NTA JEE Main 27th August 2021 Shift 1
For the following questions answer them individually
NTA JEE Main 27th August 2021 Shift 1 - Question 61
If $$x^2 + 9y^2 - 4x + 3 = 0$$, $$x, y \in R$$, then $$x$$ and $$y$$ respectively lie in the intervals
NTA JEE Main 27th August 2021 Shift 1 - Question 62
If $$S = \left\{z \in C : \frac{z-i}{z+2i} \in R\right\}$$, then
NTA JEE Main 27th August 2021 Shift 1 - Question 63
If for $$x, y \in R$$, $$x > 0$$, $$y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \ldots$$ upto $$\infty$$ terms and $$\frac{2+4+6+\ldots+2y}{3+6+9+\ldots+3y} = \frac{4}{\log_{10} x}$$, then the ordered pair $$(x, y)$$ is equal to
NTA JEE Main 27th August 2021 Shift 1 - Question 64
If $$0 < x < 1$$, then $$\frac{3}{2}x^2 + \frac{5}{3}x^3 + \frac{7}{4}x^4 + \ldots$$, is equal to
NTA JEE Main 27th August 2021 Shift 1 - Question 65
$$\sum_{k=0}^{20} \left({}^{20}C_k\right)^2$$ is equal to
NTA JEE Main 27th August 2021 Shift 1 - Question 66
Let $$A$$ be a fixed point $$(0, 6)$$ and $$B$$ be a moving point $$(2t, 0)$$. Let $$M$$ be the mid-point of $$AB$$ and the perpendicular bisector of $$AB$$ meets the y-axis at $$C$$. The locus of the mid-point $$P$$ of MC is
NTA JEE Main 27th August 2021 Shift 1 - Question 67
A tangent and a normal are drawn at the point $$P(2, -4)$$ on the parabola $$y^2 = 8x$$, which meet the directrix of the parabola at the points $$A$$ and $$B$$ respectively. If $$Q(a, b)$$ is a point such that $$AQBP$$ is a square, then $$2a + b$$ is equal to
NTA JEE Main 27th August 2021 Shift 1 - Question 68
If $$\alpha, \beta$$ are the distinct roots of $$x^2 + bx + c = 0$$, then $$\lim_{x \to \beta} \frac{e^{2(x^2+bx+c)} - 1 - 2(x^2+bx+c)}{(x-\beta)^2}$$ is equal to
NTA JEE Main 27th August 2021 Shift 1 - Question 69
The statement $$(p \wedge (p \rightarrow q) \wedge (q \rightarrow r)) \rightarrow r$$ is
NTA JEE Main 27th August 2021 Shift 1 - Question 70
Let $$\frac{\sin A}{\sin B} = \frac{\sin(A-C)}{\sin(C-B)}$$, where $$A, B, C$$ are angles of a triangle $$ABC$$. If the lengths of the sides opposite these angles are $$a, b, c$$ respectively, then
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