} a_n$$ is equal to:

If $$x = \sum_{n=0}^{\infty} (-1)^n \tan^{2n}\theta$$ and $$y = \sum_{n=0}^{\infty} \cos^{2n}\theta$$, for $$0 < \theta < \frac{\pi}{4}$$, then:

In the expansion of $$\left(\frac{x}{\cos\theta} + \frac{1}{x\sin\theta}\right)^{16}$$, if $$l_1$$ is the least value of the term independent of $$x$$ when $$\frac{\pi}{8} \le \theta \le \frac{\pi}{4}$$ and $$l_2$$ is the least value of the term independent of $$x$$ when $$\frac{\pi}{16} \le \theta \le \frac{\pi}{8}$$, then the ratio $$l_2 : l_1$$ is equal to:

If one end of a focal chord $$AB$$ of the parabola $$y^2 = 8x$$ is at $$A\left(\frac{1}{2}, -2\right)$$, then the equation of the tangent to it at $$B$$ is:

The length of the minor axis (along y-axis) of an ellipse in the standard form is $$\frac{4}{\sqrt{3}}$$. If this ellipse touches the line $$x + 6y = 8$$ then its eccentricity is:

If $$p \to (p \wedge \sim q)$$ is false, then the truth values of $$p$$ and $$q$$ are respectively:

The following system of linear equations
$$7x + 6y - 2z = 0$$
$$3x + 4y + 2z = 0$$
$$x - 2y - 6z = 0$$, has: