Let $w_1$ be the point obtained by the rotation of $z_1 = 5 + 4i$ about the origin through a right angle in the anticlockwise direction, and $w_2$ be the point obtained by the rotation of $z_2 = 3 + 5i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_1 - w_2$ is equal to:
Previous 10 Questions — JEE Main 2023 (11 April Morning Shift)
Nearest first
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Let $x_1, x_2, \ldots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to $200$.
If $y_…
Topic: JEE Main 2023 (11 April Morning Shift)
Let $S = \{ M = [a_{ij}], \; a_{ij} \in \{0, 1, 2\}, \; 1 \le i, j \le 2 \}$ be a sample space
and $A = \{ M \in S : …
Topic: JEE Main 2023 (11 April Morning Shift)
Let $R$ be a rectangle given by the lines $x = 0$, $x = 2$, $y = 0$ and $y = 5$.
Let $A(\alpha, 0)$ and $B(0, \beta)$…
Topic: JEE Main 2023 (11 April Morning Shift)
Next 10 Questions — JEE Main 2023 (11 April Morning Shift)
Ascending by ID
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Let $y = y(x)$ be a solution curve of the differential equation
\[
(1 - x^2 y^2)\,dx = y\,dx + x\,dy.
\]
If the line …
Topic: JEE Main 2023 (11 April Morning Shift)
The value of the integral
\[
\int_{-\log_e 2}^{\log_e 2} e^x \left( \log_e\!\left( e^x + \sqrt{1 + e^{2x}} \right) \r…
Topic: JEE Main 2023 (11 April Morning Shift)
Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the var…
Topic: JEE Main 2023 (11 April Morning Shift)
For any vector $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$, with $10|a_i| < 1, \; i = 1, 2, 3$,
consider the …
Topic: JEE Main 2023 (11 April Morning Shift)
Let $\mathbf{A}$ be a $2 \times 2$ matrix with real entries such that
$\mathbf{A}' = \alpha \mathbf{A} + \mathbf{I}$,…
Topic: JEE Main 2023 (11 April Morning Shift)
Let $f(x) = \lfloor x^2 - x \rfloor + | -x + \lfloor x \rfloor |$, where $x \in \mathbb{R}$
and $\lfloor t \rfloor$ d…
Topic: JEE Main 2023 (11 April Morning Shift)
Consider ellipses $\mathbf{E_k} : kx^2 + k^2y^2 = 1, \; k = 1, 2, \ldots, 20$.
Let $\mathbf{C_k}$ be the circle which…
Topic: JEE Main 2023 (11 April Morning Shift)
Area of the region
\[
\{(x, y) : x^2 + (y - 2)^2 \le 4, \; x^2 \ge 2y\}
\]
is:
Topic: JEE Main 2023 (11 April Morning Shift)
Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by
$\hat{i} + \ha…
Topic: JEE Main 2023 (11 April Morning Shift)
The number of triplets , where are distinct non negative integers satisfying , is :
Topic: JEE Main 2023 (11 April Morning Shift)
