1. The length of a rectangle is thrice its width. If the width of the rectangle is 4m, then the perimeter of the rectangle is:

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**Correct answer is option - 4**

**Explanation: **Length (l) is thrice its width (w) implies l = 3w.

If w = 4m, then l = 3 * 4 = 12m

Perimeter of a rectangle, P = 2l + 2w = 24m + 8m = 32m.

2. What is the simplified form for the given expression, b * b * b * b * b * b for ‘b’ being any real number?

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**Correct answer is option - 3**

**Explanation: **Since ‘b’ is multiplied ‘6’ times by itself, it is raised to an exponent of 6.

Therefore the answer is b^{6}.

3. If a particle travels a distance of 1.0 * 10^{6} centimeters in a straight line in a time period of 5.0* 10^{-5} seconds, then the speed of the particle is:

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**Correct answer is option - 2**

**Explanation: **Distance travelled by the particle = 1.0 * 10^{6} cm.

Time taken = 5.0 * 10^{-5} seconds.

Speed = (Distance travelled)/ time = (1.0 * 10^{6}cm)/ (5.0 * 10^{-5}seconds)

Speed = 0.2 * 10^{11} cm/sec = 2.0 * 10^{10} cm/sec.

4. If 4t = 64, then the value of t^{1/2} is:

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**Correct answer is option - 1**

**Explanation: **4t = 64 ==> t = 64/4 =16

This gives: t^{1/2} = 16^{1/2} = √16 = ± 4.

Since ‘4’ is not in the options, the answer is -4.

5. If 3x + y = -4 and x + 2y = 7, then what is the value of x + y?

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**Correct answer is option - 3**

Writing the first equation of ‘y’ in terms of ‘x’ we get: y = -3x – 4.

Substitute this value of ‘y’ in the second equation, we get: x + 2(-3x – 4) = 7.

This gives: x – 6x – 8 = 7 ==> -5x = 15 implies x = -3.

y = -3x – 4, hence y = 9 – 4 ==> y = 5.

This gives x + y = -3 + 5 = 2.

6. Which of the following is equal to √96?

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**Correct answer is option - 1**

**Explanation:**

The prime factorization of 96 = 2 * 2 * 2 * 2 * 2 * 3

Therefore √96 = √ (2 * 2 * 2 * 2 * 2 * 3) = 2 * 2 √6 = 4√6.

7. PQR is an isosceles triangle with sides PQ = PR. As shown in the diagram below, angle PRS is 110°. The measure of angle QPR is:

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**Correct answer is option - 2**

**Explanation: **Since PQR is an isosceles triangle with sides PQ = QR, hence angle PQR = angle PRQ.

Angle PRS = 110° is an exterior angle and QS is a straight line.

Therefore, angle PRQ = 180° - 110° = 70°.

This implies angle PRQ = angle PQR = 70°. Sum of angles in a triangle = 180°.

Therefore, angle QPR + 70° + 70° = 180° ==> angle QPR = 180° - 140° = 40°.

8. If (x – 1)/ (x + 3) = 5/9, then what is the value of ‘x’?

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**Correct answer is option - 3**

**Explanation: **Cross-multiplying the denominators to the numerators on each side, we get: 9 * (x – 1) = 5 * (x + 3).

This gives: 9x – 9 = 5x + 15 ==> 9x – 5x = 15 + 9 ==> 4x = 24.

This implies: x = 24/4 ==> x = 6.