NTA JEE Main 9th April 2016 Online

If the equations $$x^2 + bx - 1 = 0$$ and $$x^2 + x + b = 0$$ have a common root different from $$-1$$, then $$|b|$$ is equal to:

The point represented by $$2 + i$$ in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there $$2\sqrt{2}$$ units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by:

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is:

Let $$x$$, $$y$$, $$z$$ be positive real numbers such that $$x + y + z = 12$$ and $$x^3y^4z^5 = (0.1)(600)^3$$. Then $$x^3 + y^3 + z^3$$ is equal to

The value of $$\sum_{r=1}^{15} r^2 \left(\frac{^{15}C_r}{{}^{15}C_{r-1}}\right)$$ is equal to:

For $$x \in R$$, $$x \neq -1$$, if $$(1+x)^{2016} + x(1+x)^{2015} + x^2(1+x)^{2014} + \ldots + x^{2016} = \sum_{i=0}^{2016} a_i x_i$$, then $$a_{17}$$ is equal to

If $$m$$ and $$M$$ are the minimum and the maximum values of $$4 + \frac{1}{2}\sin^2 2x - 2\cos^4 x$$, $$x \in R$$, then $$M - m$$ is equal to:

The number of $$x \in [0, 2\pi]$$ for which $$\left|\sqrt{2\sin^4 x + 18\cos^2 x} - \sqrt{2\cos^4 x + 18\sin^2 x}\right| = 1$$ is:

If a variable line drawn through the intersection of the lines $$\frac{x}{3} + \frac{y}{4} = 1$$ and $$\frac{x}{4} + \frac{y}{3} = 1$$, meets the coordinate axes at A and B, $$(A \neq B)$$, then the locus of the midpoint of AB is:

The point $$(2, 1)$$ is translated parallel to the line $$L : x - y = 4$$ by $$2\sqrt{3}$$ units. If the new point $$Q$$ lies in the third quadrant, then the equation of the line passing through $$Q$$ and perpendicular to $$L$$ is