NTA JEE Main 29th July 2022 Shift 2

If $$z \neq 0$$ be a complex number such that $$\left|z - \frac{1}{z}\right| = 2$$, then the maximum value of $$|z|$$ is

Let $$S = \{z = x + iy : |z-1+i| \geq |z|, |z| < 2, |z+i| = |z-1|\}$$. Then the set of all values of x, for which $$w = 2x + iy \in S$$ for some $$y \in \mathbb{R}$$, is

Let $$\{a_n\}_{n=0}^{\infty}$$ be a sequence such that $$a_0 = a_1 = 0$$ and $$a_{n+2} = 3a_{n+1} - 2a_n + 1$$, $$\forall n \geq 0$$. Then $$a_{25}a_{23} - 2a_{25}a_{22} - 2a_{23}a_{24} + 4a_{22}a_{24}$$ is equal to

$$\sum_{r=1}^{20}(r^2+1)(r!)$$ is equal to

The number of elements in the set $$S = \left\{x \in \mathbb{R} : 2\cos\left(\frac{x^2+x}{6}\right) = 4^x + 4^{-x}\right\}$$ is

Let $$m_1, m_2$$ be the slopes of two adjacent sides of a square of side a such that $$a^2 + 11a + 3(m_1^2 + m_2^2) = 220$$. If one vertex of the square is $$10(\cos\alpha - \sin\alpha, \sin\alpha + \cos\alpha)$$, where $$\alpha \in (0, \frac{\pi}{2})$$ and the equation of one diagonal is $$(\cos\alpha - \sin\alpha)x + (\sin\alpha + \cos\alpha)y = 10$$, then $$72(\sin^4\alpha + \cos^4\alpha) + a^2 - 3a + 13$$ is equal to

Let $$A(\alpha, -2)$$, $$B(\alpha, 6)$$ and $$C\left(\frac{\alpha}{4}, -2\right)$$ be vertices of a $$\Delta ABC$$. If $$\left(5, \frac{\alpha}{4}\right)$$ is the circumcentre of $$\Delta ABC$$, then which of the following is NOT correct about $$\Delta ABC$$

The statement $$(p \Rightarrow q) \vee (p \Rightarrow r)$$ is NOT equivalent to:

Which of the following matrices can NOT be obtained from the matrix $$\begin{pmatrix} -1 & 2 \\ 1 & -1 \end{pmatrix}$$ by a single elementary row operation?

If the system of equations
$$x + y + z = 6$$
$$2x + 5y + \alpha z = \beta$$
$$x + 2y + 3z = 14$$
has infinitely many solutions, then $$\alpha + \beta$$ is equal to