NTA JEE Main 7th April 2013 Online
For the following questions answer them individually
NTA JEE Main 7th April 2013 Online - Question 61
The real number $$k$$ for which the equation, $$2x^3 + 3x + k = 0$$ has two distinct real roots in $$[0, 1]$$ belongs to
NTA JEE Main 7th April 2013 Online - Question 62
If the equations $$x^2 + 2x + 3 = 0$$ and $$ax^2 + bx + c = 0$$, $$a, b, c \in R$$, have a common root, then $$a : b : c$$ is:
NTA JEE Main 7th April 2013 Online - Question 63
If $$z$$ is a complex number of unit modulus and argument $$\theta$$, then $$\arg\left(\frac{1+z}{1+\bar{z}}\right)$$ can be equal to (given $$z \neq -1$$)
NTA JEE Main 7th April 2013 Online - Question 64
Let $$T_n$$ be the number of all possible triangles formed by joining vertices of an $$n$$-sided regular polygon. If $$T_{n+1} - T_n = 10$$, then the value of $$n$$ is :
NTA JEE Main 7th April 2013 Online - Question 65
If $$x$$, $$y$$, $$z$$ are positive numbers in A.P. and $$\tan^{-1}x$$, $$\tan^{-1}y$$ and $$\tan^{-1}z$$ are also in A.P., then which of the following is correct.
NTA JEE Main 7th April 2013 Online - Question 66
The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ......, is :
NTA JEE Main 7th April 2013 Online - Question 67
The term independent of $$x$$ in the expansion of $$\left(\frac{x+1}{x^{2/3} - x^{1/3} + 1} - \frac{x-1}{x - x^{1/2}}\right)^{10}$$ is
NTA JEE Main 7th April 2013 Online - Question 68
The expression $$\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A}$$ can be written as :
NTA JEE Main 7th April 2013 Online - Question 69
A ray of light along $$x + \sqrt{3}y = \sqrt{3}$$ gets reflected upon reaching X-axis, the equation of the reflected ray is
NTA JEE Main 7th April 2013 Online - Question 70
The $$x$$-coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as (0, 1), (1, 1) and (1, 0) is
