NTA JEE Main 3rd September 2020 Shift 1
For the following questions answer them individually
NTA JEE Main 3rd September 2020 Shift 1 - Question 61
If $$\Delta = \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ 2x-3 & 3x-4 & 4x-5 \\ 3x-5 & 5x-8 & 10x-17 \end{vmatrix} = Ax^3 + Bx^2 + Cx + D$$, then $$B + C$$ is equal to:
NTA JEE Main 3rd September 2020 Shift 1 - Question 62
$$2\pi - \left(\sin^{-1}\frac{4}{5} + \sin^{-1}\frac{5}{13} + \sin^{-1}\frac{16}{65}\right)$$ is equal to:
NTA JEE Main 3rd September 2020 Shift 1 - Question 63
If $$y^2 + \log_e(\cos^2 x) = y$$, $$x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$ then:
NTA JEE Main 3rd September 2020 Shift 1 - Question 64
The function, $$f(x) = (3x - 7)x^{\frac{2}{3}}$$, $$x \in R$$, is increasing for all $$x$$ lying in:
NTA JEE Main 3rd September 2020 Shift 1 - Question 65
$$\int_{-\pi}^{\pi} |\pi - |x|| \, dx$$ is equal to
NTA JEE Main 3rd September 2020 Shift 1 - Question 66
The area (in sq. units) of the region $$\{(x, y) : 0 \leq y \leq x^2 + 1, 0 \leq y \leq x + 1, \frac{1}{2} \leq x \leq 2\}$$ is
NTA JEE Main 3rd September 2020 Shift 1 - Question 67
The solution curve of the differential equation, $$(1 + e^{-x})(1 + y^2)\frac{dy}{dx} = y^2$$ which passes through the point (0, 1), is
NTA JEE Main 3rd September 2020 Shift 1 - Question 68
The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, -2, 3) and (1, 1, 0) lies on the plane
NTA JEE Main 3rd September 2020 Shift 1 - Question 69
The lines $$\vec{r} = (\hat{i} - \hat{j}) + l(2\hat{i} + \hat{k})$$ and $$\vec{r} = (2\hat{i} - \hat{j}) + m(\hat{i} + \hat{j} - \hat{k})$$
NTA JEE Main 3rd September 2020 Shift 1 - Question 70
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared at least once is
