NTA JEE Main 17th March 2021 Shift 1

The value of $$4 + \cfrac{1}{5 + \cfrac{1}{4 + \cfrac{1}{5 + \cfrac{1}{4 + \ldots \infty}}}}$$ is:

The area of the triangle with vertices $$P(z)$$, $$Q(iz)$$ and $$R(z + iz)$$ is:

Team 'A' consists of 7 boys and $$n$$ girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $$n$$ is equal to:

If the fourth term in the expansion of $$\left(x + x^{\log_2 x}\right)^7$$ is 4480, then the value of $$x$$ where $$x \in N$$ is equal to:

In a triangle $$PQR$$, the co-ordinates of the points $$P$$ and $$Q$$ are $$(-2, 4)$$ and $$(4, -2)$$ respectively. If the equation of the perpendicular bisector of $$PR$$ is $$2x - y + 2 = 0$$, then the centre of the circumcircle of the $$\triangle PQR$$ is:

The line $$2x - y + 1 = 0$$ is a tangent to the circle at the point $$(2, 5)$$ and the centre of the circle lies on $$x - 2y = 4$$. Then, the radius of the circle is:

Choose the incorrect statement about the two circles whose equations are given below:
$$x^2 + y^2 - 10x - 10y + 41 = 0$$ and $$x^2 + y^2 - 16x - 10y + 80 = 0$$

The value of $$\lim_{x \to 0^+} \frac{\cos^{-1}(x - [x]^2) \cdot \sin^{-1}(x - [x]^2)}{x - x^3}$$, where $$[x]$$ denotes the greatest integer $$\leq x$$ is:

If the Boolean expression $$(p \Rightarrow q) \Leftrightarrow (q * (\sim p))$$ is a tautology, then the Boolean expression $$p * (\sim q)$$ is equivalent to:

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?