NTA JEE Main 9th April 2013 Online

The values of 'a' for which one root of the equation $$x^2 - (a+1)x + a^2 + a - 8 = 0$$ exceeds 2 and the other is lesser than 2, are given by :

If $$Z_1 \neq 0$$ and $$Z_2$$ be two complex numbers such that $$\frac{Z_2}{Z_1}$$ is a purely imaginary number, then $$\left|\frac{2Z_1 + 3Z_2}{2Z_1 - 3Z_2}\right|$$ is equal to:

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :

Let $$a_1, a_2, a_3, \ldots$$ be an A.P, such that $$\frac{a_1 + a_2 + \ldots + a_p}{a_1 + a_2 + a_3 + \ldots + a_q} = \frac{p^3}{q^3}$$; $$p \neq q$$. Then $$\frac{a_6}{a_{21}}$$ is equal to:

The sum of the series: $$1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots$$ upto 10 terms, is:

The ratio of the coefficient of $$x^{15}$$ to the term independent of $$x$$ in the expansion of $$\left(x^2 + \frac{2}{x}\right)^{15}$$ is:

A value of $$x$$ for which $$\sin\left(\cot^{-1}(1+x)\right) = \cos\left(\tan^{-1}x\right)$$, is :

A light ray emerging from the point source placed at P(1, 3) is reflected at a point Q in the axis of x. If the reflected ray passes through the point R(6, 7), then the abscissa of Q is:

If the three lines $$x - 3y = p$$, $$ax + 2y = q$$ and $$ax + y = r$$ form a right-angled triangle then :

If each of the lines $$5x + 8y = 13$$ and $$4x - y = 3$$ contains a diameter of the circle $$x^2 + y^2 - 2(a^2 - 7a + 11)x - 2(a^2 - 6a + 6)y + b^3 + 1 = 0$$, then :