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Question : If decreasing 110 by $x\%$ gives the same result as increasing 50 by $x\%$, then $x\%$ of 650 is what percentage (correct to the nearest integer) is more than $(x-10)\%$ of 780?
Option 1: 12%
Option 2: 17%
Option 3: 14%
Option 4: 18%
Correct Answer: 14%
Solution : On decreasing 110 by $x\%$ as $110(1 - \frac{x}{100})$ and the increase of 50 by $x\%$ as $50(1 + \frac{x}{100})$. According to the question, $⇒110(1 - \frac{x}{100}) = 50(1 + \frac{x}{100})$ $⇒1100-11x=500+5x$ $⇒16x=600$ $⇒x=\frac{75}{2}$ $⇒x=37.5$% Next, we calculate $x\%$ of 650. So, 650 × $\frac{37.5}{100}$
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: EHJ
Option 2: JML
Option 3: PSR
Option 4: VYX
Correct Answer: EHJ
Solution : Let's check the options – First option: EHJ; E + 3 = H; H + 2 = J Second option: JML; J + 3 = M; M – 1 = L Third option: PSR; P + 3 = S; S – 1 = R Fourth
Question : The term of the office of the member of the UPSC is
Option 1: 3 years , or till they attain 58 years of age
Option 2: 5 years , or till they attain 60 years of age
Option 3: 6 years , or till they attain 65 years of age
Option 4: 6 years
Correct Answer: 6 years , or till they attain 65 years of age
Solution : The correct option is 6 years , or till they attain 65 years of age .
The term of office for a member of the Union Public Service Commission (UPSC) in India is six years
Question : A person lent Rs. 10,000 to B for 3 years and Rs. 6,000 to C for 4 years on Simple interest at the same rate of interest and received Rs. 5,400 in all from both of them as interest. What is the rate of interest (in percent)?
Option 1: 10
Option 2: 12.5
Option 3: 15
Option 4: 20
Correct Answer: 10
Solution : Let the rate be $r$. We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ So, interest from B = $\frac{10000×3×r}{100}=300r$ Also, interest from C = $\frac{6000×4×r}{100}=240r$ According to the question, ⇒ $300r+240r = 5400$ ⇒ $540r = 5400$ $\therefore r =10\%$ Hence, the correct
Question : The SI unit of electric charge is a ______.
Option 1: Coulomb
Option 2: watt
Option 3: newton
Option 4: joule
Correct Answer: Coulomb
Solution : The correct option is Coulomb.
One coulomb is defined as the amount of electric charge transported by a constant current of one ampere in one second. In other words, 1 C = 1 A·s (ampere-second).
C= Coloumb
A= Ampere has a fixed numerical value.
s=
Question : Which organ has finger-like outgrowths which are called Villi (Singular Villus)?
Option 1: Large Intestine
Option 2: Bladder
Option 3: Small Intestine
Option 4: Stomach
Correct Answer: Small Intestine
Solution : The correct option is the Small intestine.
Villi are tiny, finger-like extensions that line the small intestine's walls. They are composed of specialised cells and are surrounded by even smaller projections known as microvilli. The surface area of the intestinal lining is considerably
Question : P alone can complete a work in 15 days and Q alone can complete the same work in 12 days. They start the work together but after 3 days P leaves the work. How much time will Q take to finish the remaining work?
Option 1: 7.2 days
Option 2: 7.8 days
Option 3: 8.5 days
Option 4: 6.6 days
Correct Answer: 6.6 days
Solution : P alone can complete a work in 15 days. ⇒ P's 1 day's work = $\frac{1}{15}$ Q alone can complete the same work in 12 days. ⇒ Q's 1 day's work = $\frac{1}{12}$ So, (P + Q)'s 1 day's work = $\frac{1}{15}+\frac{1}{12}=\frac{3}{20}$ ⇒ (P
Question : Select the most appropriate meaning of the underlined idiom. We dodged a bullet when we didn’t fall for the agents’ words.
Option 1: To give something a try
Option 2: To narrowly avoid situation
Option 3: To be out of your comfort zone
Option 4: To start performing better
Correct Answer: To narrowly avoid situation
Solution : The second option is the correct choice.
The expression dodged a bullet is an idiomatic way of saying that someone or something narrowly avoided a potential disaster or harm. In the provided sentence, it suggests that by not falling for the
Question : If $\theta$ is positive acute angle and $7\cos^{2}\theta+3\sin^{2}\theta =4$, then the value of $\theta$ is:
Option 1: $60^{\circ}$
Option 2: $30^{\circ}$
Option 3: $45^{\circ}$
Option 4: $90^{\circ}$
Correct Answer: $60^{\circ}$
Solution : $7\cos^{2}\theta +3\sin^{2}\theta = 4$ $⇒7\cos^{2}\theta +3(1-\cos^{2}\theta) = 4$ ........[we know that $\sin^{2}\theta + \cos^{2}\theta=1$] $⇒4\cos^{2}\theta +3 = 4$ $⇒\cos^{2}\theta = \frac{1}{4}$ $⇒\cos^{2}\theta - \frac{1}{4}$ = 0 $⇒(\cos\theta + \frac{1}{2})(\cos\theta - \frac{1}{2})$ = 0 $⇒\cos\theta =\frac{1}{2}\ \text{or,} -\frac{1}{2}$ $⇒\cos\theta =\cos 60^{\circ}\ \text{or,}\cos 120^{\circ}$ Since $\theta$ is
Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$
Option 1: $\frac{1}{3}(x+y+z)$
Option 2: $(x+y+z)$
Option 3: $\frac{1}{4}(x+y+z)$
Option 4: $\frac{1}{2}(x+y+z)$
Correct Answer: $\frac{1}{2}(x+y+z)$
Solution : By polynomial identity $x^3+y^3+z^3−3xyz = (x+y+z)(x^2+y^2+z^2−xy−yz−zx)$ = $\frac{1}{2}(x+y+z)(2x^2+2y^2+2z^2−2xy−2yz−2zx)$ = $\frac{1}{2}(x+y+z)(x^2−2xy+y^2+y^2−2yz+z^2+z^2−2xz+x^2)$ = $\frac{1}{2}[(x+y+z)(x−y)^2+(y−z)^2+(z−x)^2]$ $\therefore \frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$ = $\frac{\frac{1}{2}[(x+y+z)(x−y)^2+(y−z)^2+(z−x)^2]}{(x-y)^2+(y-z)^2+(z-x)^2}$ = $\frac{1}{2}(x+y+z)$ Hence, the correct answer is $\frac{1}{2}(x+y+z)$.
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