NTA JEE Main 9th April 2019 Shift 2

The area (in sq. units) of the smaller of the two circles that touch the parabola, $$y^2 = 4x$$ at the point $$(1, 2)$$ and the x-axis is:

If the tangent to the parabola $$y^2 = x$$ at a point $$(\alpha, \beta)$$, $$(\beta > 0)$$ is also a tangent to the ellipse, $$x^2 + 2y^2 = 1$$, then $$\alpha$$ is equal to:

If $$f(x) = [x] - \left[\frac{x}{4}\right]$$, $$x \in R$$, where $$[x]$$ denotes the greatest integer function, then:

If $$p \Rightarrow (q \lor r)$$ is False, then the truth values of p, q, r are respectively, (where T is True and F is False)

The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then $$\frac{y}{x}$$ is equal to:

Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15° with the ground. Then the distance (in m) between the poles, is:

The total number of matrices $$A = \begin{pmatrix} 0 & 2y & 1 \\ 2x & y & -1 \\ 2x & -y & 1 \end{pmatrix}$$, $$(x, y \in R, x \neq y)$$ for which $$A^TA = 3I_3$$ is:

If the system of equations $$2x + 3y - z = 0$$, $$x + ky - 2z = 0$$ and $$2x - y + z = 0$$ has a non-trivial solution $$(x, y, z)$$, then $$\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$$ is equal to:

The domain of the definition of the function $$f(x) = \frac{1}{4 - x^2} + \log_{10}(x^3 - x)$$ is:

If the function $$f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}$$ is continuous at $$x = 5$$, then the value of $$a - b$$ is: