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Question : If $x^{2}+y^{2}+2x+1=0$, then the value of $x^{31}+y^{35}$ is:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
Correct Answer: –1
Solution : Given: $x^{2}+y^{2}+2x+1=0$ ⇒ $x^{2}+2x+1+y^{2}=0$ ⇒ $(x+1)^2+y^2=0$ Since the addition of the squares of the two terms is zero, So, both the terms are individually zero. Therefore, $(x+1)^2=0$ and $y^2=0$. ⇒ $x=-1$ and $y=0$ Now, $x^{31}+y^{35}$ = $(-1)^{31}+(0)^{35}$ = –1 Hence, the correct answer is –1.
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".
She does not listen to me (1) / because she is (2) / senior than me. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third part of the sentence.
The preposition that should follow "senior" is to as adjectives ending in "-ior", such as junior, senior, inferior, and superior, are followed by to and not than.
Therefore, the correct sentence is: "She does
Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figures – 1. The circle in the box is moving in a clockwise direction from one corner to another. 2. The arrow inside the box is rotating by 90° in the anticlockwise direction. 3. The letters that are present in the box
Question : The liberation of oxygen during photosynthesis is due to
Option 1: Hydrolysis of carbohydrates
Option 2: Photolysis of water
Option 3: Reduction of CO2
Option 4: Breakdown of chlorophyll
Correct Answer: Photolysis of water
Solution : The answer is the Photolysis of water.
Oxygen is created as a consequence of photosynthesis's light-dependent processes, particularly photolysis, in which water molecules are split to liberate oxygen, electrons, and protons. The reaction involved in photosynthesis is 6CO2+6H2O----sunlight----> C
Question : Who among the following has won the BBC Sports Personality of the Year 2020 award?
Option 1: Lewis Hamilton
Option 2: Michael Schumacher
Option 3: Tyson Fury
Option 4: Jordan Henderson
Correct Answer: Lewis Hamilton
Solution : The correct answer is Lewis Hamilton.
The BBC Sports Personality of the Year 2020 was awarded to Lewis Hamilton. The renowned Formula 1 driver clinched his seventh World Championship title during the 2020 season, matching the record set by Michael Schumacher. Hamilton's exceptional
Question : The tax on the salary of C is $\frac{1}{4}$th of the salary and savings are $\frac{1}{3}$rd of the salary. The ratio of the expenditures to the savings is_____.
Option 1: 4 : 5
Option 2: 4 : 3
Option 3: 5 : 4
Option 4: 3 : 4
Correct Answer: 5 : 4
Solution : Let the salary of C be $12a$. ⇒ Tax $= 12a × \frac14 = 3a$ And, savings $= 12a × \frac13=4a$ ⇒ Expenditure $= 12a - 3a - 4a=5a$ ⇒ Ratio of expenditure : saving $= 5a : 4a=5 : 4$ Hence, the
Question : Directions: In the following question, two statements are given, followed by two conclusions, I and II. You have to consider the two statements to be true, even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements. Statements: No spaghetti is noodles. Some foods are spaghetti. Conclusions: I. All noodles are food. II. All foods are noodles.
Option 1: Only Conclusion I follows
Option 2: Only Conclusion II follows
Option 3: Both Conclusions I and II follow
Option 4: Neither Conclusion I nor Conclusion II follows
Correct Answer: Neither Conclusion I nor Conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All noodles are food – According to the Venn diagram, there is no direct relation between noodles and food.
Question : The interest accrued on INR 12,000 in two years, when interest is compounded annually, is INR 3,870. What is the rate of interest per annum?
Option 1: 12.5%
Option 2: 10%
Option 3: 20%
Option 4: 15%
Correct Answer: 15%
Solution : Principal sum, $P$ = INR 12,000 Term, $n$ = 2 years Compound interest = INR 3870 Let $R$ be the interest rate. When compounded annually, Compound interest = $P(1+\frac{R}{100})^n - P$ ⇒ $3870 = 12000(1+\frac{R}{100})^2 - 12000$ ⇒ $3870 + 12000 = 12000(1+\frac{R}{100})^2 $ ⇒
Question : The total surface area of a right pyramid on a square base of side 10 cm with height 12 cm is:
Option 1: 260 cm2
Option 2: 360 cm2
Option 3: 330 cm2
Option 4: 300 cm2
Correct Answer: 360 cm2
Solution : In $\triangle$OAB, Slant height, $l$ = $\sqrt {h^2 + AB^2}$ = $\sqrt {12^2 + 5^2}$ = $\sqrt{169}$ = $13$ cm Total surface area = lateral surface area + area of the base = $\frac{1}{2}$ × perimeter of base × slant height + area
Question : Select the most appropriate one word for the expression given below. Fear of heights.
Option 1: Agoraphobia
Option 2: Claustrophobia
Option 3: Acrophobia
Option 4: Homophobia
Correct Answer: Acrophobia
Solution : The third option is the correct choice.
Explanation: The most appropriate one-word term for the fear of heights is Acrophobia because it precisely denotes the specific phobia related to high places. Acro comes from the Greek word for height or high altitude, and phobia
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