NTA JEE Main 11th April 2014 Online
For the following questions answer them individually
NTA JEE Main 11th April 2014 Online - Question 81
Let $$f(x) = x|x|$$, $$g(x) = \sin x$$ and $$h(x) = (g \circ f)(x)$$. Then:
NTA JEE Main 11th April 2014 Online - Question 82
For the curve $$y = 3\sin\theta\cos\theta$$, $$x = e^\theta\sin\theta$$, $$0 \leq \theta \leq \pi$$, the tangent is parallel to x-axis when $$\theta$$ is:
NTA JEE Main 11th April 2014 Online - Question 83
The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = $$\sqrt{3}$$ is:
NTA JEE Main 11th April 2014 Online - Question 84
The integral $$\int x \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) dx$$ ($$x > 0$$) is equal to:
NTA JEE Main 11th April 2014 Online - Question 85
If for $$n \geq 1$$, $$P_n = \int_1^e (\log x^n) dx$$, then $$P_{10} - 90P_8$$ is equal to:
NTA JEE Main 11th April 2014 Online - Question 86
If the general solution of the differential equation $$y' = \frac{y}{x} + \Phi\left(\frac{x}{y}\right)$$, for some function $$\Phi$$, is given by $$y\ln|cx| = x$$, where c is an arbitrary constant, then $$\Phi(2)$$ is equal to:
NTA JEE Main 11th April 2014 Online - Question 87
If $$|\vec{c}|^2 = 60$$ and $$\vec{c} \times (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$$, then a value of $$\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$$ is:
NTA JEE Main 11th April 2014 Online - Question 88
The plane containing the line $$\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$$ and parallel to the line $$\frac{x}{1} = \frac{y}{1} = \frac{z}{4}$$ passes through the point:
NTA JEE Main 11th April 2014 Online - Question 89
A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that $$x \in A$$ is:
NTA JEE Main 11th April 2014 Online - Question 90
If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is:
