The correct answer is option 2 i.e. 36 : 23.

Total candidate who cleared from self studies = 40/100 × 10000 = 4000

10% of them moved to coaching A i.e. 10/100 × 4000 = 400

Total candidate who cleared from Coaching A = 19/100 × 10000 = 1900

Hence, required ratio: (4000 - 400) : (1900 + 400)

= 3600 : 2300

= 36 : 23

The correct answer is Option 2 i.e. 500 m².

Area of the equilateral triangle = 49√3 m²

√3/4 × a² = 49√3

a² = 196

a = 14 m

Then Length of the rectangle = 14 + 6 = 20 m

Area of the rectangle = 20 × 25 = 500 m²

The correct answer is Option 1 i.e. Rs 396.

The surface area of the cylinder = 2πrh

Total area for leveling the ground = Number of revolutions × Surface area

The cost of leveling = Cost per unit × total area

Radius of the roller = 21/2 cm and, its length = 100 cm

Area covered by the roller in 1 revolution = 2πrh 

⇒ 2 (22/7) (21/2) × 100 = 6600 cm²

Area covered by the roller in the 1200 revolution

⇒ 1200 × 6600 = 7920000 cm² = 792 m²

The cost of leveling the ground

⇒ 792 × (50/100) = Rs.396

The correct answer is option 3 i.e. 30.

Calculate the value

6√3(cosec 60° + tan 60°) 

= 6√3(2/√3 + √3) = 6√3(5/√3) = 30

The correct answer is option 2 i.e. 4.

x⁴ + 1/x⁴ = 194

Adding 2 on both the sides

⇒ x⁴ + 1/x⁴ + 2 = 196

⇒ (x² + 1/x²)² = 196

⇒ x² + 1/x² = 14

And x²y + 1/(x²y) + y/x² + x²/y = 28

⇒ x²y + x²/y + 1/(x²y) + y/x² = 28

⇒ x² (y + 1/y) + 1/x² (y + 1/y) = 28

⇒ (x² + 1/x²) (y + 1/y) = 28

⇒ 14 × (y + 1/y) = 28

⇒ y + 1/y = 2

⇒ y² + 1 = 2y

⇒ y² – 2y + 1 = 0

⇒ (y – 1)² = 0

⇒ y = 1

Substituting y = 1 in xy¹⁵ + 1/(xy¹⁸):

xy¹⁵ + 1/(xy¹⁸) = x + 1/x

To find x + 1/x:

x² + 1/x² = 14

Adding 2 on both sides:

⇒ x² + 1/x² + 2 = 16

⇒ (x + 1/x)² = 16

⇒ x + 1/x = 4

The correct answer is Option 2 i.e. Rs. 200.

Let the cost price of the table = x

And the cost price of the chair = 500 – x

According to the question,

(500 – x) × (100 – 10)/100 + x × 115/100 = 500

500 × 9/10 – x × 9/10 + 23x/20 = 500

4500 × 2/20 – 18x/20 + 23x/20 = 500

5x/20 + 9000/20 = 500

5x = 500 × 20 – 9000

x = 1000/5

x = 200

Therefore, the cost price of the table = Rs. 200

The correct answer is option 4 i.e. 8.

x = (633)²⁴ - (277)³⁸ + (266)⁵⁴

is of the form

x = 3^4x - 7^{4x + 2} + 6

x = 1 - 9 + 6

x = 7 - 9 [17 - 9] for unit digit

x = 8

The correct answer is option 3 i.e. 7.

Concept Used:

Number = Divisor × Quotient + Remainder

Explanation:

According to the given question,

The given number is 108Q + 19.

Now, 108Q + 19 = 12 × 9 × Q + (12 + 7)

⇒ 12 × (9Q + 1) + 7

Hence the remainder is 7.

The correct answer is option 1 i.e. 16 days.

Total work = LCM (24, 18) = 72 units

The efficiency of P = 72/18

⇒ 4 units/day

The efficiency of Q = 72/24

⇒ 3 units/day

The total amount of work done in the first 6 days,

⇒ 6(4 + 3) = 42

Work left = 72 - 42 = 30 units

Number of days required by Q to complete the work = 30/3

⇒ 10 days

Total number of days = 10 + 6 = 16 days

The correct answer is Option 4 i.e. Can’t be determined.

Let the speed of the train be a.

(200 + x)/a = 2/3 × (200 + x + 150)/a

600 + 3x = 400 + 2x + 300

x = 100

(200 + 100)/a = 2/3 × (200 + 100 + 150)/a

300/a = 300/a

Can’t be determined.