Explanation

Sequence: 12, 9, 6, ...

Decreasing by 3 each time

AP with a = 12, d = -3

Tn = a + (n-1)d

T15 = 12 + (15-1)(-3)

= 12 + 14(-3)

= 12 - 42

= -30

Last verified on 28-01-2026

Explanation

Let the total number of boys be$x$.

45% of $x$ participated: $0.45\times x=135$.

Solve for $x$: $x=\frac{135}{0.45}$

$x=300$, so the total number of boys is 300.

Explanation

Original length = 72 cm, stretched length = 90 cm.

Increase in length = 90 − 72 = 18 cm.

Percentage increase = (Increase ÷ Original length) × 100.

Percentage increase = (18 ÷ 72) × 100 = 25%.

Therefore, the rope’s length increased by 25%.

Explanation

Explanation

Explanation

Givena^3=64, so side$a = 4$ cm.

Total surface area of a cube =6a^2.

6×4^2=6×16=96.

Therefore, the painted area is 96 cm².

Explanation

Step 1: Expand the factorials

First, we expand the factorial expressions for both 10! and 7!

The factorial of a number n is defined as the product of all positive integers less than or equal to n, i.e., n!=nx (n-1)x ....... 1

Thus, we can write 10!=10 x 9x 8x7x6x5x4x3x2x1

We can also express 10! in terms of 7! as 10!= 10x9x8x7

Step 2: Simplify the expression

Next, we substitute the expanded form of1 0! into the original expression:

10!/7!= 10x9x8x7!/ 7!

We can cancel out the common term 7! from both the numerator and the denominator:

10!/7!= 10x9x8

Step 3: Calculate the final value

Explanation

Explanation

99×99=9801.

Therefore, the square root of 9801 is 99.

Explanation

Given:

• Original price of car = $800,000

• Duty increases price in the ratio 9:8 (after:before)

  
  

  Step 1: Understand the ratio

The ratio 9:8 means:

$$\text{New Price}:\text{Original Price}=9:8$$

So the new price $P_{text{new}}$ is:

Pnew​=9​/8×Original Price

Step 2: Substitute the values

Pnew​=9/8​×800,000
Pnew​=9×100,000=900,000