1. Andy and Matt are walking in opposite directions along a straight line at 6miles/hr and 8 miles/hr respectively. The distance between them in ‘x’ hours is:
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Correct answer is option - 4
Explanation: Andy is walking 6 miles in 1 hour. In ‘x’ hours, he will walk 6x miles.
Matt is walking 8 miles in 1 hour. In ‘x’ hours, he will walk 8x miles.
Since they are walking in opposite direction along a straight line, hence the total distance between them is 6x + 8x = 14x miles.
2. If 23.96% of a number is 18, then the number is:
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Correct answer is option - 4
Explanation: 23.96% of a number can be written as ==> (23.96/100) * x
So, (23.96/100) * x = 18.
This gives: x = 18 * (100/23.96) which implies x = 75.
3. By how many degrees does the minute hand of a clock turn in 25 minutes?
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Correct answer is option - 4
Explanation: The minute hand makes one complete rotation in 60 minutes and therefore turns 360°.
In 25 minutes, the minute hand turns ==> (25/60) * 360° = 150°.
4. The angle of elevation of the top of a building of height 40m is 30° and 60° from two different points A and B on the ground present on either side of the building. What is the distance between the two points?
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Correct answer is option - 1
Explanation: tan(θ) = (opposite side)/ (adjacent side)
Let the distance from point A to the base of the building be‘x’.
tan(30°) = 40/x ==> x = 40/tan(30°) = 69.28m
Similarly let the distance from point B to the base of the buildingbe ‘y’.
tan(60°) = 40/y ==> y = 40/tan(60°) = 23.09m
The total distance between the points = x + y = 69.28 + 23.09 = 92.37m
5. If f(x) = x^{2} + 6x – 7, then what is f(x + a) – f(a)?
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Correct answer is option - 3
Explanation: f(x + a) = (x + a)^{2} + 6(x +a) – 7 = x^{2} + 2ax + a^{2} + 6x + 6a – 7
Similarly, f(a) = a^{2} + 6a – 7
Therefore f(x + a) – f(a) = x^{2} + 2ax + a^{2} + 6x + 6a – 7 – (a^{2} + 6a – 7)
This gives: x^{2} + 2ax + 6x.
6. The domain of the function, y = (x + 4)/ (x – 3)(x + 1) is:
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Correct answer is option - 1
Explanation:A function is not defined when the denominator of the function is 0.
To find the domain of a function, the denominator of the function should not be equal to ‘0’ since at those values the function becomes undefined.
Therefore we should write it this way: (x – 3) ≠ 0 and (x + 1) ≠ 0.
This gives: x ≠ 3 and x ≠ -1.
7. The value of 1/a + 1/b + 1/c is:
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Correct answer is option - 5
Explanation: Here we have to first take the common denominator for the terms to be added.
The common denominator for all the three terms is abc.
Multiply and divide all the three terms by ‘abc’.
This gives: (bc + ac + ab)/ abc.