| 2022-10-27 | The complex numbers \( \sin x+i \cos 2 x \) and \( \cos x-i \sin 2 x \), where \( i=\sqrt{-1} \)... |
| 2022-10-27 | If \( z_{1}, z_{2}, z_{3}, \ldots, z_{n} \) are \( n, n \)th roots of unity, then for \( k=1,2,3... |
| 2022-10-27 | A line \( l \) passing through the origin is perpendicular to the lines
\( l_{1}:(3+t) \overline... |
| 2022-10-27 | The equation \( \frac{x^{2}}{10-a}+\frac{y^{2}}{4-a}=1 \), represents an ellipse, if
(a) \( a4 \... |
| 2022-10-27 | If \( \alpha, \beta \) and \( \gamma \) are the cube roots of \( p(p0) \), then for any \( x, y ... |
| 2022-10-27 | The principal value of \( \arg (z) \), where \( z=\left(1+\cos \frac{8 \pi}{5}\right)+i \sin \fr... |
| 2022-10-27 | If \( (1+i)^{2 n}+(1-i)^{2 n}=-2^{n+1} \) (where, \( i=\sqrt{-1} \) ) for all those \( n \), whi... |
| 2022-10-27 | If \( \left|z_{1}-1\right| \leq 1,\left|z_{2}-2\right| \leq 2,\left|z_{3}-3\right| \leq 3 \), th... |
| 2022-10-27 | If \( z=(3+4 i)^{6}+(3-4 i)^{6} \), where \( i=\sqrt{-1} \), then \( \operatorname{Im}(z) \) equ... |
| 2022-10-27 | If \( \frac{3}{2+\cos \theta+i \sin \theta}=a+i b \), where \( i=\sqrt{-1} \) and \( a^{2}+b^{2}... |
| 2022-10-27 | If \( \frac{z-1}{z+1} \) is purely imaginary, then \( |z| \) is equal to
(a) \( \frac{1}{2} \)
(... |
| 2022-10-27 | Consider the hyperbola \( H: x^{2}-y^{2}=1 \) and a circle \( S \) with centre \( N\left(x_{2}, ... |
| 2022-10-27 | If \( a, b, c \) are three non-zero vectors, then which of the following statement(s) is/are tru... |
| 2022-10-27 | If \( \frac{1-i x}{1+i x}=a-i b \) and \( a^{2}+b^{2}=1 \), where \( a, b \in R \) and \( i=\sqr... |
| 2022-10-27 | If \( i=\sqrt{-1} \), the number of values of \( i^{n}+i^{-n} \) for different \( n \in I \) is
... |
| 2022-10-27 | If \( (x+i y)^{1 / 3}=a+i b \), where \( i=\sqrt{-1} \), then \( \left(\frac{x}{a}+\frac{y}{b}\r... |
| 2022-10-27 | If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three non-zero vectors, then which of the follow... |
| 2022-10-27 | The value of \( \sum_{r=-3}^{1003} i^{r}( \) where \( i=\sqrt{-1}) \) is
(a) 1
(b) \( -1 \)
(c) ... |
| 2022-10-27 | The value of \( \sum_{n=0}^{50} i^{(2 n+1) !}( \) where, \( i=\sqrt{-1}) \) is
(a) \( i \)
(b) \... |
| 2022-10-27 | Consider the following statements.
\( S_{1}:-6=2 i \times 3 i=\sqrt{(-4)} \times \sqrt{(-9)}( \)... |
| 2022-10-27 | Let \( P\left(x_{1}, y_{1}\right) \) and \( Q\left(x_{2}, y_{2}\right), y_{1}0, y_{2}0 \) be the... |
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