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Question : If $\left(x+\frac{1}{x}\right)=5$, and $x>1$, what is the value of $\left(x^8-\frac{1}{x^8}\right)?$

Option 1: $60605 \sqrt{21}$

Option 2: $60615 \sqrt{21}$

Option 3: $60705 \sqrt{21}$

Option 4: $60725 \sqrt{21}$

Team Careers360 24th Jan, 2024

Correct Answer: $60605 \sqrt{21}$


Solution : Given: $\left(x+\frac{1}{x}\right)=5$--------------(i)
Now, $\left(x^8-\frac{1}{x^8}\right)$
$=(x^4-\frac{1}{x^4})$$(x^4+\frac{1}{x^4})$
$=(x^2-\frac{1}{x^2})$$(x^2+\frac{1}{x^2})$$(x^4+\frac{1}{x^4})$
$= (x-\frac{1}{x})$$(x+\frac{1}{x})$$(x^2+\frac{1}{x^2})$$(x^4+\frac{1}{x^4})$----------(ii)
Squaring equation (i), we get,
$(x+\frac{1}{x})^2 = 5^2$
$⇒(x^2+\frac{1}{x^2}+2) = 25$
$⇒(x^2+\frac{1}{x^2}) = 23$-----------------(iii)
Squaring equation (iii), we get,
$(x^2+\frac{1}{x^2})^2 = 23^2$
$⇒(x^4+\frac{1}{x^4}+2) = 529$
$⇒(x^4+\frac{1}{x^4}) = 527$---------------(iv)
Subtracting 2 on both sides of equation (iii),

248 Views

is there a separate examination for JIPMER for the UG MBBS EXAM

mjaisinghani62 22nd Jan, 2024

Hello aspirant .

The entrance exam for ug mbbs is Neet ug.

Previously JIPMER entrance exam was there for admission  to mbbs or medical  courses . It is now replaced with neet ug.

Jawaharlal Institute of post graduate medical education and research was established in 1956.

Jipmer is ranked number

207 Views

Whats the fee structure for msc clinical embryology and assisted reproductive technology in Reva university? Also is there any entrance examination for admission to this course??

mjaisinghani62 25th Jan, 2024

Hello Annex


For msc in clinical embryology from reva university Fees charges are 80,000 for two years.

Msc in clinical embryology and assisted reproductive technology deals with study of in vitro fertilization .

( IVF)

These days invitro fertilization has proved a boon to innumerable infertile couples . Over the

17 Views

how to prepare for CDS entrance examination

Sajal Trivedi 21st Jan, 2024

Hello aspirant,

Those who want to take the CDS exam in 2024 need to start planning their study. Candidates must allot the same amount of time to each of the exam's topics. Completing the CDS syllabus 2024 on time is also beneficial. The study plan aids in maintaining goal concentration

13 Views

Question : Direction: In the following question, select the related word from the given alternatives.

Hot : Cold :: ? 

Option 1: Summer : Sun

Option 2: Germs : Diease 

Option 3: Light : Dark 

 

Option 4: Thin : Big 

Team Careers360 23rd Jan, 2024

Correct Answer: Light : Dark 

 


Solution : Given:

Hot : Cold :: ? 

The relationship is that hot is the opposite of cold. They are antonyms representing opposite temperature conditions.

Now, let's apply the same logic to all the options of the analogy:

Option first: Summer : Sun

The

177 Views

Question : A Shopkeeper marked the price as INR 15,000 on an article, and a successive discount of 5%, 10% and 20% was allowed on it. What is the selling price?

Option 1: INR 10,260

Option 2: INR 13,520

Option 3: INR 11,520

Option 4: INR 9,850

Team Careers360 19th Jan, 2024

Correct Answer: INR 10,260


Solution : A successive discount of 5%, 10%, and 20% means that these discounts are applied one after another
For three successive discounts of 5%, 10%, and 20%,
Selling price = $\frac{100-\text{Discount}_1\%}{100}× \frac{100-\text{Discount}_2\%}{100}×\frac{100-\text{Discount}_3\%}{100}×$ marked price
⇒ Selling price $=\frac{100-5}{100}×\frac{100-10}{100}×\frac{100-20}{100}×15000$
⇒ Selling price $=\frac{95}{100}×\frac{90}{100}×\frac{80}{100}×15000$
⇒ Selling price

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