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Question : If $xy=48$ and $x^2+y^2=100$, then $(x+y)$ is:
Option 1: 12
Option 2: 16
Option 3: 18
Option 4: 14
Correct Answer: 14
Solution : Given: $xy = 48$ and $x^{2}+y^{2} = 100$ We know the algebraic identity, $(x+y)^{2} = x^{2}+y^{2}+2xy$ By substituting the values in the above equation, we get: $⇒(x+y)^{2} = 100+2×48$ $⇒(x+y) = \sqrt{196}$ $\therefore (x+y) = 14$ Hence, the correct answer is 14.
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".
Unless (1) / you will study hard (2) / you cannot pass. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
The clause introduced by "unless" uses the simple present tense and not the simple future tense. Thus, "you will study" should be replaced with "you study". This makes the sentence grammatically correct as per the
Question : The following sentence has been divided into parts. One of them may contain an error. Select the part that contains the error from the given options. If you don't find any error, mark 'No error' as your answer.
Hurray! Here is the toy / what I was looking for / as my birthday gift.
Option 1: Hurray! Here is the toy
Option 2: No error
Option 3: what I was looking for
Option 4: as my birthday gift.
Correct Answer: what I was looking for
Solution : The correct choice is the third option.
Explanation: The phrase "what I was looking for" is redundant and unnecessary. The correct form should simply be, "Here is the toy I was looking for". The use of "what" adds unnecessary complexity
Question : If the selling price of 9 boxes is equal to the cost price of 15 boxes. The gain percentage is (The selling price of all boxes is the same and the cost price of all boxes is the same):
Option 1: $\frac{50}{3}\%$
Option 2: $\frac{200}{3}\%$
Option 3: $\frac{100}{3}\%$
Option 4: $\frac{140}{3}\%$
Correct Answer: $\frac{200}{3}\%$
Solution : Let the cost price of one box as C and the selling price of one box as S. Given that the selling price of 9 boxes is equal to the cost price of 15 boxes. ⇒ 9S = 15C ⇒ S = $\frac{15}{9}$C = $\frac{5}{3}$C
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 of the given conclusions logically follows the given statements. Statements: I. Some pencils are paper. II. No book is paper. Conclusions: I. Some pencils are not books. II. All books are pencils. III. Some papers are pencil.
Option 1: Both conclusions I and III follow
Option 2: Only conclusion II follows
Option 3: All conclusion follows
Option 4: Both conclusions II and III follow
Correct Answer: Both conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some pencils are not books – From the Venn diagram, we can see that there is a portion of pencils
Question : Select the correct passive form of the given sentence.
Help the migrant workers.
Option 1: By whom are the migrant workers being helped?
Option 2: Why should the migrant workers be helped?
Option 3: We should help the migrant workers.
Option 4: Let the migrant workers be helped.
Correct Answer: Let the migrant workers be helped.
Solution : The fourth option is the correct answer.
Passive voice is a grammatical construction where the subject of the sentence undergoes the action expressed by the verb rather than performing it. In the active sentence, the subject is "you," or an
Question : Choose the word that is opposite in meaning to the given word.
Subtracted
Option 1: Separated
Option 2: Recap
Option 3: Adjunct
Option 4: Annihilatory
Correct Answer: Adjunct
Subtracted means taking away or reducing something, while adjunct refers to something added or attached to a larger or more significant thing. So, it becomes the most appropriate antonym among the given options.
The meanings of the
Question : Select the correct passive form of the given sentence. The school is holding online activity classes for children.
Option 1: Online activity classes for children were held by the school.
Option 2: Online activity classes for children are being held by the school.
Option 3: Online school for children is being held by the activity classes.
Option 4: Online activity classes for children have been held by the school.
Correct Answer: Online activity classes for children are being held by the school.
Solution : The second option is the correct choice.
The passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence
Question : Directions: After interchanging the given two signs, what will be the value of the given equation? + and – 12 + 8 × 6 ÷ 3 – 11
Option 1: 7
Option 2: 5
Option 3: 9
Option 4: 8
Correct Answer: 7
Solution : Given: + and – are interchanged – 12 + 8 × 6 ÷ 3 – 11 = ?
After interchanging the given mathematical signs, we get – ⇒ 12 – 8 × 6 ÷ 3 + 11 ⇒ 12 – 8 × 2 + 11
Question : Directions: In 5 years, Rs. 5000 amounts to Rs.9000. In what time at the same rate will Rs.600 amount to Rs.900?
Option 1: 5 years
Option 2: 3 years
Option 3: 6 years
Option 4: 2 years
Correct Answer: 3 years
Solution : Given: In 5 years, Rs.5000 amounts to Rs.9000.
We have, Principal = 5000 Time = 5 yrs Amount = 9000 Rate = ? We know that, Amount (A) = P + {(P × R × T)/100} ⇒ 9000 = 5000 + {(5000 × R
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