Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi
Telugu
Bengali
Marathi
Tamil

Question

Download Solution PDF

If N + \(1\over N\) = √3, then find the value of N6 + \(1\over N^6\) + 11.

This question was previously asked in
SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 15 March, 2023 Shift 1)
Download PDF Attempt Online
View all SSC CHSL Papers >
  1. -11
  2. -2
  3. 11
  4. 9

Answer (Detailed Solution Below)

Option 4 : 9
Free Tests
View all Free tests >
Free
SSC CHSL General Intelligence Sectional Test 1
1.7 Lakh Users
25 Questions 50 Marks 18 Mins
Start Now

Detailed Solution

Download Solution PDF

Given:

N + 1/N = √3

Formula:

If x + 1/x = a, then x3 + 1/x3 = a3 - 3a

Calculation:

N3 + 1/N3 = (√3)3 - 3 × √3

⇒ N3 + 1/N3 = 0

Now square both sides

(N3 + 1/N3)2= 0

N6 + 1/N6 + 2 = 0

N6 + 1/N6  = -2

Add 11 on both sides:

N6 + 1/N6 + 11 = -2 + 11

N6 + 1/N6 + 11 = 9

∴ The required answer = 9

Download Solution PDF
Latest SSC CHSL Updates

Last updated on Jul 22, 2025

-> The Staff selection commission has released the SSC CHSL Notification 2025 on its official website.

-> The SSC CHSL New Application Correction Window has been announced. As per the notice, the SCS CHSL Application Correction Window will now be from 25.07.2025 to 26.07.2025.   

-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government. 

-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).

-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.  

->UGC NET Final Asnwer Key 2025 June has been released by NTA on its official site

->HTET Admit Card 2025 has been released on its official site

‹‹ Previous Ques
Next Ques ››

More Fractions Questions

Q1.5/6 of a number is 675, find the 9/20 of the same number?
Q2.Convert 0.363636...... into a fraction.
Q3.\(\left\{\left(\frac{16}{36}\right) \div\left(\frac{16}{10}\right)\right\} \div\left(\frac{2}{7} \times \frac{14}{6}+\frac{5}{12}\right)+\frac{10}{4} \div \frac{39}{17} \text { of } \frac{17}{4}\). Keep it simple 
Q4.Find the value of the following .\( \frac{1}{6}+\frac{2}{6}+\frac{1}{12}+\frac{2}{6}-2=\)
Q5.Find x in the following: \(6\frac{7}{15}+x=8\frac{3}{5}\)
Q6.Simplify : \(\frac{1\frac{1}{4}+18.75-12\frac{2}{6}-7\frac{6}{9}}{0.6\times 8.7-6.98\times 10.9}\)
Q7.What is the simplest fractional form of 0.625?
Q8.The value of \(9^3-2^2+\left(\frac{42}{3}\right)^2-6+5\times 0= \) _______
Q9.Simplify \(\rm \left(\frac{2}{3}\times \frac{6}{5}\right)+\rm \left(\frac{12}{25}\times \frac{20}{3}\right) \)
Q10.Find the reciprocal of the sum of the reciprocals of the given numbers. \(\frac{2}{5}, \frac{5}{4}, \frac{6}{8}, \frac{6}{5}, \frac{9}{6}\)

More Simplification Questions

Q1.Simplify: \({625^{0.17}} \times {625^{0.08}} = {25^?} \times {25^{ - \frac{3}{2}}}\)
Q2.If 395 × x = 2765, then x is -
Q3.What appro×imate value should come in the place of ‘?’ in the following questions. 345.5 + 125 + 112 - 34 = ?
Q4.What appro×imate value should come in the place of ‘?’ in the following questions. \((?)^3+ (600) = 725\)
Q5.What appro×imate value should come in the place of ‘?’ in the following questions. 12.5 + 155.5 + 120 - 130 = 125 + ? 
Q6.What appro×imate value should come in the place of ‘?’ in the following questions. ? × 12 × 3/4 + 120 = 786
Q7.What appro×imate value should come in the place of ‘?’ in the following questions. 2252 + 1176 + ? + 75 = 3503
Q8.What appro×imate value should come in the place of ‘?’ in the following questions. \({(18\times?)}\div120 \times60 + 48 = 54\)
Q9.What appro×imate value should come in the place of ‘?’ in the following questions. 17/8 × ?/51 × 4/9 = 20/27
Q10.What appro×imate value should come in the place of ‘?’ in the following questions. 72 × 105 ÷ ? + 63 = 567 
Suggested Test Series
View All >
SSC CHSL (Tier I & Tier II) Mock Test Series 2025 (New)
1411 Total Tests with 1 Free Tests
Start Free Test
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with   1 Free Tests
Start Free Test

More Quantitative Aptitude Questions

Q1.Perimeter of a rectangular field is equal to the perimeter of a triangular field whose sides are in the ratio 3:2:4 respectively. lf area of rectangular field is 500 m2 and sides are in the ratio 5:4 respectively, then calculate the longer side of the triangular field.
Q2.A cistern has an inlet pipe and an outlet pipe. Inlet pipe can fill three-fourth of the cistern in 24 minutes while outlet pipe can empty the one-third filled cistern in 16 minutes. If both the pipes are opened together, then the cistern will be completely filled in-
Q3.In a family, three sons were born for every 3 years one after the other. If the ratio of present ages of father and the eldest son is 15:7 and the average of the present ages of the 3 sons is 18 years. What will be the ratio of the ages of the father and the youngest son after 5 years?
Q4.Train A of length 80m while moving crosses a pole in 16 seconds. lf it is known that the lengths of train B and train A is in the ratio of 3:1, then how long would it take train B to cross a platform which is half the length of train A if the speed of train B is same as that of train A?
Q5.Can A and Can B contain a mixture of soda and water in the ratio of 5 : 3 and 7 : 2 respectively If soda and water are taken out in the ratio of P : Q from can A and B respectively to form a new mixture in which the ratio of soda and water is 12 : 5 respectively, then find the value Of P:Q?
Q6.A boat can covers a certain distance in upstream and same distance in downstream in total of 7 hours 48 minutes, If upstream speed of the boat is 62.5%. of downstream speed of the boat and speed of the stream is 3 km/h, what is the total distance covered by the boat?
Q7.M and R went for shopping and bought two sarees each at different cost. Cost price of saree bought by R is Rs.250 more than the cost price of saree bought by M. Shopkeeper earned a profit of 20% on selling both the sarees together to R and M which he bought them at total Rs.6000. At what cost did M buy saree?
Q8.There are three numbers m, n, and p, such that sum of m and n is 144, sum of thrice of n and five times of p is 464, and sum of p and m is 160, then what is the value of p?
Q9.While calculating average marks of 60 students, the two digits of original marks of a student are written reversed and thereby average of marks is increased by 0.6 Find the difference between the two digits of marks of the student?  
Q10.Simple interest received on a certain sum at a rate of simple interest of 5% for 2 years is Rs.780. If the rate of interest remains same, what will be the total amount at the time of withdrawal at the end of 5 years.  
Exams
Cut Off
Eligibility
Coaching
Previous Year Papers
Syllabus
Test Series
Important Exams
Super Coaching
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti master online teen patti 50 bonus teen patti star login real cash teen patti teen patti casino