Sum of first n natural numbers = n(n+1)/2.

Here n=10, so sum = 10(11)/2 = 110/2 = 55

Check: 21=3×7 (not prime), 23 is only divisible by 1 and 23 (prime), 25=5×5 (not prime), 27=3×9 (not prime).

So 23 is the smallest prime greater than 20.

Factors of 48: 1,2,3,4,6,8,12,16,24,48.

Factors of 64: 1,2,4,8,16,32,64.

Common factors: 1,2,4,8,16. HCF = 16

If a number is divisible by both 3 and 5, and 3 and 5 are coprime (HCF=1), then the number must be divisible by their product: 3×5 = 15

First five prime numbers are 2, 3, 5, 7, 11.

Product = 2 × 3 × 5 × 7 × 11 = 2310

This question asks us to identify which number is a perfect square (a number that equals an integer multiplied by itself).

A perfect square is a number that can be expressed as n × n where n is an integer.

Test each option by finding if its square root is a whole number.

Only 169 has a whole number square root.

169 is a perfect square because 13 × 13 = 169, making the correct answer (B).

Largest 3-digit number = 999, Smallest 3-digit number = 100.

Difference = 999 - 100 = 899

This question asks us to find an unknown number based on a sequence of arithmetic operations performed on it.

Let the unknown number be x. According to the problem, when x is multiplied by 8 and then 15 is subtracted, the result is 49.

Add 15 to both sides of the equation to move the constant to the right side.

Divide both sides by 8 to find the value of x.

The number is 8, which corresponds to answer choice (B).

This question asks us to find the average value of the numbers 1 through 15.

The first 15 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Use the formula for sum of first n natural numbers: \[\text{Sum} = \frac{n(n+1)}{2}\]

Average is the sum divided by the count of numbers.

The average of the first 15 natural numbers is 8.

To find the remainder when a number is divided by another, use the division algorithm: \(\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}\)

Step 1: Set up the division

We need to express 527 in the form:

where \(q\) is the quotient and \(r\) is the remainder with \(0 \leq r < 15\).

Step 2: Divide 527 by 15

Perform the division:

The quotient is \(q = 35\).

Step 3: Calculate the product

Step 4: Find the remainder

Subtract the product from the dividend:

Since \(0 \leq 2 < 15\), this is a valid remainder.

Verification:

To find the remainder when 527 is divided by 15:

15×35=525

Now subtract:

527−525=2

Therefore, the remainder is 2.

Answer: The remainder is \(2\) (Option A)