NTA JEE Main 11th April 2015 Online

Let $$k$$ and $$K$$ be the minimum and the maximum values of the function $$f(x) = \frac{(1+x)^{0.6}}{1+x^{0.6}}$$ in $$[0, 1]$$, respectively, then the ordered pair $$(k, K)$$ is equal to:

If $$\int \frac{\log\left(t + \sqrt{1+t^2}\right)}{\sqrt{1+t^2}} dt = \frac{1}{2}(g(t))^2 + c$$, where c is a constant, then $$g(2)$$ is equal to

Let $$f : R \rightarrow R$$ be a function such that $$f(2-x) = f(2+x)$$ and $$f(4-x) = f(4+x)$$, for all $$x \in R$$ and $$\int_0^2 f(x)dx = 5$$. Then the value of $$\int_{10}^{50} f(x)dx$$ is

Let $$f : (-1, 1) \rightarrow R$$ be a continuous function. If $$\int_0^{\sin x} f(t) dt = \frac{\sqrt{3}}{2}x$$, then $$f\left(\frac{\sqrt{3}}{2}\right)$$ is equal to:

The solution of the differential equation $$ydx - (x + 2y^2)dy = 0$$ is $$x = f(y)$$. If $$f(-1) = 1$$, then $$f(1)$$ is equal to

In a parallelogram $$ABCD$$, $$\left|\overrightarrow{AB}\right| = a$$, $$\left|\overrightarrow{AD}\right| = b$$ and $$\left|\overrightarrow{AC}\right| = c$$. $$\overrightarrow{DB} \cdot \overrightarrow{AB}$$ has the value:

A plane containing the point $$(3, 2, 0)$$ and the line $$\frac{x-1}{1} = \frac{y-2}{5} = \frac{z-3}{4}$$ also contains the point

The shortest distance between the z-axis and the line $$x + y + 2z - 3 = 0 = 2x + 3y + 4z - 4$$, is

If the mean and the variance of a binomial variate $$X$$ are 2 and 1 respectively, then the probability that $$X$$ takes a value greater than or equal to one is:

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is: