NTA JEE Main 25th April 2013 Online

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60° on the circumference of the first circle, then the radius of the arc is:

A point on the ellipse, $$4x^2 + 9y^2 = 36$$, where the normal is parallel to the line, $$4x - 2y - 5 = 0$$, is :

Consider the system of equations : $$x + ay = 0$$, $$y + az = 0$$ and $$z + ax = 0$$. Then the set of all real values of 'a' for which the system has a unique solution is:

Let $$p$$ and $$q$$ be any two logical statements and $$r : p \rightarrow (\sim p \vee q)$$. If $$r$$ has a truth value $$F$$, then the truth values of $$p$$ and $$q$$ are respectively:

In a set of $$2n$$ observations, half of them are equal to 'a' and the remaining half are equal to '-a'. If the standard deviation of all the observations is 2; then the value of |a| is :

A common tangent to the conics $$x^2 = 6y$$ and $$2x^2 - 4y^2 = 9$$ is:

Let $$S = \left\{\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} : a_{ij} \in \{0, 1, 2\}, a_{11} = a_{22}\right\}$$. Then the number of non-singular matrices in the set S is :

Consider the function : $$f(x) = [x] + |1 - x|$$, $$-1 \leq x \leq 3$$ where [x] is the greatest integer function.
Statement 1: $$f$$ is not continuous at $$x = 0, 1, 2$$ and 3.
Statement 2: f(x) =$$\begin{cases}-x, & -1 \le x < 0 \\1 - x, & 0 \le x < 1 \\1 + x, & 1 \le x < 2 \\2 + x, & 2 \le x \le 3\end{cases}$$

A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in cm$$^2$$/min.) of the balloon when its diameter is 14 cm, is :

Let $$f(1) = -2$$ and $$f'(x) \geq 4.2$$ for $$1 \leq x \leq 6$$. The possible value of $$f(6)$$ lies in the interval :