Graduate Aptitude Test in Engineering
Question : A chord of length 48 cm is at a distance of 7 cm from the centre of the circle. What is the length of the chord of the same circle which is at a distance of 15 cm from the centre of the circle?
Option 1: 40 cm
Option 2: 45 cm
Option 3: 35 cm
Option 4: 42 cm
Correct Answer: 40 cm
Solution : The perpendicular from the centre of a circle to a chord bisects the chord. By Pythagoras theorem: Hypotenuse2 = Base2 + Perpendicular2 MP = PN = $\frac{\text{MN}}{2}$ = $\frac{48}{2}$ = 24 cm Distance from the centre as $d_{1}$ = 15 cm
Question : If the radius of a right circular cylinder open at both ends is decreased by 25% and the height of the cylinder is increased by 25%, the curved surface area of the cylinder thus formed:
Option 1: remains unaltered
Option 2: is increased by $25\%$
Option 3: is increased by $6.25\%$
Option 4: is decreased by $6.25\%$
Correct Answer: is decreased by $6.25\%$
Solution : The curved surface area of a right circular cylinder before the change, where $r$ is the radius and $h$ is the height $ = 2\pi rh$ The radius is decreased by $25\%$, $r' = 0.75r$ The height is increased by $25\%$, $h'
Question : Select the most appropriate option that expresses the given sentence in passive voice.
The student asked the teacher a question during class.
Option 1: A question was asked by the student to the teacher during class.
Option 2: A question is being asked by the student to the teacher during class.
Option 3: A question asked by the student to the teacher during class.
Option 4: A question will be asked by the student to the teacher during class.
Correct Answer: A question was asked by the student to the teacher during class.
Solution : The correct choice is the first option.
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 : The oath of office is administered to the Governor by the:
Option 1: Chief Justice of India
Option 2: Speaker of Legislative Assembly
Option 3: Chairman of Legislative Council
Option 4: Chief Justice of the High Court
Correct Answer: Chief Justice of the High Court
Solution : The correct answer is Chief Justice of the High Court.
A state's governor is chosen by the president and serves at his pleasure for five years. The governor's oath is administered by the Chief Justice of the relevant State
Question : Select the option that arranges the given sentences in the correct sequence The first sentence is in the correct position.
A. Mrs. Salmon who lived in 15, Northwood Street had been unable to sleep. B. He had a hammer in his hand and had just come out of her house. C. But when she went to the window she saw Adams standing on the steps of Mrs. Parker's house. D. She heard a door click shut and thought it was her own gate.
Option 1: ABCD
Option 2: ADCB
Option 3: ADBC
Option 4: ACBD
Correct Answer: ADCB
Solution : The correct choice is the second option.
The paragraph starts with sentence A, which introduces Mrs Salmon and her situation, mentioning that she was unable to sleep, followed by sentence D, which describes an auditory event that Mrs. Salmon experiences followed by
Question : Total revenue from operations Rs. 9,00,000, Cash revenue from operations Rs. 3,00,000, Debtors Rs. 1,00,000, B/R Rs. 20,000. Trade Receivables Turnover Ratio will be :
Option 1: 5:1
Option 2: 10:1
Option 3: 7.5:1
Option 4: 9:1
Correct Answer: 10:1
Solution : The formula for trade receivables turnover ratio is equal to
Credit revenue from operations / average trade receivable
Credit revenue from operations= Total revenue for operations- cash revenue from operations.= 9,00,000-3,00,000= 6,00,000
Average trade receivables= 1,00,000+20,000/2 = 1,20,000/2= 60,000
trade receivables turnover ratio = 6,00,000/60,000=
Question : If $x-\frac{1}{x}=1$, then what is the value of $\left (\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} \right)\;$?
Option 1: $\pm \sqrt{5}$
Option 2: $\frac{2}{5}$
Option 3: $\pm\frac{2}{\sqrt{5}}$
Option 4: $\pm\frac{\sqrt{5}}{2}$
Correct Answer: $\pm\frac{2}{\sqrt{5}}$
Solution : Given: $x-\frac{1}{x}=1$ $⇒x^{2}-1=x$ $⇒x^{2}+1=x+2$ $\left (\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} \right)$ $=(\frac{2}{x^{2}-1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1})$ $=(\frac{1}{x^{2}-1}+\frac{1}{x^{2}+1})$ $=(\frac{2x^{2}}{(x^{2}-1)(x^{2}+1)})$ Using $x^{2}-1=x$ and $x^{2}+1=x+2$, we get, $=(\frac{2x^{2}}{(x)(x+2)})$ $=\frac{2x}{x+2}$ Solving $x^{2}-x-1=0$, we get $x=\frac{1\pm\sqrt{5}}{2}$ So, $x+2=\frac{5\pm\sqrt{5}}{2}$ When $x=\frac{1+\sqrt{5}}{2}$, $\frac{2x}{x+2}=\frac{2}{\sqrt{5}}$ When $x=\frac{1-\sqrt{5}}{2}$, $\frac{2x}{x+2}=-\frac{2}{\sqrt{5}}$ Hence, the correct answer is $\pm\frac{2}{\sqrt{5}}$.
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
It is said that everyone lives (1) _________selling something. What you can (2) ____________from this statement is that teachers live by selling knowledge, philosophers live by selling wisdom and priests earn their living by selling spiritual comfort. Though it may be possible to measure the value of material goods in terms of money, it is extremely difficult to (3) __________the true value of the services which people perform for us. There are times when we would (4) ___________give everything we possess to save our lives, yet we might grudge paying a surgeon a high fee for offering us precisely the same service. The (5) ____________of society are such that skills have to be paid for in the same way that goods are paid for at a shop.
Question: Select the most appropriate option to fill in the blank number 2.
Option 1: separate
Option 2: derive
Option 3: revive
Option 4: choose
Correct Answer: derive
Solution : The second option is correct.
The sentence would read: "What you can derive from this statement is that teachers live by selling knowledge..."
In this context, derive means to obtain or receive, suggesting that one can obtain something (knowledge, in this case) from the given
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