NTA JEE Main 19th April 2014 Online

The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola $$\frac{x^2}{4} - \frac{y^2}{5} = 1$$, meets the x-axis and y-axis at A and B, respectively. Then $$OA^2 - OB^2$$, where O is the origin, equals:

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is:

Let $$\bar{x}$$, M and $$\sigma^2$$ be respectively the mean, mode and variance of n observations $$x_1, x_2, \ldots, x_n$$ and $$d_i = -x_i - a$$, i = 1, 2, ..., n, where a is any number.
Statement I: Variance of d$$_1$$, d$$_2$$, ..., d$$_n$$ is $$\sigma^2$$.
Statement II: Mean and mode of d$$_1$$, d$$_2$$, ..., d$$_n$$ are $$-\bar{x} - a$$ and $$-M - a$$, respectively.

Let A and B be any two $$3 \times 3$$ matrices. If A is symmetric and B is skew symmetric, then the matrix AB $$-$$ BA is:

If $$\Delta_r = \begin{vmatrix} r & 2r-1 & 3r-2 \\ \frac{n}{2} & n-1 & a \\ \frac{1}{2}n(n-1) & (n-1)^2 & \frac{1}{2}(n-1)(3n+4) \end{vmatrix}$$, then the value of $$\sum_{r=1}^{n-1} \Delta_r$$:

The principal value of $$\tan^{-1}\left(\cot\frac{43\pi}{4}\right)$$ is:

The function $$f(x) = |\sin 4x| + |\cos 2x|$$, is a periodic function with a fundamental period:

Let $$f : R \to R$$ be defined by $$f(x) = \frac{|x|-1}{|x|+1}$$, then f is:

If the function $$f(x) = \begin{cases} \frac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x \neq \pi \\ k, & x = \pi \end{cases}$$ is continuous at $$x = \pi$$, then k equals:

Let $$f : R \to R$$ be a function such that $$|f(x)| \leq x^2$$, for all $$x \in R$$. Then, at x = 0, f is: