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15 Views

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

Team Careers360 27th Jan, 2024

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

408 Views

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: $\sqrt{61}$

Team Careers360 27th Jan, 2024

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

10 Views

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

Team Careers360 26th Jan, 2024

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

15 Views

Question : Select the INCORRECTLY spelt word.

Option 1: Bonafide

Option 2: Cultural

Option 3: Solusion

Option 4: Trustworthy

Team Careers360 26th Jan, 2024

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.

10 Views

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

Team Careers360 26th Jan, 2024

Correct Answer: standard


Solution : The correct choice is the fourth option.

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

18 Views

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)

Team Careers360 27th Jan, 2024

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,

8 Views

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

Team Careers360 27th Jan, 2024

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

193 Views

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

Team Careers360 26th Jan, 2024

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.

19 Views

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

Team Careers360 27th Jan, 2024

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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