JEE Mains · Maths · STD 11 - 4.1 complex nubers
The largest value of \(r\) for which the region represented by the set \(\{ \omega \, \in \,C|\,\omega \, - \,4\, - \,i|\, \le \,r\} \) is contained in the region represented by the set \((z\, \in \,c/|\,z\, - \,1\,\,\left| \le \right|\,z\, + \,i|),\) is equal to
- A \(\frac{5}{2}\sqrt 2 \)
- B \(2\sqrt 2\)
- C \(\frac{3}{2}\sqrt 2 \)
- D \(\sqrt {17}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{2}\sqrt 2 \)
Step-by-step Solution
Detailed explanation
Radius \(CP\,=\,\frac {4+1}{\sqrt 2}\) \(=\,\frac {5}{\sqrt 2}\) \(=\,\frac {5}{2}\sqrt 2\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\vec{p}=2 \hat{i}+3 \hat{j}+k\) and \(\vec{q}=\hat{i}+2 \hat{j}+k\) be two vectors. If \(a\) vector \(\vec{r}=(a \hat{i}+\beta \hat{j}+\gamma k)\) is perpendicular to each of the vectors \((\vec{p}+\bar{q})\) and \((\vec{p}-\vec{q})\), and \(|\vec{r}|=\sqrt{3}\), then \(|\alpha|+|\beta|+|\gamma|\) is equal to \(.....\)JEE Mains 2021 Hard
- The foot of the perpendicular drawn from the origin, on the line, \(3x + y = \lambda \,\left( {\lambda \ne 0} \right)\) is \(P\). If the line meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\), then the ratio \(BP : PA\) isJEE Mains 2018 Hard
- Let \(\alpha, \beta \in \mathbb{R}\) be such that the system of linear equations
\(x + 2y + z = 5\)
\(2x + y + \alpha z = 5\)
\(8x + 4y + \beta z = 18\)
has no solution. Then \(\dfrac{\beta}{\alpha}\) is equal to :JEE Mains 2026 Medium - A value of \(\theta \in (0, \pi /3)\), for which \(\left| {\begin{array}{*{20}{c}}
{1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta }
\end{array}} \right| = 0\), isJEE Mains 2019 Hard - If \(\mathop {\lim }\limits_{x \to 1} \frac{{{x^2}\,\, - \,ax\, + \,b}}{{x\, - \,1}}\,\, = \,3,\) then \(a + b\) is equal toJEE Mains 2019 Hard
- A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let \(X\) denote the number of defective pens. Then the variance of X isJEE Mains 2025 Easy
More PYQs from JEE Mains
- Let \(A B C\) be a triangle formed by the lines \(7 x-6 y+3=0, x+2 y-31=0\) and \(9 x-2 y-19=0\). Let the point \((h, k)\) be the image of the centroid of \(\Delta A B C\) in the line \(3 x+6 y-53=0\). Then \(h^2+k^2+h k\) is equal to:JEE Mains 2025 Easy
- For \(t \gt -1\), let \(\alpha_t\) and \(\beta_t\) be the roots of the equation
\(((t+2)^{\frac{1}{7}}-1) x^2+((t+2)^{\frac{1}{6}}-1) x~+\) \(((t+2)^{\frac{1}{21}}\) \(-~1)=0\)
If \(\lim _{t \rightarrow-1^{+}} \alpha_t=a\) and \(\lim _{t \rightarrow-1^{+}} \beta_t=b\), then \(72(a+b)^2\) is equal to ________.JEE Mains 2025 Medium - The function \(f ( x )= xe x ^{ x (1- x )}, x \in R\), isJEE Mains 2022 Medium
- For all complex numbers \(z\) of the form \(1 + i\alpha\), \(\alpha \in R\) , if \(z^2\, = x + iy\), thenJEE Mains 2014 Hard
- If \(c\) is a point at which Rolle's theorem holds for the function, \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\frac{\mathrm{x}^{2}+\alpha}{7 \mathrm{x}}\right)\) in the interval \([3,4],\) where \(\alpha \in \mathrm{R},\) then \(f^{\prime \prime}(\mathrm{c})\) is equal toJEE Mains 2020 Hard
- Two number \(\mathrm{k}_1\) and \(\mathrm{k}_2\) are randomly chosen from the set of natural numbers. Then, the probability that the value of \(\mathrm{i}^{\mathrm{k}_1}+\mathrm{i}^{\mathrm{k}_2},(\mathrm{i}=\sqrt{-1})\) is non-zero, equalsJEE Mains 2025 Medium