Examination
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: $60725 \sqrt{21}$
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),
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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
Correct Answer: Light : Dark
Solution : Given:
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
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
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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