NTA JEE Main 7th April 2013 Online
For the following questions answer them individually
NTA JEE Main 7th April 2013 Online - Question 81
If $$y = \sec(\tan^{-1}x)$$, then $$\frac{dy}{dx}$$ at $$x = 1$$ is equal to
NTA JEE Main 7th April 2013 Online - Question 82
The intercepts on the $$x$$-axis made by tangents to the curve, $$y = \int_0^x |t| \ dt$$, $$x \in R$$, which are parallel to the line $$y = 2x$$, are equal to
NTA JEE Main 7th April 2013 Online - Question 83
If $$\int f(x)dx = \psi(x)$$, then $$\int x^5 f(x^3)dx$$, is equal to
NTA JEE Main 7th April 2013 Online - Question 84
Statement - II : $$\int_a^b f(x)dx = \int_a^b f(a + b - x)dx$$.
NTA JEE Main 7th April 2013 Online - Question 85
The area (in square units) bounded by the curves $$y = \sqrt{x}$$, $$2y - x + 3 = 0$$, X-axis and lying in the first quadrant is
NTA JEE Main 7th April 2013 Online - Question 86
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers $$x$$ is given by $$\frac{dP}{dx} = 100 - 12\sqrt{x}$$. If the firm employs 25 more workers, then the new level of production of items is
NTA JEE Main 7th April 2013 Online - Question 87
If the vectors $$\vec{AB} = 3\hat{i} + 4\hat{k}$$ and $$\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$$ are the sides of a triangle $$ABC$$, then the length of the median through $$A$$ is:
NTA JEE Main 7th April 2013 Online - Question 88
If the lines $$\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$$ and $$\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$$ are coplanar, then $$k$$ can have
NTA JEE Main 7th April 2013 Online - Question 89
Distance between two parallel planes $$2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is
NTA JEE Main 7th April 2013 Online - Question 90
A multiple choice examination has 5 questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
