NTA JEE Main 3rd April 2016 Offline

For $$x \in R$$, $$f(x) = |\log 2 - \sin x|$$ and $$g(x) = f(f(x))$$, then

Consider $$f(x) = \tan^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right)$$, $$x \in \left(0, \frac{\pi}{2}\right)$$. A normal to $$y = f(x)$$ at $$x = \frac{\pi}{6}$$ also passes through the point

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = $$x$$ units and a circle of radius = $$r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then

The integral $$\int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx$$, is equal to

The area (in sq. units) of the region $$\{(x, y) : y^2 \geq 2x$$ and $$x^2 + y^2 \leq 4x$$, $$x \geq 0$$, $$y \geq 0\}$$ is

If a curve $$y = f(x)$$ passes through the point $$(1, -1)$$ and satisfies the differential equation, $$y(1 + xy)dx = x\,dy$$, then $$f\left(-\frac{1}{2}\right)$$ is equal to

Let $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ be three unit vectors such that $$\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2}(\vec{b} + \vec{c})$$. If $$\vec{b}$$ is not parallel to $$\vec{c}$$, then the angle between $$\vec{a}$$ and $$\vec{b}$$ is

If the line, $$\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$$ lies in the plane, $$lx + my - z = 9$$, then $$l^2 + m^2$$ is equal to

The distance of the point $$(1, -5, 9)$$ from the plane $$x - y + z = 5$$ measured along the line $$x = y = z$$ is

Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $$E_1$$ is the event that die $$A$$ shows up four, $$E_2$$ is the event that die $$B$$ shows up two and $$E_3$$ is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?