Explanation

Note: The answer given in the FPSC answer key is (a) but the actual answer is (b)

To simplify the expression (x^(1/2)) * (x^(-1/2)), we can use the rule of exponents:

x^a * x^b = x^(a+b)

Applying this rule, we get:

(x^(1/2)) * (x^(-1/2)) = x^(1/2 + (-1/2)) = x^0

Any number raised to the power of 0 is equal to 1.

Therefore, (x^(1/2)) * (x^(-1/2)) = 1.

Explanation

To calculate the average (or mean) of a data set, you use the formula:

Average=Sum of all values/Number of values​

Given:

• The sum of all 10 values in the data set is 10.
• The number of values is 10.

Using the formula:

Average=10/10​=1

Explanation

Explanation

To solve the equation:

x​/2−x​/4=2

we can start by finding a common denominator for the terms on the left side.

The common denominator for $frac{x}{2}$ and $frac{x}{4}$is 4, so we rewrite the equation as:

$$frac{2x}{4} - frac{x}{4} = 2$$

Now, combine the fractions on the left side:

2x−x​/4=2

This simplifies to:

x/4​=2

Now, multiply both sides by 4 to isolate $x$

$$x = 8$$

Explanation

Note: The answer given in the FPSC answer key is (c) but the actual answer is 512.

Explanation

The sum of the three angles of any triangle, including an isosceles triangle, is always:180∘

Explanation

A pie chart is a way of summarizing a set of nominal data or displaying the different values of a given variable.

Explanation

A cube can be made with equal blocks for length breadth and height.

Let's see, 1*1*1=1 2*2*2=8 3*3*3=27 4*4*4=64.

Oops, larger than 59. So we need only 27 blocks.

That means that we can take away 50-27=23 blocks.

Explanation

• The series alternates between subtracting 1 and adding 2:
  • 12 → 11 (subtract 1)
  • 11 → 13 (add 2)
  • 13 → 12 (subtract 1)
  • 12 → 14 (add 2)
  • 14 → 13 (subtract 1)

Following this alternating pattern, the next step should be adding 2 to 13:

$$13 + 2 = 15$$

Explanation

This is a simple division series; each number is one-half of the previous number.

In other terms to say, the number is divided by 2 successively to get the next result.

4/2 = 2

2/2 = 1

1/2 = 1/2

1/2/2 = 1/4

1/4/2 = 1/8 and so on.