NTA JEE Main 10th January 2019 Shift 2
For the following questions answer them individually
NTA JEE Main 10th January 2019 Shift 2 - Question 61
The value of $$\lambda$$ such that sum of the squares of the roots of the quadratic equation, $$x^2 + (3-\lambda)x + 2 = \lambda$$ has the least value is:
NTA JEE Main 10th January 2019 Shift 2 - Question 62
Let $$z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5$$. If $$R(z)$$ and $$I(z)$$ respectively denote the real and imaginary parts of $$z$$, then:
NTA JEE Main 10th January 2019 Shift 2 - Question 63
If $$\sum_{r=0}^{25} \{^{50}C_r \cdot ^{50-r}C_{25-r}\} = K \cdot ^{50}C_{25}$$, then $$K$$ is equal to:
NTA JEE Main 10th January 2019 Shift 2 - Question 64
The positive value of $$\lambda$$ for which the co-efficient of $$x^2$$ in the expansion $$x^2\left(\sqrt{x} + \frac{\lambda}{x^2}\right)^{10}$$ is 720, is:
NTA JEE Main 10th January 2019 Shift 2 - Question 65
The value of $$\cos\frac{\pi}{2^2} \cdot \cos\frac{\pi}{2^3} \cdots \cos\frac{\pi}{2^{10}} \cdot \sin\frac{\pi}{2^{10}}$$ is:
NTA JEE Main 10th January 2019 Shift 2 - Question 66
Two vertices of a triangle are $$(0, 2)$$ and $$(4, 3)$$. If its orthocenter is at the origin, then its third vertex lies in which quadrant?
NTA JEE Main 10th January 2019 Shift 2 - Question 67
Two sides of a parallelogram are along the lines, $$x + y = 3$$ and $$x - y + 3 = 0$$. If its diagonals intersect at $$(2, 4)$$, then one of its vertex is:
NTA JEE Main 10th January 2019 Shift 2 - Question 68
If the area of an equilateral triangle inscribed in the circle $$x^2 + y^2 + 10x + 12y + c = 0$$ is $$27\sqrt{3}$$ sq. units, then $$c$$ is equal to:
NTA JEE Main 10th January 2019 Shift 2 - Question 69
The length of the chord of the parabola $$x^2 = 4y$$ having equation $$x - \sqrt{2}y + 4\sqrt{2} = 0$$ is:
NTA JEE Main 10th January 2019 Shift 2 - Question 70
Let $$S = \left\{(x, y) \in R^2 : \frac{y^2}{1+r} - \frac{x^2}{1-r} = 1\right\}$$, where $$r \neq \pm 1$$. Then $$S$$ represents:
