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Question : A cuboid whose sides are 8 cm, 27 cm, and 64 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?
Option 1: 307 : 216
Option 2: 291 : 203
Option 3: 349 : 248
Option 4: 329 : 237
Correct Answer: 307 : 216
Solution : Sides of cuboid = 8 cm, 27 cm, and 64 cm Let $a$ be the side of the cube. The volume of the cuboid = volume of the cube $lbh$ = $a^3$ 8 × 27 × 64 = $ a^3$ $a$ = $\sqrt[3]{8
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. Individuals might not always do just what we (1)________ like them to do. No matter how justified or marginal our requirements (2)_________ we will occasionally be disheartened. Instinctually, when our expectations are not fulfilled, we become hurt and upset. Altercations terrify us since they are uncomfortable and have the potential to destroy relationships. However, avoiding confrontation does not (3)___________ the dispute, as unanswered questions also have a detrimental (4)__________ on relationships. Indeed, the true source of (5)___________ is our confrontational style, not the problem itself.
Question:
Select the most appropriate option to fill in the blank number 4.
Option 1: side
Option 2: influence
Option 3: affect
Option 4: effect
Correct Answer: effect
Solution : The correct choice is the fourth option.
In the passage, the statement discusses the negative consequences of unanswered questions about relationships. Effect is a term commonly used to convey the idea of a result, impact, or influence. In this context, it effectively communicates that
Question : In an equilateral $\triangle$ PQR, S is the point on the side QR such that QR = 3QS. If PQ = 9 cm, then what will be the length (in cm) of PS?
Option 1: $\sqrt{60} $
Option 2: $\sqrt{63}$
Option 3: $\sqrt{62}$
Option 4: $\sqrt{61}$
Correct Answer: $\sqrt{63}$
Solution : Draw PT perpendicular to QR. PT = $\frac{\sqrt3}{2}\times 9=\frac{9\sqrt3}{2}$ cm QT = $\frac{9}{2}$ cm Given, QR = 3QS ⇒ QS = $\frac{9}{3}$ = 3 cm ST = QT – QS =$\frac{9}{2} -3$ = $\frac{3}{2}$ Using Pythagoras' theorem: Hypotenuse2 = Base2 + Perpendicular2
Question : Directions: Words given on the left side of (::) are related by some Logic/Rule /Relation. Select the missing word/word pair on the right side of (::) from the given alternatives based on the same Logic/Rule/Relation. Car : Vehicle :: ?
Option 1: Table : Furniture
Option 2: Profession : Teaching
Option 3: Figure: Triangle
Option 4: Stationery : Pen
Correct Answer: Table : Furniture
Solution : Given: Car : Vehicle :: ? (This depicts the relation between things and the category they belong to. Like, a car is a type of vehicle.)
Let's check each option – First option: Table : Furniture; Table is a type of furniture. Second
Question : Select the INCORRECTLY spelt word.
Option 1: Bonafide
Option 2: Cultural
Option 3: Solusion
Option 4: Trustworthy
Correct Answer: Solusion
Solution : The correct answer is in the third option.
The correctly spelled word is solution, which means a method to solve a problem or deal with a situation. The provided spelling makes incorrect use of consonants in the word.
Question : Directions: In the given 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.
I'm very pleased with my new secretary. Her work is of a high _______.
Option 1: condition
Option 2: degree
Option 3: capacity
Option 4: standard
Correct Answer: standard
Standard means a level of quality or attainment, and is the appropriate word to fill the blank with, as it helps in correctly conveying the intended meaning that the work of the secretary is of a certain level
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".
Hardly had I reached the (1) / exhibition where I learnt (2) / about the major robbery (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The correct answer is the second option.
"Where" should be replaced with "when" to convey the intended meaning that the speaker learnt about the robbery as soon as they reached the exhibition. "Hardly...when" is the correct correlative conjunction to be used in the sentence.
Therefore,
Question : Directions: In a certain code language, ACID is written as ZBHC, and LAND is written as KZMC. How will GOLD be written in that language?
Option 1: FNKB
Option 2: FNKC
Option 3: FNJC
Option 4: FMKC
Correct Answer: FNKC
Solution : Given: ACID is written as ZBHC and LAND is written as KZMC.
Subtract 1 from each alphabet to obtain the code. ACID→ A – 1 = Z; C – 1 = B; I – 1 = H; D – 1 = C Thus, ACID is
Question : How many numbers from 1 to 430 are divisible by 7 and 11 both?
Option 1: 5
Option 2: 11
Option 3: 9
Option 4: 7
Correct Answer: 5
Solution : LCM of 7 and 11 = 77 The number divisible by 7 and 11 both should be divisible by 77. The required numbers are 77, 154, 231, 308, and 385 and the next number will be greater than 430. Hence, the correct answer is 5.
Question : A vertical pole and vertical tower are standing on the same level of ground. The height of the pole is 10 m. From the top of the pole, the angle of elevation of the top of the tower and the angle of depression of the foot of the tower are 60° and 30° respectively. The height of the tower is:
Option 1: 20 m
Option 2: 30 m
Option 3: 40 m
Option 4: 50 m
Correct Answer: 40 m
Solution : Let $AB$ be the tower and $CD$ be the pole. $CD = BE = 10$ m In $\triangle BCE$, $\tan$ 30° = $\frac{10}{CE}$ ⇒ $\frac{1}{\sqrt3}$ = $\frac{10}{CE}$ ⇒ $CE = 10\sqrt3$ In $\triangle ACE$, $\tan$ 60° = $\frac{h}{CE}$ ⇒ $\sqrt3$ = $\frac{h}{10\sqrt3}$ ⇒ $h$
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