NTA JEE Main 26th July 2022 Shift 2
For the following questions answer them individually
NTA JEE Main 26th July 2022 Shift 2 - Question 61
The minimum value of the sum of the squares of the roots of $$x^2 + (3-a)x = 2(a-1)$$ is
NTA JEE Main 26th July 2022 Shift 2 - Question 62
If $$z = x + iy$$ satisfies $$z - 2 = 0$$ and $$z-i - z+5i = 0$$, then
NTA JEE Main 26th July 2022 Shift 2 - Question 63
$$\displaystyle\sum_{\substack{i,j=0 \\ i \neq j}}^{n}$$Â Â $$^n C_{i}$$Â $$^n C_{j}$$ is equal toÂ
NTA JEE Main 26th July 2022 Shift 2 - Question 64
Let the abscissae of the two points $$P$$ and $$Q$$ on a circle be the roots of $$x^2 - 4x - 6 = 0$$ and the ordinates of $$P$$ and $$Q$$ be the roots of $$y^2 + 2y - 7 = 0$$. If $$PQ$$ is a diameter of the circle $$x^2 + y^2 + 2ax + 2by + c = 0$$, then the value of $$a + b - c$$ is
NTA JEE Main 26th July 2022 Shift 2 - Question 65
The equation of a common tangent to the parabolas $$y = x^2$$ and $$y = -(x-2)^2$$ is
NTA JEE Main 26th July 2022 Shift 2 - Question 66
The acute angle between the pair of tangents drawn to the ellipse $$2x^2 + 3y^2 = 5$$ from the point $$(1, 3)$$ is
NTA JEE Main 26th July 2022 Shift 2 - Question 67
If the line $$x - 1 = 0$$ is a directrix of the hyperbola $$kx^2 - y^2 = 6$$, then the hyperbola passes through the point
NTA JEE Main 26th July 2022 Shift 2 - Question 68
Let $$\beta = \displaystyle\lim_{x \to 0} \dfrac{\alpha x - (e^{3x} - 1)}{\alpha x(e^{3x} - 1)}$$ for some $$\alpha \in \mathbb{R}$$. Then the value of $$\alpha + \beta$$ is:
NTA JEE Main 26th July 2022 Shift 2 - Question 69
Negation of the Boolean expression $$p \leftrightarrow (q \rightarrow p)$$ is
NTA JEE Main 26th July 2022 Shift 2 - Question 70
Let $$A = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$$ and $$B = \begin{pmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & -14^2 \\ -15^2 & 16^2 & 17^2 \end{pmatrix}$$, then the value of $$A'BA$$ is
