The correct answer is option 3 i.e. 500.

Total number of mobile and laptop sold = 500 + 600 = 1100

Total number of Radio, TVs, and watches sold = 100 + 300 + 200 = 600

ATQ:-

Difference = 1100 - 600 = 500

The correct answer is Option 4 i.e. 3 : 2.

Let the lengths of the parallel sides of the trapezium be a (smallest) and a + 4 (greatest), and let the height be a + 8 (highest term).

The area of a trapezium = 1/2 × sum of parallel sides × height

⇒ 160 = 1/2 × (a + a + 4) × (a + 8)

⇒ 160 = 1/2 × (2a + 4) × (a + 8)

⇒ 160 = (a + 2)(a + 8)

⇒ 160 = a² + 8a + 2a + 16

⇒ 160 = a² + 10a + 16

⇒ a² + 10a - 144 = 0

Solving this quadratic equation using the formula

⇒ a = 16/2, -36/2

⇒ a = 8, -18

So, a = 8

Smallest side = a = 8

Greatest side = a + 4 = 12

Thus,

Required ratio = 12/8 = 3/2 = 3 : 2

The correct answer is option 4 i.e. 3080m³

Radius r = 7 m

Height h = 20 m

the volume of a cylinder V = πr²h

⇒ 22/7 × 7² × 20 = 3080m³

The correct answer is option 1 i.e. 608/425.

Given,

Tan A = 15/8 and Tan B = 7/24

we know that,

Tan θ = P/B and Cos θ = B/H

For Tan A = 15/8

⇒ H_A = √(P_A² + B_A²) = √(225 + 64) = √289 = 17

Now,  for Tan B = 7/24

⇒ H_B = √(P_B² + B_B²) = √(49 + 576) = √625 = 25

Now,

Cos A + Cos B

= B_A/H_A + B_B/H_B

= 8/17 + 24/25

= (200 + 408)/425

= 608/425

The correct answer is Option 3 i.e. 76.

x - 1/x = k

x³ - 1/x³ = k³ + 3k

The correct answer is option 2 i.e. Rs 2770

The correct answer is option 3 i.e. 16%.

Let the initial number be 100 then,

First, it decreases by 30 i.e. it becomes 70

Then it increases by 20% i.e,

⇒ 70 + 20% of 70 = 84

Net decrease = (100 - 84)/100 × 100 = 16%

The correct answer is Option 1 i.e. 80/27.

8 ÷ [(9 - 5) ÷ {(7 - 2) ÷ (3 + 9 ÷ 24)}]

⇒ 8 ÷ [(9 - 5) ÷ {(7 - 2) ÷ (3 + 9/24)}]

⇒ 8 ÷ [(9 - 5) ÷ {(5) ÷ (3 + 3/8)}]

⇒ 8 ÷ [(4) ÷ {(5) ÷ 27/8}]

⇒ 8 ÷ [(4) ÷ {40/27}]

⇒ 8 ÷ [4 × 27/40]

⇒ 8 ÷ [27/10]

⇒ 8 × 10/27

⇒ 80/27

The correct answer is option 2 i.e. 192.

The LCM of 48 = 2⁴ × 3

LCM of 72 =  2³ × 3²

LCM of 576 =  2⁶ × 3²

Let's assume the third number is x.

The third number should be the multiple of x = 2⁶ × 3^k = 64 × 3^k

if k = 0 then x = 64

k = 1 then x = 192

k = 2 then x = 576

The value of the third number cannot be more than 576.

So, From the options, the third number will be 192.

The correct answer is option 2 i.e. 6 days.

Aaravya is 50% more efficient than Atul

Ratio of efficiency (Aaravya : Atul) = 3 : 2

Let the efficiency of Aaravya and Atul be 3x and 2x.

Total work = Number of days taken by Atul × Efficiency of Atul = 18 × 2x

⇒ 36x

Number of days taken by Aaravya = 36x/3x = 12 days

Hence, the required difference = 18 - 12 = 6 days