NTA JEE Main 9th April 2017 Online

If $$f\left(\frac{3x - 4}{3x + 4}\right) = x + 2$$, $$x \neq -\frac{4}{3}$$, and $$\int f(x)dx = A \log|1 - x| + Bx + C$$, then the ordered pair $$(A, B)$$ is equal to

If $$\int_1^2 \frac{dx}{(x^2 - 2x + 4)^{\frac{3}{2}}} = \frac{k}{k+5}$$, then $$k$$ is equal to

If $$\lim_{n \to \infty} \left(\frac{1^a + 2^a + \ldots + n^a}{(n+1)^{a-1}[(na+1) + (na+2) + \ldots + (na+n)]}\right) = \frac{1}{60}$$ for some positive real number $$a$$, then $$a$$ is equal to

Let $$f$$ be a polynomial function such that $$f(3x) = f'(x) \cdot f''(x)$$, for all $$x \in R$$. Then:

A tangent to the curve, $$y = f(x)$$ at $$P(x, y)$$ meets x-axis at $$A$$ and y-axis at $$B$$. If $$AP : BP = 1 : 3$$ and $$f(1) = 1$$, then the curve also passes through the point

If the vector $$\vec{b} = 3\hat{j} + 4\hat{k}$$ is written as the sum of a vector $$\vec{b_1}$$, parallel to $$\vec{a} = \hat{i} + \hat{j}$$ and a vector $$\vec{b_2}$$, perpendicular to $$\vec{a}$$, then $$\vec{b_1} \times \vec{b_2}$$ is equal to:

If the line, $$\frac{x - 3}{1} = \frac{y + 2}{-1} = \frac{z + \lambda}{-2}$$ lies in the plane, $$2x - 4y + 3z = 2$$, then the shortest distance between this line and the line, $$\frac{x - 1}{12} = \frac{y}{9} = \frac{z}{4}$$ is

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at $$A$$, $$B$$ & $$C$$, then the locus of the centroid of $$\triangle ABC$$ is

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is:

Let $$E$$ & $$F$$ be two independent events. The probability that $$E$$ & $$F$$ happen is $$\frac{1}{12}$$ and the probability that neither $$E$$ nor $$F$$ happens is $$\frac{1}{2}$$, then a value of $$\frac{P(E)}{P(F)}$$ is: