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Q:

# The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

 A) 10 & 12 B) 10 & 18 C) 12 & -18 D) -12 & 18

Explanation:

Given, difference of the squares of two numbers is 180.

k2 - l2 - 180

Also, square of the smaller number is 8 times the larger.

= l= 8k

Thus, k2 - 8a - 180 = 0

k2 – 18k + 10k - 180 = 0

→  k(k - 18) + 10(k – 18) = 0

= (k + 10)(k – 18) = 0

→  k = -10, 18

Thus, the other number is

324 - 180 = l2

→ Numbers are 12, 18 or -12, 18.

Q:

What is the value of 4 in 475?

 A) 4 B) 400 C) 475 D) 40

Explanation:

The value of 4 in 475 means the place value of 4 in 475 and not its face value. Face value means the digit itself though it is at any place in the given number. But place value means the value of digit in its place in the given number.

Here the place value of 4 in 475 can be determined by as 4 is in 100's place in 475.

Hence, the place value of 4 in 475 is 4x100 = 400.

4 338
Q:

First four multiples of 9?

A multiple of a number is the number multiplied by an integer.

The first four multiples of 9 are given by multiying the first 4 integers with number 9.

That is,

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

Hence, first four multiples of 9 are 9, 18, 27, 36.

364
Q:

In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students can understand each and every step

1. Which is greater than 4?

(a) 5,

(b) -5,

(c) -1/2,

(d) -25.

 A) 5 B) 20 C) 2 D) 3

Explanation:

Solution:

5 greater than 4.

1 405
Q:

Which of the following is the largest?

 A) 12/49 B) 7/30 C) 13/56 D) 11/46

Explanation:

In the given options,

12/49 can be written as 1/(49/12) = 1/4.083

7/30 can be written as 1/(30/7) = 1/4.285

13/56 can be written as 1/(56/13) = 1/4.307

11/46 can be written as 1/(46/11) = 1/4.1818

Here in the above,

1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.

4 580
Q:

7, 16, 36, 78, 144, ?

which number come in place of question mark

 A) 168 B) 196 C) 222 D) 256

Explanation:

21 1248
Q:

Which of the following is a rational number?

 A) 0.241 B) 1.732 C) 4 D) All of the above

Explanation:

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

5 984
Q:

Which expression is equivalent to $i233$?

 A) i B) 1 C) -i D) -1

Explanation:

We know that,

7 2724
Q:

The product of a number and its multiplicative inverse is

 A) 1 B) 0 C) -1 D) Infinity

Explanation:

The mutiplicative inverse of a number is nothing but a reciprocal of a number.

Now, the product of a number and its multiplicative inverse is always equal to 1.

For example :

Let the number be 15

Multiplicative inverse of 15 = 1/15

The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.