1. If 7(x – 2) = 4x – 14 + 3x, then the solution of ‘x’ is?

Show me the answers!

**Correct answer is option - 5**

**Explanation: **Simplifying the given expression we get: 7x – 14 = 4x – 14 + 3x.

This gives: 7x – 14 = 7x – 14.

Subtracting 7x on both sides we get: 7x – 7x – 14 = 7x – 7x – 14.

This implies: -14 = -14.

The above statement is true always for any value of ‘x’ and hence the solution for ‘x’ is all real numbers.

2. If (a + b)^{2} = 36 and a^{2} + b^{2} = 6, then what is the value of ‘ab’?

Show me the answers!

**Correct answer is option - 1**

**Explanation:**The expression (a + b)^{2} can be expanded according to its formula as: (a + b)^{2} = a^{2} + 2ab + b^{2} and given a^{2} + b^{2} = 6 and (a + b)^{2} = 36.Hence we get: (a + b)^{2} = a^{2} + 2ab + b^{2} ==> 36 = 6 + 2ab.

This gives: 2ab = 36 – 6 ==> 2ab = 30 ==>ab = 30/2 ==>ab = 15.

3. What is the simplified value of √(1800)/ √6?

Show me the answers!

**Correct answer is option - 1**

**Explanation: **The given expression can also be written as: √(1800/6) = √(300).

300 can be prime factorized as: 300 = 2 * 2 * 3 * 5 * 5

Hence √300 = √(2 * 2 * 3 * 5 * 5) ==> √300 = 10√3.

4. What is the value of the expression 3/ (1/5 – 1/k) when k = 8?

Show me the answers!

**Correct answer is option - 2**

**Explanation: **We can first simplify the denominator by taking the common denominator between them.

This gives: (1/5 – 1/k) = (k – 5)/ 5k.

Now writing the whole expression together, we get: 3/ [(k – 5)/ 5k].

We should take the reciprocal here, which gives: (3 * 5k)]/ (k – 5) ==> 15k/ (k – 5).

Since given k = 8, we get: (15 * 8)/ (8 – 5) = (15 * 8)/ 3 ==> 40.

5. What is the value of 5*2 – 3*2 - |8| + |-4|?

Show me the answers!

**Correct answer is option - 1**

**Explanation: **Considering the order of operations, multiplication comes first and then subtraction follows.

Therefore we get: 10 – 6 - |8| + |-4| ==> 4 - |8| + |-4|.

The absolute value of any number is a positive number.

Hence we get: 4 – 8 + 4 = 8 – 8 = 0.

6. In the figure shown below, the length of the rectangle is 12cm and the width of the rectangle is one-fourth the length. If the width of the rectangle is equal to the altitude of the triangle, then the area of the triangle in ‘cm^{2}’ is?

Show me the answers!

**Correct answer is option - 4**

**Explanation: **Given the length of the rectangle, l = 12cm

Width is one-fourth the length, w = 1/4 * 12cm = 3cm.

Altitude of the triangle = width of the rectangle = 3cm.

From the figure, the base of the triangle is on the length of the rectangle.

Area of the triangle, A = 1/2 * base * height = 1/2 * 12 * 3 = 18 cm^{2}.

7. In the figure below, XYZ is an obtuse triangle and the side YX is extended till ‘M’. If the measure of the angle XYZ is 110° and the angle YZX measures 25°. What is the measure of the angle ZXM?

Show me the answers!

**Correct answer is option - 4**

**Explanation: **In a triangle, the exterior angle is always equal to the sum of interior opposite angles.

This gives the measure of angle ZXM = angle XYZ + angle YZX.

This implies: angle ZXM = 110° + 25° = 135°.

(Or) An alternate method is to consider that the sum of the angles in a triangle is 180° and therefore find the third angle.

Since XY is straight line, subtracting the third angle from 180° gives the exterior angle!