NTA JEE Main 12th January 2019 Shift 2

The number of integral values of m for which the quadratic expression $$(1 + 2m)x^2 - 2(1 + 3m)x + 4(1 + m)$$, $$x \in R$$, is always positive, is

Let $$z_1$$ and $$z_2$$ be two complex numbers satisfying $$|z_1| = 9$$ and $$|z_2 - 3 - 4i| = 4$$. Then the minimum value of $$|z_1 - z_2|$$ is:

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is:

If the sum of the first 15 terms of the series $$\left(\frac{3}{4}\right)^3 + \left(1\frac{1}{2}\right)^3 + \left(2\frac{1}{4}\right)^3 + 3^3 + \left(3\frac{3}{4}\right)^3 + \ldots$$ is equal to 225K, then K is equal to:

If $$\sin^4 \alpha + 4\cos^4 \beta + 2 = 4\sqrt{2} \sin\alpha \cos\beta$$, $$\alpha, \beta \in [0, \pi]$$, then $$\cos(\alpha + \beta) - \cos(\alpha - \beta)$$ is equal to

If $$^nC_4$$, $$^nC_5$$ and $$^nC_6$$ are in A.P., then n can be

The total number of irrational terms in the binomial expansion of $$\left(7^{1/5} - 3^{1/10}\right)^{60}$$ is

If a straight line passing through the point P(-3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:

If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is:

The equation of a tangent to the parabola, $$x^2 = 8y$$, which makes an angle $$\theta$$ with the positive direction of x-axis, is