The correct answer is option 1 i.e. 2 : 3

Calculations:

Amount spent on food products = 2000

Amount spent on cleaning products = 3000

Required ratio = 2000 : 3000 = 2 : 3

The correct answer is Option 1 i.e. 2 : 3.

The diagonal of the cube = a√3

The diagonal of the cube = 2√12

a√3 = 2√(2 × 2× 3)

a√3 = 4√3

a = 4

Volume of cube = a³ = 4³ = 64

Total surface area = 6a² = 6(4)² = 6 × 16 = 96

Required ratio = 64 : 96 = 2 : 3

The correct answer is Option 1 i.e. 50%.

The surface area of the sphere = 4πr² = 4π × 10²

Now

The total surface area of the half-sphere = 3πr² = 3π × 10²

Here, Ratio = The surface area of the sphere/(2 × The total area of the half-sphere)

= 4π × 10²/[2 × 3π × 10²] = 2 : 3

Difference = 3 - 2 = 1

Hence, Percentage change = 1/2 × 100 = 50%

The correct answer is Option 2 i.e. 60°.

We know that:

sin A + sin B = 2 sin {(A + B)/2} cos{(A - B)/2}

cos A + cos B = 2 cos {(A + B)/2} cos {(A - B)/2}

Substituting these formulas in the given equation:

⇒ 2 sin {(A + B)/2} cos{(A - B)/2} = √3 [2 cos {(A + B)/2} cos {(A - B)/2}]

⇒ sin {(A + B)/2} = √3cos{(A + B)/2}

⇒ tan {(A + B) /2} = √3

⇒ (A + B)/2 = 60°

⇒ A + B = 120°

Hence,

⇒ ∠C = 180° - (A + B) [∵ Angle Sum property of triangle]

⇒ ∠C = 60°

The correct answer is option 4 i.e. 1233.

x³ + 27x² + 243x + 631

⇒ x(x² + 27x + 243) + 631

Now, put the value of x = 2

⇒ 2(2² + 27 × 2 + 243) + 631

⇒ 2(4 + 54 + 243) + 631

⇒ 2(301) + 631

⇒ 602 + 631 = 1233

The correct answer is option 4 i.e. 11.1%.

Cost price = Rs 30

Selling price = Rs 33.33

Profit percentage = (Selling price - Cost price)/cost price × 100

⇒ (33.33 - 30)/30 × 100

⇒ 3.33/30 × 100

⇒ 11.1%

The correct answer is option 3 i.e. -660.

20% of 300 - {40 ÷ 1/(2)^-1}[5.64 + 0.36]²

By using the BODMAS rule:

= (20/100) × 300 - (40 ÷ 2)[6.00]²

= 60 - 20 [36]

= 60 - 720

= -660

The correct answer is option 1 i.e. 2

For the number to be divisible by 99, it should be divisible by 9 and 11

Divisibility by 9:

Sum of the digits should be divisible by 9

1 + x + 4 + x + 3 + 0 + y + 5 = 13 + 2x + y should be divisible by 9

Case I:

13 + 2x + y = 18

2x + y = 5

Case II:

13 + 2x + y = 27

2x + y = 14

x,y ≤ 5

2x + y + 13 ≤ 27

Divisibility of 11:

Sum of odd digits – Sum of even digits = 0 or Number divisible by 11

x + x + 0 + 5 – (1 + 4 + 3 + y) = 0 or divisible by 11

2x - y – 3 = 0 or divisible by 11

But maximum value 2x – y – 3 = 7 [∵ x,y ≤ 5]

∴ 2x – y = 3

Case I:

2x + y = 5

2x – y = 3

Adding both the equation

4x = 8

x = 2

Substituting in equation 2

4 – y = 3

∴ y = 1

In that case x/y = 2

Case II:

2x + y = 14

2x – y = 3

Adding both the equation

4x = 17

x = 17/4, Not possible [∵ x is a digit hence has to be a natural number]

So, x = 2 and y = 1

∴ x/y = 2/1 = 2

The correct answer is option 4 i.e. 16.

We know that, M₁D₁H₁/W₁ = M₂D₂H₂/W₂

Where M₁, M₂ is the number of men, D₁, D₂ is the number of days, H₁, H₂ is the number of hours per day, and W₁, W₂ is the amount of work.

Here work in both cases is the same.

⇒ 20 × 10 × 12 = 25 × 6 × D₂

⇒ D₂ = 16 days

The correct answer is Option 1 i.e. 51 km/h.

Let the speed of the train be x km/h.

When the train crosses these cars it covers its own length.

Distance = Speed(Time)

Relative speed when train crosses 1st car = (x - 25) km/h

Relative speed when train crosses 2nd car = (x - 35) km/h

Time taken to cross 1st car = 4 sec = 4/3600 h

Time taken to cross 2nd car = 6.5 sec = 6.5/3600 h

According to question-

⇒ (x - 25)(4/3600) = (x - 35)(6.5/3600)

⇒ 4x - 100 = 6.5x - 227.5

⇒ 6.5x - 4x = 227.5 - 100

⇒ 2.5x = 127.5

⇒ x = 127.5/2.5 = 51 km/h