1. If 5p – 3q = 7, then which of the following can be the values of ‘p’ and ‘q’?
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Correct answer is option - 4
Explanation: By substituting the values p = 2 and q = 1 in the given equation.
This gives: 5(2) – 3(1) = 10 – 3 = 7.
Since the statement is true, hence the answer!
2. By how much is 0.260 greater than 1/4?
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Correct answer is option - 2
Explanation:1/4 can be written in decimal form as 0.250.
0.260 – 0.250 = 0.01
Converting 0.01 to fraction form we get: 0.01 = 1/100.
3. In an X-Y plane, an isosceles triangle ABC has the coordinates of vertices B and C as (4, 2) and (12, 2) respectively. If the height of the triangle is 3, then what is the coordinate of vertex A?
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Correct answer is option - 4
Explanation: For an isosceles triangle, the height divides the base, BC into two equal parts.
Hence the x- coordinate of A is the midpoint of the x-coordinates of B and C = (4 + 12)/2 = 16/2 = 8
And the y-coordinate of A = 2 + 3 = 5 on the Y-axis.
Hence the point A = (8, 5).
4. John is standing on the ground and is looking at the roof of the building at an angle of 60 degrees. If the height of the building is 40m, then how far is he approximately standing from the base of the building?
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Correct answer is option - 2
Explanation: According to the trigonometric function, tan(θ) = opposite side/adjacent side.
This gives: tan(60°) = 40m/ adjacent side.
Therefore, the adjacent side = 40/tan(60°) = 23m approximately.
5. If (2^{-3} * 16^{3})/ 32^{3}, then what is the value of this simplified expression?
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Correct answer is option - 4
Explanation: Using the Law of Exponents, we first simplify the numerator.
This implies: 2^{-3} * 16^{3} = 2^{-3} * (2^{4})^{3} = 2^{-3} * 2^{12} = 2^{-3 + 12} = 2^{9}.
Now we get: 2^{9}/ 32^{3} = 2^{9}/ (2^{5})^{3} = 2^{9}/ 2^{15} = 2^{9 – 15} = 2^{-6}.
2^{-6} = 1/ 2^{6} = 1/64.
6. On an X-Y coordinate plane, which of the following values of ‘x’ and ‘y’ does not make the given inequality, 2x + 3y <= -15 true?
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Correct answer is option - 4
Explanation:(-8, 1) means x = -8 and y = 1. If we plug-in these values into the expression 2x + 3y, it gives: 2(-8) + 3(1) = -16 + 3 = -13.
Since the given inequality is 2x + 3y ≤ -15 and -13 is not less than -15, hence it is the answer.
7. Edward starts from point A and travels 9km north to reach point B. He then travels 12m towards East to reach point C. He later decides to return back to point A by taking the shortest route and hence travels with a speed of 3km/hr. In how much time will he reach back to his starting point?
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Correct answer is option - 1
Explanation: The shortest route is achieved only when Edward travels directly from point C to point A.
This forms a right triangle where AB = 9 and BC = 12. Hence the Pythagorean Theorem gives AC^{2} = 9^{2} + 12^{2} = 81 + 144 = 225. This implies AC = √225 = 15km.
Since, time = distance/speed = 15/3, hence time taken to reach back = 5 hrs.