1. Equation of a line if 4x – 5y + 6 = 0. What is the slope of the line perpendicular to the given line?

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**Correct answer is option - 1**

**Explanation: **The given line can be rearranged as 5y = 4x + 6 which gives y = (4/5) x + 6/5. This is in the form of y = mx + b where ‘m’ is the slope and ‘b’ is the y-intercept.

Hence the slope of the given line, m_{1} = 4/5.

If two lines are perpendicular to each other, then the product of the slopes m_{1} * m_{2} = -1.

This gives the slope of the second line, m_{2} = -5/4.

2. For what value of ‘m’ will the ratio (4 + m)/ (10 + m) = 3/5?

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**Correct answer is option - 3**

**Explanation: **Cross -multiply the denominators to the other side of the equation.

5 (4 + m) = 3 (10 + m) which gives 20 + 5m = 30 + 3m.

Combining the like terms gives: 5m – 3m = 30 – 20.

2m = 10 ==> m = 5.

3. By how much does the expression 5x^{3} + y^{2} lesser than 5y^{2} + x^{3}if x = 2 and y = 3?

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**Correct answer is option - 4**

**Explanation**: When x = 2 and y = 3, 5x^{3} + y^{2} = 5(2)^{3} + 3^{2} = 40 + 9 = 49

And, 5y^{2} + x^{3} = 5(3)^{2} + 2^{3} = 45 + 8 = 53.

Therefore the difference is 53 – 49 = 4.

4. Which of the following is a factor of the polynomial, 3x^{2} – 10x + 8?

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**Correct answer is option - 3**

**Explanation: **The given quadratic expression can be expanded as: 3x^{2} – 6x – 4x + 8.

This gives 3x (x – 2) – 4 (x – 2).

This implies (x – 2) (3x – 4) are the factors of the given polynomial.

Since x – 2 is not in the options, 3x - 4 is the answer!

5. What is the value of √-(-5)^{2}?

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**Correct answer is option - 2**

**Explanation:**

√-(-5)^{2} = √-(25) = √25 * √-1 = √25 * i = ± 5i.

Since there is no -5i in the options, the answer is 5i.

6. A circle has the center at the origin (0, 0) and passes through the point (6,8). Which of the following gives the equation of the circle?

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**Correct answer is option - 5**

**Explanation: **Equation of a circle with center at (h, k) is (x – h)^{2} + (y – k)^{2} = r^{2}.

(x – 0)^{2} + (y – 0)^{2} = r^{2} ==> x^{2} + y^{2} = r^{2}.

Substituting the point (6, 8) we get, 36 + 64 = r^{2}. This gives r = 10.

Therefore the equation of the circle is x^{2} + y^{2} = 100.

7. ABCD is an isosceles trapezoid and the angle CAB = 115°. The angle ‘x’ as shown in the diagram is:

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**Correct answer is option - 4**

**Explanation: **An isosceles trapezoid has side AB parallel to side CD and side AC = side BD.

Since it is an isosceles triangle, angle CAB = angle DBA = 115° and angle ACD = angle BDC = x

This gives 115° + 115° + x + x = 360° which implies 230° + 2x = 360°.

2x = 360° - 230° = 130° which gives, x = 130°/2 = 65°.