NTA JEE Main 25th April 2013 Online

If $$p$$ and $$q$$ are non-zero real numbers and $$\alpha^3 + \beta^3 = -p$$, $$\alpha\beta = q$$, then a quadratic equation whose roots are $$\frac{\alpha^2}{\beta}$$, $$\frac{\beta^2}{\alpha}$$ is :

Let z satisfy $$|z| = 1$$ and $$z = 1 - \bar{z}$$.
Statement 1 : z is a real number.
Statement 2 : Principal argument of z is $$\frac{\pi}{3}$$.

5-digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits. If $$p$$ be the number of such numbers that exceed 20000 and $$q$$ be the number of those that lie between 30000 and 90000, then $$p : q$$ is:

Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is :

The value of $$1^2 + 3^2 + 5^2 + \ldots + 25^2$$ is :

If for positive integers $$r > 1$$, $$n > 2$$, the coefficients of the $$(3r)^{th}$$ and $$(r+2)^{th}$$ powers of $$x$$ in the expansion of $$(1 + x)^{2n}$$ are equal, then $$n$$ is equal to:

Let $$A = \{\theta : \sin(\theta) = \tan(\theta)\}$$ and $$B = \{\theta : \cos(\theta) = 1\}$$ be two sets. Then :

If the image of point P(2, 3) in a line L is Q(4, 5), then the image of point R(0, 0) in the same line is:

Let $$x \in (0, 1)$$. The set of all $$x$$ such that $$\sin^{-1}x > \cos^{-1}x$$, is the interval:

Statement 1: The only circle having radius $$\sqrt{10}$$ and a diameter along line $$2x + y = 5$$ is $$x^2 + y^2 - 6x + 2y = 0$$.
Statement 2: $$2x + y = 5$$ is a normal to the circle $$x^2 + y^2 - 6x + 2y = 0$$.