NTA JEE Main 11th April 2014 Online

If $$\alpha$$ and $$\beta$$ are roots of the equation, $$x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0$$ for some $$k$$, and $$\alpha^2 + \beta^2 = 66$$, then $$\alpha^3 + \beta^3$$ is equal to:

If $$z_1, z_2$$ and $$z_3, z_4$$ are 2 pairs of complex conjugate numbers, then $$\arg\left(\frac{z_1}{z_4}\right) + \arg\left(\frac{z_2}{z_3}\right)$$ equals:

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:

The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + ... and 1 + 6 + 11 + 16 + ... is:

The coefficient of $$x^{50}$$ in the binomial expansion of $$(1+x)^{1000} + x(1+x)^{999} + x^2(1+x)^{998} + \ldots + x^{1000}$$ is:

If $$2\cos\theta + \sin\theta = 1$$ ($$\theta \neq \frac{\pi}{2}$$), then $$7\cos\theta + 6\sin\theta$$ is equal to:

The base of an equilateral triangle is along the line given by $$3x + 4y = 9$$. If a vertex of the triangle is $$(1, 2)$$, then the length of a side of the triangle is:

The set of all real values of $$\lambda$$ for which exactly two common tangents can be drawn to the circles $$x^2 + y^2 - 4x - 4y + 6 = 0$$ and $$x^2 + y^2 - 10x - 10y + \lambda = 0$$ is the interval:

Let L$$_1$$ be the length of the common chord of the curves $$x^2 + y^2 = 9$$ and $$y^2 = 8x$$, and L$$_2$$ be the length of the latus rectum of $$y^2 = 8x$$, then: