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Question : If $3a=4b=6c$ and $a+b+c=27\sqrt{29}$, then $\sqrt{a^{2}+b^{2}+c^{2}}$ is equal to:
Option 1: 87
Option 2: $3\sqrt{29}$
Option 3: 82
Option 4: 83
Correct Answer: 87
Solution : Given: $3a=4b=6c$ ⇒ $3a=6c$ ⇒ $a=2c$ $4b=6c$ ⇒ $b=\frac{3}{2}c$ Putting these values in the equation, we get, $a+b+c=27\sqrt{29}$ ⇒ $2c+\frac{3}{2}c+c=27\sqrt{29}$ ⇒ $\frac{9}{2}c=27\sqrt{29}$ ⇒ $c=6\sqrt{29}$ now we have to find $\sqrt{a^2+b^2+c^2}$, then: $\sqrt{a^2+b^2+c^2}=\sqrt{(a+b+c)^2–2(ab+bc+ca)}$ Putting the values ⇒ $\sqrt{a^2+b^2+c^2}=\sqrt{(27\sqrt{29})^2–2(2c×\frac{3}{2}c+\frac{3}{2}c×c+c×2c)}$ ⇒ $\sqrt{a^2+b^2+c^2}=\sqrt{(27\sqrt{29})^2–2(3c^2+\frac{3}{2}c^2+2c^2)}$ ⇒ $\sqrt{a^2+b^2+c^2}=\sqrt{(729×29)–2×\frac{13}{2}c^2}$ ⇒ $\sqrt{a^2+b^2+c^2}=\sqrt{(729×29)–13c^2}$ ⇒ $\sqrt{a^2+b^2+c^2}=\sqrt{21141–13(6\sqrt{29})^2}$
Question : ___________has been awarded the SASTRA Ramanujan Prize, 2019.
Option 1: Manjul Bhargava
Option 2: Adam Harper
Option 3: Akshay Venkatesh
Option 4: Maryam Mirzakhani
Correct Answer: Adam Harper
Solution : The correct answer is Adam Harper.
Adam Harper was awarded the SASTRA Ramanujan Prize in 2019. Adam Harper is an assistant professor at the University of Warwick, England. The SASTRA Ramanujan Award is an annual award given to young mathematicians for their outstanding contributions
Question : Find the part of the given sentence that has an error in it. If there is no error, choose "No error".
Just because I am quiet doesn't mean I can't scold you.
Option 1: Just because I am
Option 2: quiet doesn't mean
Option 3: I can't scold you.
Option 4: No error
Correct Answer: No error
Solution : The correct choice is the fourth option.
It is a complex sentence that uses a conditional statement and a negation to convey the idea that being quiet doesn't mean an inability to scold or speak up. It is grammatically correct.
Therefore, the given
Question : Directions: If the given words are arranged as per an English dictionary, then which word will appear second?
Option 1: Curtains
Option 2: Cumbersome
Option 3: Curious
Option 4: Cucumber
Correct Answer: Cumbersome
Solution : Given: 1. Curtains 2. Cumbersome 3. Curious 4. Cucumber
Step 1: Compare the first and second letters of each word. Since all the words start with the same letter C and are followed by u, then move on to the next letter. Step 2:
Question : Directions: In the following question, some parts of the sentence may have 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."
The captain along with his team (1) / are practising very hard (2) / for the forthcoming match. (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 main subject of the sentence is singular, as "the captain" and "his team" are treated as a singular unit, as they are combined with the help of "along". Hence, the verb should be
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
Human life is (1)____ a unique blessing, which in turn depends on the (2)______ of the Self. He who is not aware of the Self can neither have peace nor can he foster peaceful coexistence. We have to link our soul with God and the body with the physical world for substance. (3)_____ the formless God is invisible to the naked eye, our mind often wanders wherever it goes. (4)_____, we are unable to develop any love for the Divine. And religion like the white light of heavens (5)______ multi-coloured fragmentations by the prisms of men and loses its gravity. Instead of uniting, it becomes a major dividing force. French philosopher Tail hard de Chardin, thinking deeply on the meaning of our existence and relationship with the Divine, expounds, "We are not human beings having a spiritual experience, we are spiritual beings having a human experience".
Question:
Select the most appropriate option to fill in blank no. 1.
Option 1: considering
Option 2: to consider
Option 3: considered
Option 4: consider
Correct Answer: considered
Solution : The correct choice is the third option.
Considered means an opinion, which is reached after a lot of thought and correctly fits in the sentence, as the sentence tells us that human life is a unique blessing. The other options do not provide the correct
Question : Which Indian actress was also one of the dancers to be honoured with the Padma Shri award in 1968?
Option 1: Hema Malini
Option 2: Sridevi
Option 3: Vyjayanthimala
Option 4: Madhubala
Correct Answer: Vyjayanthimala
Solution : The correct answer is Vyjayanthimala
Vyjayanthimala is a distinguished former Indian actress, dancer, and parliamentarian. Renowned as one of Indian cinema's finest talents. Starting her career at 16 in the Tamil film "Vaazhkai" (1949), she achieved prominence with Hindi films like "Bahar" (1951) and "Nagin"
Question : An article is sold at a loss of 10%. Had it been sold for Rs. 90 more, there would have been a gain of 5%. The original sale price of the article (in Rs.) is:
Option 1: Rs. 540
Option 2: Rs. 600
Option 3: Rs. 628
Option 4: Rs. 650
Correct Answer: Rs. 540
Solution : Here CP denotes cost price and SP denotes selling price. If the CP of the article is Rs. $x$, then Difference in the selling price = Difference in the profits ⇒ Rs. 90 = (10% + 5%) of $x$ ⇒ $x$ = Rs. 600
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error. Maruti likes / adventure / stories, especially / an adventures of Tarzan.
Option 1: stories, especially
Option 2: an adventures of Tarzan
Option 3: Maruti likes
Option 4: adventure
Correct Answer: an adventures of Tarzan
Solution : The second option is the correct choice.
Explanation: The indefinite articles "a" and "an" are used to modify singular nouns. Plural nouns can take either the definite article "the" or no article at all. Here, we need to
Question : Select the correct passive form of the given sentence.
How many glasses of water do you drink daily?
Option 1: How many glasses of water is drank by you daily?
Option 2: How many glasses of water are drank by you daily?
Option 3: How many glasses of water are drunk by you daily?
Option 4: How many glasses of water have been drunk by you daily?
Correct Answer: How many glasses of water are drunk by you daily?
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 voice becomes the
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