NTA JEE Main 15th April 2018 Shift 1

If $$\lambda \in R$$ is such that the sum of the cubes of the roots of the equation, $$x^2 + (2 - \lambda)x + (10 - \lambda) = 0$$ is minimum, then the magnitude of the difference of the roots of this equation is:

The set of all $$\alpha \in R$$, for which $$w = \frac{1+(1-8\alpha)z}{1-z}$$ is a purely imaginary number, for all $$z \in C$$ satisfying $$|z| = 1$$ and Re(z) $$\neq$$ 1, is:

n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is:

If b is the first term of an infinite G.P whose sum is five, then b lies in the interval:

If $$x_1, x_2, \ldots, x_n$$ and $$\frac{1}{h_1}, \frac{1}{h_2}, \ldots, \frac{1}{h_n}$$ are two A.P.s such that $$x_3 = h_2 = 8$$ and $$x_8 = h_7 = 20$$, then $$x_5 \cdot h_{10}$$ equals:

If n is the degree of the polynomial, $$\left[\frac{1}{\sqrt{5x^3+1} - \sqrt{5x^3-1}}\right]^8 + \left[\frac{1}{\sqrt{5x^3+1} + \sqrt{5x^3-1}}\right]^8$$ and m is the coefficient of $$x^n$$ in it, then the ordered pair (n, m) is equal to:

If $$\tan A$$ and $$\tan B$$ are the roots of the quadratic equation, $$3x^2 - 10x - 25 = 0$$ then the value of $$3\sin^2(A+B) - 10\sin(A+B) \cdot \cos(A+B) - 25\cos^2(A+B)$$ is:

In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are $$x + y = 5$$ and $$x = 4$$ respectively. Then area of $$\triangle ABC$$ (in sq. units) is:

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $$y - 4x + 3 = 0$$, then its radius is equal to:

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is: