NTA JEE Main 3rd September 2020 Shift 2

The set of all real values of $$\lambda$$ for which the quadratic equation $$(\lambda^2 + 1)x^2 - 4\lambda x + 2 = 0$$ always have exactly one root in the interval (0, 1) is:

If $$z_1, z_2$$ are complex numbers such that $$Re(z_1) = |z_1 - 1|$$ and $$Re(z_2) = |z_2 - 1|$$ and $$\arg(z_1 - z_2) = \frac{\pi}{6}$$, then $$Im(z_1 + z_2)$$ is equal to:

If the sum of the series $$20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5} + \ldots$$ up to $$n^{th}$$ term is 488 and the $$n^{th}$$ term is negative, then:

If the term independent of $$x$$ in the expansion of $$\left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9$$ is $$k$$, then $$18k$$ is equal to:

If a $$\triangle ABC$$ has vertices $$A(-1, 7)$$, $$B(-7, 1)$$ and $$C(5, -5)$$, then its orthocentre has coordinates:

Let the latus rectum of the parabola $$y^2 = 4x$$ be the common chord to the circles $$C_1$$ and $$C_2$$ each of them having radius $$2\sqrt{5}$$. Then, the distance between the centres of the circles $$C_1$$ and $$C_2$$ is:

Let $$e_1$$ and $$e_2$$ be the eccentricities of the ellipse $$\frac{x^2}{25} + \frac{y^2}{b^2} = 1$$ $$(b < 5)$$ and the hyperbola $$\frac{x^2}{16} - \frac{y^2}{b^2} = 1$$ respectively satisfying $$e_1 e_2 = 1$$. If $$\alpha$$ and $$\beta$$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $$(\alpha, \beta)$$ is equal to:

$$\lim_{x \to a}\frac{(a+2x)^{\frac{1}{3}} - (3x)^{\frac{1}{3}}}{(3a+x)^{\frac{1}{3}} - (4x)^{\frac{1}{3}}}$$ $$(a \neq 0)$$ is equal to:

Let $$p$$, $$q$$, $$r$$ be three statements such that the truth value of $$(p \wedge q) \to (\sim q \vee r)$$ is $$F$$. Then the truth values of $$p$$, $$q$$, $$r$$ are respectively:

Let $$x_i (1 \leq i \leq 10)$$ be ten observations of a random variable X. If $$\sum_{i=1}^{10}(x_i - p) = 3$$ and $$\sum_{i=1}^{10}(x_i - p)^2 = 9$$ where $$0 \neq p \in R$$, then the standard deviation of these observations is: