1. If slope of one straight line is 2/3 and the slope of another line is -3/2, which of the following is true about the lines?
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Correct answer is option - 3
Explanation: If two lines are perpendicular (forms 90 ° angle at their intersection point), then the product of their slopes should be equal to -1. 2/3 * -3/2 = -1 and therefore option ‘c’ is the correct answer.
2. Given a, b are two numbers. If a& b = (a + b)/ (a – b), then what is the value of 4 & (3 & 1).
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Correct answer is option - 4
Explanation: Since a & b = (a + b)/ (a – b), 3 & 1 = (3 + 1)/ (3 – 1) = 4/2 = 2.
Now 4 & (3 & 1) = 4 & 2 = (4 + 2)/ (4 – 2) = 6/2 = 3
3. In a bag there are 4 oranges, 5 apples and 6 peaches. If one fruit is pulled out from the bag, what is the probability that it is an apple or a peach?
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Correct answer is option - 3
Explanation: The total number of fruits present in the bag are (4 + 5 + 6) = 15 fruits. The total number of apples and peaches are (5 + 6) = 11.
Therefore the probability of getting an apple or a peach is 11/15.
4. If a – b = p, then what is a^{2} – 2ab + b^{2}?
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Correct answer is option - 4
Explanation: According to the formula: (a – b) ^{2} = a^{2} – 2ab + b^{2}.
Hence if a – b = p, then a^{2} – 2ab + b^{2} = (a – b) ^{2} = p^{2}.
5. If 3^{(6x – 2)} = 9^{(x + 3)}, then x is
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Correct answer is option - 3
Explanation: We should apply the rule: if the bases are the same the powers can be equated.
This means we make them same bases by taking 9 = 3^{2}. This gives: 3^{(6x – 2)} = 3^{2(x + 3)}
Now equate the exponents: 6x – 2 = 2(x +3) implies 6x – 2 = 2x + 6.
Solve for x: 4x = 8 which gives x = 2.
6. If the equation of a parabola is given to be y = -2x2 +5x – 4, then what is the x-coordinate of the highest point on the graph of the parabola in an X-Y plane?
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Correct answer is option - 1
Explanation: If the equation of a parabola is in form of y = ax^{2} + bx + c and if a < 0, then the parabola opens downward.
This makes the vertex the highest point on the graph of the parabola.
So, x-coordinate of the vertex, x = -b/2a which gives, x = -5/-4 = 5/4.
7. In the following figure, lines P and Q are parallel and are intersected by the line R. The measure of angles m and nrespectively are:
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Correct answer is option - 2
Explanation:If a line intersects a pair of parallel lines, then the alternate angles are equal. Therefore the measure of angle ‘n’ is also 60°.
And, sum of the angles on a straight line is 180°, so m + n = 180°.
This gives, m = 180° - 60° = 120°.