1. In a bookstore, the latest version of a certain book whose price was originally $35.00 has now been increased by 16%due to additional information added in the book. The new cost of the book is?
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Correct answer is option - 5
Explanation: Original price of the book = $35.00
16% of the book price = (16/100) * $35 = $5.60
Since the price of the book is increased by 16%, hence the new price of the book ==> $35 + $5.60 = $40.60.
2. If f(x) = 3x^{2} – 2x + 7 then what is the value of f(-1) + f(1)?
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Correct answer is option - 3
Explanation: For the given function, f(x) = 3x^{2} – 2x + 7, the value of f(-1) = 3(-1)^{2} – 2(-1) + 7.
This gives: f(-1) = 3 + 2 + 7 ==> f(-1) = 12.
Similarly, f(1) = 3(1)^{2} – 2(1) + 7 which implies f(1) = 3 – 2 + 7 ==> f(1) = 8.
Hence f(-1) + f(1) = 12 + 8 = 20.
3. The simplified form of the expression (where p, q ≠ 0), (-24 p^{5} q^{7})/ (4 p^{-3} q^{5}) is?
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Correct answer is option - 4
Explanation: In order to simplify the given expression, we have to use the law of exponents.
This gives: -24/4 = -6
Simplifying each variable we get: p^{5}/ p^{-3} = p^{(5 – (-3))} = p^{5 + 3} = p^{8}
Similarly we get: q^{7}/ q^{5} = q^{(7 – 5)} = q^{2}.
Hence we get: (-24 p^{5} q^{7})/ (4 p^{-3} q^{5}) = -6 p^{8} q^{2}.
4. There are 12 balls in a box out of which 4 are red, 5 are yellow and 3 are purple. After sometime, 1 red and 1 yellow ball are removed from the box. Now what is the probability of picking a yellow ball at random from the box?
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Correct answer is option - 3
Explanation: Total number of balls in the box = 12
Out of them, 2 balls are removed (1 red and 1 yellow) = 12 – 2 = 10 balls in the box!
Now number of yellow balls in the box = 5 – 1 = 4.
Therefore the probability of picking yellow ball at random = 4/10.
5. In a standard coordinate plane of X-axis and Y-axis, the equation of a circle is given as, (x – 4)^{2} + (y + 2)^{2} = 9. The circumference of this circle is?
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Correct answer is option - 4
Explanation:The equation of a circle on a coordinate plane is gives as: (x – h)^{2} + (y – k)^{2} = r^{2}.
Here, (h, k) is the center of the circle and ‘r’ is the radius of the circle.
The given equation can also be written as: (x – 4)^{2} + (y + 2)^{2} = 3^{2}.
This means r^{2} = 3^{2} which implies radius, r = 3.
Hence the circumference of the circle = 2 * π * r ==> 2 * π * 3 ==> 6π.
6. Which of the following is equivalent to: 6.0 * 10^{-6}?
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Correct answer is option - 5
Explanation: Since the exponent on ‘10’ is a negative exponent, hence it implies that the number is a very small number and should contain the decimal point.
Since the exponent is ‘-6’, it means that the decimal point has to be shifted 6 places to the left.
This gives: 0.000006 as the answer!
7. If given x < 0, then the solution of the equation x^{2} – 4 = 0 is?
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Correct answer is option - 2
Explanation: Solving the given equation, we get: x^{2} = 4.
Taking square root on both sides gives: x = √4 ==> x = ± 2.
Since x < 0, which means ‘x’ is only a negative number, hence x = -2 is the only solution!