NTA JEE Main 8th April2023 Shift 1
For the following questions answer them individually
NTA JEE Main 8th April2023 Shift 1 - Question 61
Let $$\alpha, \beta, \gamma$$ be the three roots of the equation $$x^3 + bx + c = 0$$ if $$\beta\gamma = 1 = -\alpha$$ then $$b^3 + 2c^3 - 3\alpha^3 - 6\beta^3 - 8\gamma^3$$ is equal to
NTA JEE Main 8th April2023 Shift 1 - Question 62
If for $$z = \alpha + i\beta$$, $$|z + 2| = z + 4(1+i)$$, then $$\alpha + \beta$$ and $$\alpha\beta$$ are the roots of the equation
NTA JEE Main 8th April2023 Shift 1 - Question 63
The number of arrangements of the letters of the word 'INDEPENDENCE' in which all the vowels always occur together is
NTA JEE Main 8th April2023 Shift 1 - Question 64
The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together is
NTA JEE Main 8th April2023 Shift 1 - Question 65
Let $$S_K = \dfrac{1+2+\ldots+K}{K}$$ and $$\sum_{j=1}^n S_j^2 = \dfrac{n}{A}(Bn^2 + Cn + D)$$ where $$A, B, C, D \in N$$ and $$A$$ has least value, then
NTA JEE Main 8th April2023 Shift 1 - Question 66
If the coefficients of three consecutive terms in the expansion of $$(1+x)^n$$ are in the ratio 1:5:20 then the coefficient of the fourth term is
NTA JEE Main 8th April2023 Shift 1 - Question 67
Let $$C(\alpha, \beta)$$ be the circumcentre of the triangle formed by the lines $$4x + 3y = 69$$, $$4y - 3x = 17$$, and $$x + 7y = 61$$. Then $$(\alpha - \beta)^2 + \alpha + \beta$$ is equal to
NTA JEE Main 8th April2023 Shift 1 - Question 68
Let $$R$$ be the focus of the parabola $$y^2 = 20x$$ and the line $$y = mx + c$$ intersect the parabola at two points P and Q. Let the points G(10, 10) be the centroid of the triangle PQR. If $$c - m = 6$$, then $$PQ^2$$ is
NTA JEE Main 8th April2023 Shift 1 - Question 69
$$\lim_{x \to 0} \left(\left(\dfrac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\dfrac{\sin^3(4x)}{(\log_e(2x+1))^5}\right)\right)$$ is equal to
NTA JEE Main 8th April2023 Shift 1 - Question 70
Negation of $$(p \to q) \to (q \to p)$$ is
