1. If the circumference of a circle is 12pae, then what is the area of the circle?
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Correct answer is option - 4
Explanation:
Circumference of the circle is 2πr, where ‘r’ is the radius of the circle.
Therefore, 2πr = 12π. This gives, 2r = 12 implies r = 6.
Area of a circle, A = πr^{2} which implies A = π(6)^{2} = 36π.
2. In an X-Y coordinate plane, what is the midpoint of the line segment joining the point A (-5, 4) and B (3, 2)?
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Correct answer is option - 3
Explanation:
Midpoint of a line segment joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is [(x_{1} + x_{1)}/2, (y_{1} + y_{2})/2]
Therefore we get, midpoint of the line segment AB = [(-5 + 3)/2, (4 + 2)/2] = (-2/2, 6/2)
Hence the answer is (-1, 3).
3. If the age of Ben’s son 3 years ago was one-fifth of Ben’s age, then what is the present age of Ben’s son? Consider Ben’s present age to be ‘x’ years.
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Correct answer is option - 3
Explanation:
Ben’s present age = ‘x’ years. So Ben’s age 3 years ago is = x – 3.
Ben’s son age 3 years back is 1/5^{th} of (x – 3) = (x -3)/ 5.
Therefore, the present age of Ben’s son is = (x – 3)/5 + 3.
4. 6liters of water is poured into a rectangular tank of dimensions length 30cm, width 20cm and height 15cm. How high in ‘cm’ will the water rise in the tank? (1L = 100cm).
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Correct answer is option - 2
Explanation:
6 liters of water means 6000cm^{3} volume of water.
Area of the base of the tank, A = length * width = 30cm * 20cm = 600cm^{2}.
Volume of the tank = Area of the base of the tank * height of the water
This implies: 6000cm^{3} = 600cm^{2} * height.
Therefore, height of the rise in the water = 6000/600 = 10cm.
5. For the given sequence, -32, -24, -16, -8… which of the following numbers do not belong to the sequence?
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Correct answer is option - 5
Explanation: The numbers in the given sequence are in Arithmetic sequence.
The n^{th} term of a number in this sequence is n^{th} term = a + (n – 1)d.
Here ‘n’ is an integer, first term, a = -32 and common difference, d = 8.
If -32 + (n – 1)8 = 540, then -32 + 8n – 8 = 540, then this gives: 8n – 40 = 540 implies 8n = 580.
Hence, n = 580/8 is not an integer and hence it’s the answer.
6. In the given equation, 81 * 3p = 9^{q + 3}, the value of p = 2. The value of ‘q’ is:
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Correct answer is option - 1
Explanation: 81 can be written as 3^{4 }and 9 can be written as 3^{2}. This gives 3^{4} * 3^{p} = 3^{2(q + 3)}
So we get, 3^{4 + p} = 3^{2q + 6}. Since the bases are the same, the powers can be equated.
We get 4 + p = 2q + 6. Since p = 2, 4 + 2 = 2q + 6 which gives 6 = 2q + 6.
This implies, 2q = 6 – 6 = 0 and hence q = 0.
7. In the figure shown below, ABC is a right triangle with sides 6m and 8m and is attached to the square. The area of the square is:
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Correct answer is option - 4
Explanation: Since ABC is a right triangle, according to the Pythagorean Theorem we get: AC^{2} = AB^{2} + BC^{2}.
So, side AC^{2} = 6^{2} + 8^{2} = 36 + 64 = 100. This implies AC = √100 = 10m.
Area of the square, ACDE = side * side = 10m * 10m = 100m^{2}.