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Question : If $x+y+z = 22$ and $xy+yz+zx = 35$, then what is the value of $\small (x-y)^{2}+(y-z)^{2}+(z-x)^{2}$?
Option 1: 793
Option 2: 681
Option 3: 758
Option 4: 715
Correct Answer: 758
Solution : Given: $x+y+z = 22$ and $xy+yz+zx = 35$ We know that $(x+y+z)^2 = x^2+y^2+z^2+2(xy+yz+zx)$ ⇒ $22^2 = x^2+y^2+z^2+2\times 35$ ⇒ $484 = x^2+y^2+z^2+70$ ⇒ $x^2+y^2+z^2 = 484-70 = 414$ So, $(x-y)^2+(y-z)^2+(z-x)^2 = 2[x^2+y^2+z^2-(xy+yz+zx)]$ ⇒ $(x-y)^2+(y-z)^2+(z-x)^2 = 2[414-35]$ $\therefore(x-y)^2+(y-z)^2+(z-x)^2 = 758$ Hence, the correct answer is
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
Women candidates are (exempted to) paying the application fee.
(1) exempted for
(2) exempted from
(3) exempted in
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The second option is the correct choice.
The original sentence contains a prepositional error. To indicate that someone is free from a certain obligation (paying the application fee in this case), we use the preposition "from" after "exempted".
Therefore, the correct sentence is: Women candidates
Question : Which of the following numbers is not a factor of $5^p7^q,(p\neq 0,q\neq 0)$?
Option 1: 35
Option 2: 175
Option 3: 1225
Option 4: 735
Correct Answer: 735
Solution : Checking the factors of all the options for divisibility by 5 and 7. 35 = 5 × 7 175 = 5 × 5 × 7 1225 = 5 × 5 × 7 × 7 735 = 5 × 7 × 7 × 3 735 has
Question : Directions: the following pie chart shows the export of automobiles from India to the 10 countries given below in 2014. The 10 countries imported 47.8% of the total exports of India. Observe the chart given below and answer the following question. The number of automobiles exported to the U.S.A. is equal to combined exports to which two countries?
Option 1: Sri Lanka and Turkey
Option 2: Sri Lanka and Bangladesh
Option 3: Mexico and UAE
Option 4: UK and Turkey
Correct Answer: UK and Turkey
Solution : According to given pie chart in question, Percentage of exports to the United States = 8.40% Percentage of exports to United Kingdom and Turkey = (4.4 + 4)% = 8.4% Hence, the correct answer is the UK and Turkey.
Question : Direction: In the following question, a statement is given followed by two conclusions / Assumptions. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statement.
Statement
If people are intelligent they should be creative.
Assumptions
I. Creativity and intelligence are related.
II. Creative people are intelligent.
Option 1: Both assumptions I and II are invalid
Option 2: Only assumption I is valid
Option 3: Only assumption II is valid
Option 4: Both assumptions I and II are valid
Correct Answer: Only assumption I is valid
Solution : Given:
If people are intelligent, they should be creative.
Now, let's assess the assumptions:
I. Creativity and intelligence are related. This assumption is supported by the statement. The statement implies that there is a relationship between intelligence and creativity. It
Question : If two successive discounts of 20% and 30% are given, what is the net discount (in %)?
Option 1: 40
Option 2: 44
Option 3: 56
Option 4: 60
Correct Answer: 44
Solution : Single equivalent discount = $(a+b-\frac{a×b}{100}$)%, where $a$% and $b$% are successive discounts. So, the single discount of two successive discounts of 20% and 30% $=20+30-\frac{20×30}{100}=44\%$ Hence, the correct answer is 44.
Question : Market-Based Economic Dispatch (MBED) mechanism is related to which of the following ministries?
Option 1: Ministry of Power
Option 2: Ministry of Corporate Affairs
Option 3: Ministry of Finance
Option 4: Ministry of Micro, Small and Medium Enterprises
Correct Answer: Ministry of Power
Solution : The correct answer is the Ministry of Power.
The market-based economic dispatch (MBED) mechanism, which is handled by the Union Ministry of Power, represents a significant departure from the current voluntary, decentralised pool-based electricity market.
Question : Select the most appropriate option to fill in the blank.
Those unfamiliar with the saga are bound to be mystified by the more ______ plot twists.
Option 1: arcane
Option 2: arbitrary
Option 3: aesthetic
Option 4: anoint
Correct Answer: arcane
Solution : The correct choice is the first option.
Explanation: In this context, the sentence discusses plot twists, and the adjective "arcane" accurately conveys the idea of something mysterious, secret, or understood by only a few. It fits well with the notion that those unfamiliar with
Question : Study the given graph and answer the question that follows. The total production of computers in 2013, 2015, and 2018 is x% of the total exports of computers by the company during the six years. The value of x is:
Option 1: $46 \frac{1}{3}$
Option 2: $52 \frac{1}{3}$
Option 3: $53 \frac{1}{3}$
Option 4: $49 \frac{2}{3}$
Correct Answer: $53 \frac{1}{3}$
Solution : Production of computers in 2013 = 180, in 2015 = 300, in 2018 = 320 Exports of computers in 2013 = 140, in 2014 = 240, in 2015 = 200, in 2016= 350, in 2017 = 300, in 2018 = 270 Calculation: The production
Question : Directions: In a certain code language, SHORT is written as 1, and THEME is written as 2. How will TRAIN be written in that language?
Option 1: 4
Option 2: 1
Option 3: 2
Option 4: 3
Correct Answer: 2
Solution : Given: SHORT is written as 1, and THEME is written as 2.
Write the total number of vowels present in the word SHORT to obtain the required code – In SHORT, there is only one vowel i.e. O. Thus, SHORT is coded as 1. And,
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