1. Triangles ABC and XYZ are similar triangles and ratio of their sides is 4: 9. What is the ratio of the areas of the two triangles?
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Correct answer is option - 4
Explanation:
If two triangles are similar triangles, then the ratio of their areas is square of the similarity ratio of their sides.
This implies: ratio of areas of the triangles ABC and XYZ = 4^{2}: 9^{2} ==> 16: 81.
2. At what point does the graph of the line with equation 5x + 7y – 6 = 0 intersect the X-axis on a coordinate plane?
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Correct answer is option - 3
Explanation:
Whenever a graph of an equation intersects the X-axis, the value is called the x-intercept and the point can be calculated by taking the y-value as ‘0’.
This implies: 5x + 7(0) – 6 = 0.
This gives: 5x – 6 = 0 ==> 5x = 6 which implies x = 6/5.
Hence the point is (6/5, 0).
3. Which of the following is simplified form of the expression, (x^{2} – 3x – 18)/ (x^{2} – x – 30)?
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Correct answer is option - 1
Explanation:
In order to simplify the given expression, we should first simplify the numerator and the denominator.
Since both the expressions are quadratic expression, hence we can factor them.
Factoring the numerator, we get: x^{2} – 3x – 18 = (x – 6) (x + 3).
Similarly factoring the denominator, we get: x^{2} – x – 30 = (x – 6) (x + 5).
Here we can observe that (x – 6) is the common factor for both the expressions, and hence we cancel it.
Therefore the answer is (x + 3)/ (x + 5).
4. The length of a rectangle is twice the width of the rectangle. If the perimeter of the rectangle is 36, then the area of the rectangle is?
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Correct answer is option - 3
Explanation:
Given length, l of the rectangle is twice the width, w ==> l = 2w
Perimeter of the rectangle = 2l + 2w = 36==> 2(l + w) = 36 ==> l + w = 36/2 = 18.
This gives: l + w = 18 ==> 2w + w = 18 which implies 3w = 18 ==> width, w = 6.
Therefore the length of the rectangle, l = 2w = 12.
Hence the area of the rectangle, A = l * w = 12 * 6 = 72.
5. Which of the following is the simplified form of the given expression, 5/ (1 – 2i)?
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Correct answer is option - 2
Explanation:
In order to simplify the given expression, we should first rationalize the denominator.
Hence multiply and divide (1 + 2i) in the numerator and the denominator.
This gives: 5 (1 + 2i)]/ [(1 - 2i) (1 + 2i)] = 5 (1 + 2i)/ (1 – (2i)^{ 2}).
This gives: 5 (1 + 2i)/ (1 – 4i^{2}) ==>5 (1 + 2i)/ (1 + 4) ==> 5 (1 + 2i)/ 5 = 1 + 2i.
6. The number in the numerator of a fraction is 5 more than that of the number in the denominator. If the fraction equals 7/6, then what is the numerator of the fraction?
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Correct answer is option - 4
Explanation:
Let the number in the denominator be = x.
Then the number in the numerator = x + 5.
This gives: (x + 5)/ x = 7/6.
Now we can cross-multiply the numbers and we get: 6 (x + 5) = 7x ==> 6x + 30 = 7x.
This implies: 7x – 6x = 30 ==> x = 30.
Hence the number in the numerator is x + 5 = 30 + 5 ==> x = 35.
7. 82 is what percent of 1640?
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Correct answer is option - 3
Explanation:
Let ‘x’ be the percent of the number ‘82’.
Then, 82 = (x/100) * 1640.
By cross-multiplying we get: 8200/1640 = x.
This implies: x = 5%.