JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let a complex number \(z ,| z | \neq 1\), satisfy \(\log _{\frac{1}{\sqrt{2}}}\left(\frac{| z |+11}{(| z |-1)^{2}}\right) \leq 2 .\) Then, the largest value of \(|z|\) is equal to ............
- A \(8\)
- B \(7\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
\(\log _{\frac{1}{\sqrt{2}}}\left(\frac{|z|+11}{(|z|-1)^{2}}\right) \leq 2\) \(\frac{|z|+11}{(|z|-1)^{2}} \geq \frac{1}{2}\) \(2|z|+22 \geq(|z|-1)^{2}\) \(2|z|+22 \geq|z|^{2}+1-2|z|\) \(|z|^{2}-4|z|-21 \leq 0\) \(\Rightarrow|z| \leq 7\) \(\therefore \quad\) Largest value of…
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
- If \(\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{b^2}}&{{c^2}} \\
{{{(a + \lambda )}^2}}&{{{(b + \lambda )}^2}}&{{{(c + \lambda )}^2}} \\
{{{(a - \lambda )}^2}}&{{{(b - \lambda )}^2}}&{{{(c - \lambda )}^2}}
\end{array}} \right|\) \( = \,k\lambda \,\,\left| {{\mkern 1mu} {\mkern 1mu} \begin{array}{*{20}{c}}
{{a^2}}&{{b^2}}&{{c^2}} \\
a&b&c \\
1&1&1
\end{array}} \right|,\lambda \, \ne \,0\) then \(k\) is equal toJEE Mains 2014 Hard - Let \(S=\left\{x \in R: 0 < x < 1\right.\) and \(\left.2 \tan ^{-1}\left(\frac{1-x}{1+x}\right)=\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right\}\). If \(n ( S )\) denotes the number of elements in \(S\) then:JEE Mains 2023 Hard
- If the variance of the following frequency distribution is \(50\) then \(x\) is equal to:
Class \(10-20\) \(20-30\) \(30-40\) Frequency \(2\) \(x\) \(2\) JEE Mains 2020 Medium - Let \(\alpha\) and \(\beta\) be two real numbers such that \(\alpha+\beta=1\) and \(\alpha \beta=-1 .\) Let \(p _{ n }=(\alpha)^{ n }+(\beta)^{ n },p _{ n -1}=11\) and \(p _{ n +1}=29\) for some integer \(n \geq 1 .\) Then, the value of \(p _{ n }^{2}\) is .... .JEE Mains 2021 Hard
- If \(\sum \limits_{i=1}^{n}\left(x_{i}-a\right)=n\) and \(\sum \limits_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a,(n, a>1)\) then the standard deviation of \(n\) observations \(x _{1}, x _{2}, \ldots, x _{ n }\) isJEE Mains 2020 Medium
- Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and det \((( A + I )(\operatorname{Adj}( A )+ I ))=4\). Then the sum of the diagonal elements of \(A\) can be.JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(f(x)=2 x+\tan ^{-1} x\) and \(g(x)=\log _e\left(\sqrt{1+x^2}+x\right)\), \(x \in[0,3]\). ThenJEE Mains 2023 Hard
- The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and \(\mathrm{x}= \pm \frac{4}{\sqrt{3}}\), respectively. Let the line \(y-\sqrt{3} \mathrm{x}+\sqrt{3}=0\) touch this hyperbola at \(\left(\mathrm{x}_0, \mathrm{y}_0\right)\). If \(\mathrm{m}\) is the product of the focal distances of the point \(\left(\mathrm{x}_0, \mathrm{y}_0\right)\), then \(4 \mathrm{e}^2+\mathrm{m}\) is equal to ...........JEE Mains 2024 Hard
- If \(\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x\), then \(\int_0^{21} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x\) equals :JEE Mains 2025 Hard
- If \(\lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17\), then \(5 a ^2+ b ^2\) is equal toJEE Mains 2023 Hard
- If the sum of the coefficients of all the positive powers of \(x\), in the binomial expansion of \(\left(x^{n}+\frac{2}{x^{5}}\right)^{7}\) is \(939 ,\) then the sum of all the possible integral values of \(n\) isJEE Mains 2022 Hard
- If the sum of the coefficients in the expansion of \((x+y)^{n}\) is \(4096,\) then the greatest coefficient in the expansion is .... .JEE Mains 2021 Medium