NTA JEE Main 8th January 2020 Shift 2
For the following questions answer them individually
NTA JEE Main 8th January 2020 Shift 2 - Question 61
Let $$f : (1, 3) \rightarrow R$$, be a function defined by $$f(x) = \frac{x[x]}{1+x^2}$$, where $$[x]$$ denotes the greatest integer $$\le x$$. Then the range of $$f$$, is
NTA JEE Main 8th January 2020 Shift 2 - Question 62
Let $$S$$, be the set of all functions $$f : [0, 1] \rightarrow R$$, which are continuous on [0, 1], and differentiable on (0, 1). Then for every $$f$$ in $$S$$, there exists $$c \in (0, 1)$$, depending on $$f$$, such that.
NTA JEE Main 8th January 2020 Shift 2 - Question 63
The length of the perpendicular from the origin, on normal to the curve, $$x^2 + 2xy - 3y^2 = 0$$, at the point (2, 2), is.
NTA JEE Main 8th January 2020 Shift 2 - Question 64
$$\lim_{x \to 0} \frac{\int_0^x t \sin(10t) dt}{x}$$ is equal to
NTA JEE Main 8th January 2020 Shift 2 - Question 65
If $$I = \int_1^2 \frac{dx}{\sqrt{2x^3 - 9x^2 + 12x + 4}}$$, then
NTA JEE Main 8th January 2020 Shift 2 - Question 66
The area (in sq. units) of the region $$\{(x, y) \in R^2 : x^2 \le y \le 3 - 2x\}$$, is.
NTA JEE Main 8th January 2020 Shift 2 - Question 67
The differential equation of the family of curves, $$x^2 = 4b(y + b)$$, $$b \in R$$, is.
NTA JEE Main 8th January 2020 Shift 2 - Question 68
Let $$\vec{a} = \hat{i} - 2\hat{j} + \hat{k}$$ and $$\vec{b} = \hat{i} - \hat{j} + \hat{k}$$ be two vectors. If $$\vec{c}$$ is a vector such that $$\vec{b} \times \vec{c} = \vec{b} \times \vec{a}$$ and $$\vec{c} \cdot \vec{a} = 0$$, then $$\vec{c} \cdot \vec{b}$$ is equal to.
NTA JEE Main 8th January 2020 Shift 2 - Question 69
The mirror image of the point (1, 2, 3), in a plane is $$\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$$. Which of the following points lies on this plane?
NTA JEE Main 8th January 2020 Shift 2 - Question 70
Let $$A$$ and $$B$$, be two events such that the probability that exactly one of them occurs is $$\frac{2}{5}$$, and the probability that $$A$$ or $$B$$, occurs is $$\frac{1}{2}$$, then the probability of both of them occur together is.
