NTA JEE Main 4th April 2015 Offline
For the following questions answer them individually
NTA JEE Main 4th April 2015 Offline - Question 81
The normal to the curve $$x^2 + 2xy - 3y^2 = 0$$, at (1, 1)
NTA JEE Main 4th April 2015 Offline - Question 82
Let $$f(x)$$ be a polynomial of degree four and having its extreme values at $$x = 1$$ and $$x = 2$$. If $$\lim_{x \to 0}\left[1 + \frac{f(x)}{x^2}\right] = 3$$, then $$f(2)$$ is equal to
NTA JEE Main 4th April 2015 Offline - Question 83
The integral $$\int \frac{dx}{x^2(x^4+1)^{3/4}}$$ equals to
NTA JEE Main 4th April 2015 Offline - Question 84
The integral $$\int_2^4 \frac{\log x^2}{\log x^2 + \log(6-x)^2} dx$$ is equal to
NTA JEE Main 4th April 2015 Offline - Question 85
The area (in sq. units) of the region described by $$\{(x,y) : y^2 \leq 2x$$ and $$y \geq 4x - 1\}$$ is
NTA JEE Main 4th April 2015 Offline - Question 86
Let $$y(x)$$ be the solution of the differential equation $$(x \log x)\frac{dy}{dx} + y = 2x \log x$$, $$(x \geq 1)$$. Then $$y(e)$$ is equal to
NTA JEE Main 4th April 2015 Offline - Question 87
Let $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ be three non-zero vectors such that no two of them are collinear and $$(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$$. If $$\theta$$ is the angle between vectors $$\vec{b}$$ and $$\vec{c}$$, then a value of $$\sin \theta$$ is
NTA JEE Main 4th April 2015 Offline - Question 88
The distance of the point (1, 0, 2) from the point of intersection of the line $$\frac{x-2}{3} = \frac{y+1}{4} = \frac{z-2}{12}$$ and the plane $$x - y + z = 16$$, is
NTA JEE Main 4th April 2015 Offline - Question 89
The equation of the plane containing the line of intersection of $$2x - 5y + z = 3$$; $$x + y + 4z = 5$$, and parallel to the plane, $$x + 3y + 6z = 1$$, is
NTA JEE Main 4th April 2015 Offline - Question 90
If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is
