NTA JEE Main 9th April 2016 Online

A circle passes through $$(-2, 4)$$ and touches the y-axis at $$(0, 2)$$. Which one of the following equations can represent a diameter of this circle?

If the tangent at a point on the ellipse $$\frac{x^2}{27} + \frac{y^2}{3} = 1$$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is

Let $$a$$ and $$b$$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation $$9e^2 - 18e + 5 = 0$$. If $$S(5, 0)$$ is a focus and $$5x = 9$$ is the corresponding directrix of this hyperbola, then $$a^2 - b^2$$ is equal to

If $$f(x)$$ is a differentiable function in the interval $$(0, \infty)$$ such that $$f(1) = 1$$ and $$\lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1$$, for each $$x \gt 0$$, then $$f\left(\frac{3}{2}\right)$$ is equal to

If $$\lim_{x \to \infty} \left(1 + \frac{a}{x} - \frac{4}{x^2}\right)^{2x} = e^3$$, then $$a$$ is equal to

Consider the following two statements:
$$P$$: If 7 is an odd number, then 7 is divisible by 2.
$$Q$$: If 7 is a prime number, then 7 is an odd number.
If $$V_1$$ is the truth value of the contrapositive of $$P$$ and $$V_2$$ is the truth value of contrapositive of $$Q$$, then the ordered pair $$(V_1, V_2)$$ equals

If the mean deviation of the numbers $$1, 1+d, \ldots, 1+100d$$ from their mean is 255, then a value of $$d$$ is:

If $$P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$$, $$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$ and $$Q = PAP^T$$, then $$P^T Q^{2015} P$$ is:

The number of distinct real roots of the equation, $$\begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0$$ in the interval $$\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]$$ is:

For $$x \in R$$, $$x \neq 0$$, $$x \neq 1$$, let $$f_0(x) = \frac{1}{1-x}$$ and $$f_{n+1}(x) = f_0(f_n(x))$$, $$n = 0, 1, 2, \ldots$$. Then the value of $$f_{100}(3) + f_1\left(\frac{2}{3}\right) + f_2\left(\frac{3}{2}\right)$$ is equal to: