If the number formed by the last two digits of a number is divisible by 4, then the number is also divisible by 4. Here, the number is 13. Also, 13 is not divisible by 4. Therefore, 256413 is not divisible by 4.

For a number to be divisible by 9, the sum of the digits of the number should be divisible by 9. For 263125, the sum of the digits = 19. As we know 19 is not divisible by 9, so 231462 is also not divisible by 9.

k = 142 x 22 x 21 = 65604k When rounded to the nearest hundred, it becomes 65600.

M = 65 x 12 x 13 = 9984 When rounded to the nearest tens, it becomes 9980.

s = 147 x 47 x 21 = 145089 When rounded to the nearest thousand, it becomes 145000.

Z = 112 x 127 = 1422414224 When rounded to the nearest tens, it becomes 14220.

Since it contains two algebraic terms, so it is binomial.

2 k + [k - 2 { 2 k - 4}] = 1 2 k + [ k - 4 k + 8 ] = 1 2 k + [ - 3 k + 8 ] = 1

• k + 8 = 1
• k = - 7 k = 7

2(k - 2) = 4 2k - 4 = 4 2k = 8 k = 4 Also, 2 (y + 2 X 0 - 1) + y = 4 + 4 2y - 2 + y = 8 3y = 10 y = 10/3

Speed of train = (54 X 5)/18 m/sec = 15 m/sec Therefore, time taken by the train to cross the tunnel = 40 sec Therefore, T = 40 Therefore, 2T/60 = 80/60 = 4/3

Length of the cuboid = 4 m Breadth of the cuboid = 2 m Height of the cuboid = 2 m Therefore, total surface area of the cuboid = 2 (lb + bh + hl) = 2 (4 X 2 + 2 X 2 + 2 X 4) = 2 (8 + 4 + 8) = 2 (20) = 40 sq. m

If m = 2, then K becomes 52362. Last two digits of K = 62 and 62 is not divisible by 4. Therefore, 52362 is also not divisible by 4.

Dipali earns Rs. 2400 in 4 days. Dipali earns Rs. 600 in 1 day. Dipali earns Rs. 2700 in 45 days. Therefore, Z = 2700  Now, 4K = 27000 + 1000 Or, 4K = 28000 Or, K = 7000

1 km = 1000 m Therefore, required ratio = 2 : 1000 = 1 : 500

For a number to be divisible by 6, the number must be an even number and also the number should be divisible by 3. Here, 521424 is an even number, also the sum of the digits is 18, which is divisible by 3 and hence, the number is also divisible by 3. Therefore, the given number is divisible by 6.

If the sum of all the digits is divisible by 3, then the number is also divisible by 3. Therefore, sum of digits = 2 + 1 + 4 + 5 + 1 + 1 = 1414 is not divisible by 3. Therefore, 214511 is also not divisible by 3

For a number to be divisible by 8, the last three digits of the number must be divisible by 8. For 216664, last three digits come out to be 664 which is divisible by 8. Hence, the number is also divisible by 8.

224 = 1 X 2 X 112 As 224 has more than two factors, so 224 is not a prime number.

If k is divisible by 3, then the sum of the digits must be divisible by 3. Here, k = 231mn05. Therefore, 2 + 3 + 1 + (m + n) + 0 + 5 = L (say). Putting the value of (m + n) = 1, we get L = 16, which is not divisible by 3. Hence, for (m + n) = 5, k will not be divisible by 3.

Place value of 9 = 9 X 10000 = 90000