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1. The GCF of the numbers 27, 36 and 42 is:
1
3
9
27
42
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Correct answer is option  2 Explanation: In order to find the GCF, first write prime factors of all the numbers.
Prime factorization of 27 = 3 * 3 * 3
Prime factorization of 36 = 2 * 2 * 3 * 3
Prime factorization of 42 = 2 * 3 * 7
Hence, the GCF = 3 since it is the common factor for all the given numbers 27, 36 and 42.
2. If (5  x/4) = (6 – x/3), then the value of (1 – x/12) is:
1
1/3
1/4
1/12
0
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Correct answer is option  5 Explanation: If (5  x/4) = (6 – x/3) then combine the like terms together.
This gives: x/3 – x/4 = 6 – 5 which implies (4x – 3x)/ 12 = 1 and hence x/12 = 1.
(1 – x/12) = 1 – 1 = 0.
3. In triangle PQR, the measure of angle P is 30° more than the measure of angle Q and is thrice the measure of angle R. What are the measures of angles P, Q and R respectively?
Correct answer is option  1 Explanation:
Let measure of angle R be = x.
Then angle P is thrice of angle R = 3x
Also, angle P is 30° more than angle Q ==> P = Q + 30°.
But angle P = 3x, so 3x = Q + 30° ==> Q = 3x – 30°.
Now sum of angles in a triangle = 180°.
Therefore 3x + (3x  30°) + x = 180° ==> 7x = 180° + 30° = 210°
This gives x = angle R= 210°/7 = 30°.
Hence angle Q= 3x  30° = 60° and angle P = 3x = 90°.
4. The value of (7 + √(16i) ) – (2 + 3√(9i)) is:
5 – 5i
5 – 5i
5 + 5i
5 – 7i
5 + 7i
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Correct answer is option  2 Explanation: The value of the imaginary number, i = √1.
Now (7 + √(16i) ) can also be written as: 7 + (√16* √1) = 7 + 4i
Similarly, (2 + 3√(9i)) can also be written as: 2 + 3(√9 * √1) = 2 + (3 * 3i) = 2 + 9i
This gives: 7 + 4i – (2 + 9i) = 7 + 4i – 2 – 9i = 5 – 5i.
5. The graph of the function, y = x^{2}  11x + 24 cuts the Xaxis at the points:
(0,0) and (24, 0)
(8, 0) and (3, 0)
(0, 0) and (8, 0)
(3, 0) and (0, 0)
(3, 0) and (8, 0)
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Correct answer is option  5 Explanation: The points where the graph of the function cuts the Xaxis are called the xintercepts.
To find xintercepts, we should plugin y = 0 in the function.
So, x^{2} – 11x + 24 = 0 can be factored as (x – 3) (x – 8) = 0.
This gives: x – 3 = 0 and x – 8 = 0.
Hence the points are (3, 0) and (8, 0).
6. The equation of a line passing through (3, 2) and parallel to the line 3x – y – 6 = 0 is :
3x + y – 7 = 0
3x – y – 11 = 0
x + 3y + 11 = 0
x – 3y = 11
3x – y – 8 = 0
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Correct answer is option  2 Explanation: The given line 3x – y – 6 = 0 can be rearranged as: y = 3x – 6.
It is in the slopeintercept form of y = mx + b where ‘m’ is the slope. Hence slope of this line is m = 3.
Parallel lines have equal slopes and hence slope of the unknown line is also m = 3.
Using the pointslope form of a line: y – y_{1} = m(x – x_{1}) gives y + 2 = 3(x – 3).
This gives: y + 2 = 3x – 9 which implies 3x – y – 11 = 0.
7. Triangle OXY is an isosceles triangle with sides OX = XY as shown in the figure. If point is (4, 10), then what is the area of the triangle OXY?
20
30
40
50
60
Show me the answers!
Correct answer is option  3 Explanation: Area of a triangle = 1/2 * base * height
Since it’s an isosceles triangle, the height of the triangle passes through ‘X’ and divides the base OY into two equal parts.
So the length from ‘O’ till the midpoint of OY is 4, which means the entire base length is 8.
Height of the triangle is the ‘y’ coordinate of X = 10.
Therefore the area of the triangle OXY = 1/2 * 8 * 10 = 40.
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