NTA JEE Main 3rd April 2016 Offline

Let $$P$$ be the point on the parabola, $$y^2 = 8x$$ which is at a minimum distance from the center $$C$$ of the circle, $$x^2 + (y+6)^2 = 1$$. Then the equation of the circle, passing through $$C$$ and having its center at $$P$$ is

The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is

$$\lim_{n \to \infty} \left(\frac{(n+1)(n+2)\ldots 3n}{n^{2n}}\right)^{1/n}$$ is equal to

Let $$P = \lim_{x \to 0^+} \left(1 + \tan^2\sqrt{x}\right)^{1/2x}$$, then $$\log P$$ is equal to

The Boolean Expression $$(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$$ is equivalent to

If the standard deviation of the numbers 2, 3, $$a$$ and 11 is 3.5, then which of the following is true?

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point $$A$$ on the path, he observes that the angle of elevation of the top of the pillar is $$30°$$. After walking for 10 minutes from $$A$$ in the same direction, at a point $$B$$, he observes that the angle of elevation of the top of the pillar is $$60°$$. Then the time taken (in minutes) by him, from $$B$$ to reach the pillar, is

If $$A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$$ and $$A \cdot adj A = A A^T$$, then $$5a + b$$ is equal to

The system of linear equations
$$x + \lambda y - z = 0$$
$$\lambda x - y - z = 0$$
$$x + y - \lambda z = 0$$
has a non-trivial solution for

If $$f(x) + 2f\left(\frac{1}{x}\right) = 3x$$, $$x \neq 0$$, and $$S = \{x \in R : f(x) = f(-x)\}$$, then $$S$$