MHT CET · Maths · Complex Number
The value of \(\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1=\)
- A \(-1\)
- B \(-2\)
- C \(-3\)
- D \(-4\)
Answer & Solution
Correct Answer
(B) \(-2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{i^{584}\left(i^8+i^6+i^4+i^2+1\right)}{i^{574}\left(i^8+i^6+i^4+i^2+1\right)}-1=\frac{i^{584}}{i^{574}}-1 \\ & \quad=i^{10}-1=-1-1=-2\end{aligned}\)
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 \(\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}\), then the value of \(x\) isMHT CET 2023 Hard
- The principal value of \(\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)\) isMHT CET 2022 Medium
- Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks isMHT CET 2023 Medium
- \(\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=\)MHT CET 2023 Medium
- The order and degree of the differential equation \(\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0\) are respectively.MHT CET 2021 Easy
- The particular solution of the differential equation \(\frac{d y}{d x}=\frac{x+y+1}{x+y-1}\) when \(\mathrm{x}=\frac{2}{3}\) and \(\mathrm{y}=\frac{1}{3}\) isMHT CET 2021 Hard
More PYQs from MHT CET
- The length of latus -rectum of the parabola \(x^{2}+2 y=8 x-7\) isMHT CET 2020 Easy
- A horizontal pipeline carries water in a stream-line flow. At a point along the pipe, where the cross-sectional area is \(10 \mathrm{~cm}^2\), the velocity of water is \(1 \mathrm{~m} / \mathrm{s}\) and pressure is 2000 Pa . The pressure of water at another point where the cross-sectional area \(5 \mathrm{~cm}^2\) is
\(\left[\text { Given } \rightarrow \text { density of water }=1000 \mathrm{~kg} / \mathrm{m}^3\right]\)MHT CET 2025 Medium - \(\left[\sin \left(\tan ^{-1} \frac{3}{4}\right)\right]^{2}+\left[\sin \left(\tan ^{-1} \frac{4}{3}\right)\right]^{2}=\)MHT CET 2020 Easy
- The opening and closing of stomata takes place as a result of active transport of ___________ ions in guard cells.MHT CET 2019 Easy
- Which among the following oxides of nitrogen is brown coloured gas?MHT CET 2020 Easy
- Calculate the quantity of electricity required to liberate \(0.224 \mathrm{dm}^3\) of chlorine at STP during the electrolysis of fused sodium chloride?MHT CET 2025 Medium