NTA JEE Main 1st February 2023 Shift 1
For the following questions answer them individually
NTA JEE Main 1st February 2023 Shift 1 - Question 61
Let $$S = \{x : x \in \mathbb{R}$$ and $$\sqrt{3} + \sqrt{2}^{x^2-4} + \sqrt{3} - \sqrt{2}^{x^2-4} = 10\}$$. Then $$nS$$ is equal to
NTA JEE Main 1st February 2023 Shift 1 - Question 62
If the center and radius of the circle $$\frac{z-2}{z-3} = 2$$ are respectively $$\alpha, \beta$$ and $$\gamma$$, then $$3(\alpha + \beta + \gamma)$$ is equal to
NTA JEE Main 1st February 2023 Shift 1 - Question 63
The sum to 10 terms of the series $$\frac{1}{1+1^2+1^4} + \frac{2}{1+2^2+2^4} + \frac{3}{1+3^2+3^4} + \ldots$$ is:
NTA JEE Main 1st February 2023 Shift 1 - Question 64
The value of $$\frac{1}{1!50!} + \frac{1}{3!48!} + \frac{1}{5!46!} + \ldots + \frac{1}{49!2!} + \frac{1}{51!1!}$$ is
NTA JEE Main 1st February 2023 Shift 1 - Question 65
The combined equation of the two lines $$ax + by + c = 0$$ and $$a'x + b'y + c' = 0$$ can be written as $$ax + by + ca'x + b'y + c' = 0$$. The equation of the angle bisectors of the lines represented by the equation $$2x^2 + xy - 3y^2 = 0$$ is
NTA JEE Main 1st February 2023 Shift 1 - Question 66
If the orthocentre of the triangle, whose vertices are $$1, 2$$, $$2, 3$$ and $$3, 1$$ is $$\alpha, \beta$$, then the quadratic equation whose roots are $$\alpha + 4\beta$$ and $$4\alpha + \beta$$, is
NTA JEE Main 1st February 2023 Shift 1 - Question 67
The negation of the expression $$q \vee ((\sim q) \wedge p)$$ is equivalent to
NTA JEE Main 1st February 2023 Shift 1 - Question 68
The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is
NTA JEE Main 1st February 2023 Shift 1 - Question 69
For a triangle $$ABC$$, the value of $$\cos 2A + \cos 2B + \cos 2C$$ is least. If its inradius is 3 and incentre is $$M$$, then which of the following is NOT correct?
NTA JEE Main 1st February 2023 Shift 1 - Question 70
Let $$R$$ be a relation on $$\mathbb{R}$$, given by $$R = \{a, b : 3a - 3b + \sqrt{7}$$ is an irrational number$$\}$$. Then $$R$$ is
