Graduate Aptitude Test in Engineering
Question : DEF is an isosceles triangle such that DE = DF = 60 cm and EF = 96 cm. DG is a median to base EF. What is the length of DG?
Option 1: 22 cm
Option 2: 36 cm
Option 3: 24 cm
Option 4: 32 cm
Correct Answer: 36 cm
Solution : Given: DE = DF = 60 cm, EF = 96 DG median cuts EF into two halves. So, EG = $\frac{96}{2}=48$ cm In $\triangle$DEG, DE2 = DG2 + EG2 ⇒ DG = $\sqrt{60^2-48^2}=\sqrt{1296}=36$ cm Hence, the correct answer is 36 cm.
Question : Directions: In this question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
Night came on and the room ___ dark.
Option 1: is growing
Option 2: has grown
Option 3: grew
Option 4: will grow
Correct Answer: grew
Solution : The correct choice to fill in the blank is the third option.
Grew is the past tense of grow and correctly fits into the sentence, which helps convey the intended meaning, which is that the room gradually went dark along with the night. Other
Question : What was the primary purpose of translating Ain-i-Akbari into different languages?
Option 1: To spread Akbar's religious beliefs
Option 2: To facilitate trade negotiations
Option 3: To make the administrative record accessible
Option 4: To promote cultural exchange
Correct Answer: To make the administrative record accessible
Solution : Correct Option: Option 3 Explanation: The primary purpose of translating Ain-i-Akbari into different languages was to make the administrative record accessible to officials and scholars who spoke different languages, thereby ensuring effective governance.
Question : Parts of the following sentence have been given as options. Select the option that contains an error. The committee was divided on the issue, and neither side were willing to compromise on the compensation amount to be given.
Option 1: and neither side were willing to
Option 2: amount to be given
Option 3: compromise on the compensation
Option 4: The committee was divided on the issue
Correct Answer: and neither side were willing to
Solution : The correct choice is the first option.
Explanation:
The subject in this sentence is "neither side", which refers to a singular subject. Therefore, it should be followed by a singular verb.
So, the correct sentence would be: "The committee was
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Question : It is necessary for products which are not produced according to predetermine specifications such as in the case of agriculture products. Which function of marketing is highlighted in the given statement?
Option 1: Packaging
Option 2: Labelling
Option 3: Standardization
Option 4: Grading
Correct Answer: Grading
Solution : Grading is the process of classification of products into different groups on the basis of some of its important characteristics such as quality,size,etc. Grading is particularly necessary for products which are not produced according to predetermined specifications.
Hence, option D is correct.
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'
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