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Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$
Option 1: 2
Option 2: 16
Option 3: 32
Option 4: 64
Correct Answer: 2
Solution : Given: $a^{4}+1=\frac{a^{2}}{b^{2}}( 4b^{2}-b^{4}-1)$ ⇒ $\frac{(a^{4}+1)}{a^2}=\frac{1}{b^{2}}( 4b^{2}-b^{4}-1)$ ⇒ $a^2+\frac{1}{a^2}=4 -b^2-\frac{1}{b^2}$ ⇒ $a^2+\frac{1}{a^2}+2+b^2+\frac{1}{b^2} +2 =0$ ⇒ $(a-\frac{1}{a})^2+(b-\frac{1}{b})^2=0$ So, $(a-\frac{1}{a})^2=0 \;$and$\; (b-\frac{1}{b})^2=0$ ⇒ $a-\frac{1}{a}=0 \; $ and$\; b-\frac{1}{b}=0$ ⇒ $a=\frac{1}{a} \; $ and$\; b=\frac{1}{b}$ ⇒ $a^2=1 \;$ and $\; b^2 = 1$ $\therefore a^{4}+b^{4}=2$ Hence, the correct answer
Question : Which of the following is one of the Trustees of the PM CARES Fund?
Option 1: Shri Azim Premji
Option 2: Shri Gautam Adani
Option 3: Shri Mukesh Ambani
Option 4: Shri Ratan N. Tata
Correct Answer: Shri Ratan N. Tata
Solution : The correct answer is Shri Ratan N. Tata.
The PM CARES Fund has appointed veteran entrepreneur Ratan Tata, former deputy speaker of the Lok Sabha Kariya Munda, and former Supreme Court judge K. T. Thomas as trustees. On March 27, 2020,
Question : Till which year did the High Court of Delhi continue to exercise jurisdiction over Himachal Pradesh?
Option 1: 1969
Option 2: 1967
Option 3: 1971
Option 4: 1968
Correct Answer: 1971
Solution : The correct option is 1971.
Until 1971, the High Court of Delhi had jurisdiction over Himachal Pradesh. Himachal Pradesh was granted its own High Court, known as the Himachal Pradesh High Court, in 1971, and it began operating autonomously. Before that, the Delhi High Court
Question : The given sentence is divided into three segments. Select the option that has the segment with a grammatical error. If there is no error, select "No error" as your answer.
She won't be / watch the news / on the BBC channel.
Option 1: on the BBC channel
Option 2: watch the news
Option 3: She won't be
Option 4: No error
Correct Answer: watch the news
Solution : The correct choice is the second option.
The given sentence contains a grammatical error in the segment "watch the news". This segment has an error because it should use the continuous form "watching" after "be". Grammatically, when we use "be" followed by a
Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which conclusions logically follow the given statements. Statements: I. Some T are M. II. No T is Y. Conclusions: I. Some M is not Y. II. Some M are T. III. All M are Y.
Option 1: Both conclusions II and III follow
Option 2: Neither conclusion follows
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions – Conclusion I: Some M is not Y – Since no T is Y and some M is T. Thus, M that is
Question : The demand for the commodity is direct but the demand for a factor of production is called a:
Option 1: crossed demand
Option 2: joint demand
Option 3: derived demand
Option 4: independent demand
Correct Answer: derived demand
Solution : The correct answer is derived demand.
Demand for a factor of production, such as labour or capital, is referred to as "derived demand". Derived demand means that the demand for these factors is derived from the demand for the final goods or services
Question : If 20% of $(x + y)$ = 30% of $(x - y)$, then $x$ is what percentage of $y$?
Option 1: 0.5%
Option 2: 5%
Option 3: 500%
Option 4: 50%
Correct Answer: 500%
Solution : Given: 20% of $(x + y)$ = 30% of $(x - y)$ ⇒ $\frac{20}{100}×(x+y)=\frac{30}{100}×(x-y)$ ⇒ $2x+2y=3x-3y$ ⇒ $x=5y$ ⇒ $\frac{x}{y}=\frac{5}{1}$ Required percentage = $\frac{x}{y}×100=\frac{5}{1}×100=500$% So, $x$ is 500% of y. Hence, the correct answer is 500%.
Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:
Option 1: 6
Option 2: 9
Option 3: 0
Option 4: 1
Correct Answer: 0
Solution : Given: $x+y+z=9$ Solution: Let $(x–4) = a, (y−2) = b, (z−3) = c$ So, this equation stands to $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ = $a^3+b^3+c^3–3abc$ Also, We know that $a^3+b^3+c^3–3abc$ = $(a+b+c)(a^2+b^2+c^2–bc–ab–ac) $. So, $a+b+c = x−4+y−2+z−3$ ⇒ $a+b+c = x+y+z−9$ ⇒ $a+b+c = 9−9$ ⇒ $a+b+c = 0$
Question : Ethanol containing 5% water is known as :
Option 1: Dilute alcohol
Option 2: Power alcohol
Option 3: Rectified spirit
Option 4: Absolute alcohol
Correct Answer: Rectified spirit
Solution : The correct option is Rectified spirit.
Rectified spirit is a highly concentrated and pure type of alcohol that is often produced from grains or sugarcane. Because of its high alcohol concentration, which typically exceeds 95% alcohol by volume (ABV), it is frequently employed in
Question : Directions: A series is given with one term missing. Select the correct alternative from the given ones that will complete the series. ANS, CJU, EFW, GBY, ?
Option 1: IXA
Option 2: JWA
Option 3: JXB
Option 4: IWA
Correct Answer: IXA
Solution : Given: ANS, CJU, EFW, GBY, ?
In the above-given series, add 2 to the place values of the first and third letters, and subtract 4 from the place value of the second letter to obtain the next letter cluster. ANS→A + 2 = C; N
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