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Staff Selection Commission Combined Graduate Level Exam

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Question : If $x^2+4y^2=17$ and $xy = 2$, where $x > 0, y > 0$, then what is the value of $x^3+8y^3$?

Option 1: 95

Option 2: 85

Option 3: 65

Option 4: 76

Team Careers360 18th Jan, 2024

Correct Answer: 65


Solution :

$x^2 + 4y^2 = 17$ and $xy = 2$, where $ x > 0, y > 0$
$⇒ xy = 2$
$⇒4xy = 8$
Now, $(x + 2y)^2= x^2 + 4y^2 + 4xy = 17 + 8 = 25$
$⇒ (x + 2y) = 5$

29 Views

Question : Directions: Advik's birthday is on Monday, June 19th. On what day of the week will Nishith's birthday be in the same year if Nishith was born on November 17th?

Option 1: Saturday

Option 2: Wednesday

Option 3: Friday

Option 4: Sunday

Team Careers360 23rd Jan, 2024

Correct Answer: Friday


Solution : Let's calculate the number of days between June 19th and November 17th.
Remaining days in June = 11
Days in July = 31
Days in August = 31
Days in September = 30
Days in October = 31
Days in November till 17th = 17

30 Views

Question : Emperor Ashoka conquered Kalinga after how many years of his coronation?

Option 1: 5 years

Option 2: 8 years

Option 3: 11 years

Option 4: 15 years

Team Careers360 21st Jan, 2024

Correct Answer: 8 years


Solution : The correct answer is 8 years.

Ashoka was known as one of the most significant emperors of the Mauryan dynasty. He was also known as Ashoka The Great and was the third king of the Mauryan dynasty. King Ashoka was crowned in 269 BCE

43 Views

Question : Direction: Select the missing number from the given alternatives.

  8   13   72  117
 21   7  189    63
  4   6   36   ?

 

 

 

Option 1: 65

Option 2: 54

Option 3: 72

Option 4: 110

Team Careers360 19th Jan, 2024

Correct Answer: 54


Solution : Given: 

  8   13   72  117
 21   7  189    63
  4   6   36   ?

In the first row, (8 x 9) = 72 and (13 x 9) = 117

In the second row, (21 x 9) = 189 and (7 x 9) = 63

In the

5 Views

Question : Which of the following is another name for starch found mainly in the pulp of seeds, fruits, tubers, roots and stems of plants, especially in corn, potatoes, wheat and rice?

Option 1: Amylum

Option 2: Xanthan

Option 3: Olestra

Option 4: Saponin

Team Careers360 24th Jan, 2024

Correct Answer: Amylum


Solution : The correct option is Amylum.

The substance described is commonly known as Amylum, which is another term for starch. Starch is a complex carbohydrate that serves as a storage form of energy in plants. It is found predominantly in the pulp of seeds, fruits, tubers,

31 Views

Question : A jeep travels to a place 300 km away at an average speed of 60 km/hr and returns at a speed of 30 km/hr. What is the average speed (in km/hr) for the whole journey?

Option 1: 75

Option 2: 80

Option 3: 40

Option 4: 60

Team Careers360 23rd Jan, 2024

Correct Answer: 40


Solution : Distance for one-way journey = 300 km/hr
Average speed for the first part of the journey = 60 km/h
Average speed for the return part of the journey = 30 km/hr
We know, Time = $\frac{\text{Distance}}{\text{Speed}}$
So, Time taken for first part of journey =

10 Views

Question : Which of the following countries do not have a written constitution?

Option 1: United Kingdom

Option 2: Australia

Option 3: United States of America

Option 4: Bangladesh

Team Careers360 18th Jan, 2024

Correct Answer: United Kingdom


Solution : The correct answer is the United Kingdom.

A written constitution is a carefully planned document that outlines all the fundamental laws, institutions and rules. An 'unwritten' constitution is what the UK is said to have. The various texts that comprise the laws of the

20 Views

Question : In $\triangle$ABC, D and E are points on AB and AC, respectively, such that DE || BC and DE divide the $\triangle$ABC into two parts of equal areas. The ratio of AD and BD is:

Option 1: $1:1$

Option 2: $1:(\sqrt2-$1)

Option 3: $1:\sqrt2$

Option 4: $1:(\sqrt2+$1)

Team Careers360 23rd Jan, 2024

Correct Answer: $1:(\sqrt2-$1)


Solution :
Area($\triangle$ADE) = Area(trapezium BCED)
⇒ Area($\triangle$ADE) + Area($\triangle$ADE) = Area(trapezium BCED) + Area($\triangle$ADE)
⇒ 2 × Area($\triangle$ADE) = Area($\triangle$ABC)
In $\triangle$ADE and $\triangle$ABC,
$\angle$ADE = $\angle$ABC [i.e., corresponding angles in DE || BC]
$\angle$A = $\angle$A [common angle]
⇒ $\triangle$ADE ~ $\triangle$ABC
⇒ $\frac{\text{Area($\triangle$ADE)}}{\text{Area($\triangle$ABC)}}$ =

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