1. If sin(θ) = 13/14 where ‘θ is an acute angle, then what is the value of cos(θ)?

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**Correct answer is option - 3**

**Explanation: **According to the Trigonometric identity we have: sin^{2}(θ) + cos^{2}(θ) = 1

This gives: cos^{2}(θ) = 1 – sin^{2}(θ) and given sin(θ) = 13/14 ==> sin^{2}(θ) = 169/196.

cos^{2}(θ) = 1 – (169/196) = (196 – 169)/ 196 ==> cos^{2}(θ) = 27/196.

Taking square root on both sides gives: cos(θ) = √(27/196) = (3√3)/ 14.

2. A circle with center O (-3, 2) has the X-axis as the tangent to the circle. The radius of this circle?

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**Correct answer is option - 2**

**Explanation: b **Since the X-axis is the tangent to the circle, hence the circle touches the X-axis at a certain point.

Given the center of the circle is (-3, 2).

Plotting this point on a coordinate plane shows that the distance from the center to the point where it touches the X-axis is ‘2’ units. Hence the radius of the circle = 2.

3. Which of the following is equivalent to the expression, (x^{2} + 5x – 36)/ (x – 4)?

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**Correct answer is option - 4**

**Explanation: **In order to simplify the given expression, we first factor the numerator.

This gives: (x^{2} + 5x – 36) = (x + 9) (x – 4).

In the given expression, the denominator is (x – 4).

Now we get: [(x +9) (x -4)]/ (x – 4) and here we can cancel (x – 4).

This gives: (x^{2} + 5x – 36)/ (x – 4) = (x + 9).

4. Which of the following gives the solution set for the equation: 3(x + 2) = 6x + 5 – 3x?

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**Correct answer is option - 5**

**Explanation: **Simplifying the give equation: 3x + 6 = 6x + 5 – 3x

Combining the like terms we get: 3x + 6 = 3x + 5.

Subtracting 3x on both sides, we get: 3x – 3x + 6 = 3x – 3x + 5 ==> 6 = 5

Now we should observe both sides of the equation.

On the left side we have ‘6’ and the right side we have ‘5’ and we all know that ‘6’ is never equal to ‘5’.

Therefore there is no solution for the given equation!

5. In the X-Y plane, where does the line 4x– 2y + 10= 0 intersect the line x= -3?

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**Correct answer is option - 1**

**Explanation: **In order to find the point of intersection, we have to solve the given two equations.

Since the second line is x = -3, plug in this value in the first equation to get the ‘y’ value.

This gives: 4(-3) – 2y + 10 = 0 which implies -12 – 2y+ 10 = 0 ==> -2y - 2 = 0.

Hence we get: -2y = 2 ==> y = 2/ (-2) ==> y = -1.

Therefore the point of intersection is (-3, -1).

6. If an object travels at an average speed of 30m/sec, then how far did the object travel in 1.5mins?

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**Correct answer is option - 4**

**Explanation: **Given average speed of the object = 30m/sec

Time taken by the object = 1.5mins. Since the units must be consistent, we should first convert minutes to seconds.

This means 1.5 minutes * (60 seconds/ 1minute) = 90 seconds.

Distance = Speed * time ==> Distance = 30m/sec * 90 seconds = 2700m.

7. What is the value of ‘p’ if the equation of the line is 6x + py + 1 = 0 and its slope is 2?

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**Correct answer is option - 2**

**Explanation: **The given equation can be rearranges as: py = -6x – 1 ==> y = (-6/p)x – (1/p).

This equation is in the form of y = mx + b where ‘m’ is the slope of the line.

Hence we can equate the slope which means ==> -6/p = m ==> -6/p = 2.

Therefore p = -6/2 ==> p = -3.