1. The simplified expression of 3x^{2} – 4xy + 5 – 6x + 2x^{2} – 5xy – 4 + 2x is?
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Correct answer is option - 2
Explanation:In order to simplify a polynomial expression, we should first group the like terms together and then combine them.
This gives: 3x^{2} + 2x^{2} - 4xy – 5xy + 5 – 4 – 6x + 2x = 5x^{2} – 9xy + 1 – 4x.
This can be rearranged as 5x^{2} – 9xy – 4x + 1.
2. Which of the following gives the value for the expression, -√(-81)^{2}?
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Correct answer is option - 4
Explanation: Taking the expression step-by-step: √(-81)^{2} = √(81)^{2} = 81. This is because the negative sign inside the square root is also being squared due to which (-1)^{2} = 1, and hence it becomes positive sign.
Therefore we get: -√(-81)^{2} = -(81) = -81
3. What is the mean proportional of -8 and -32?
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Correct answer is option - 3
Explanation: Let ‘x’ be the mean proportional of -8 and -32.
Then, -8/x = x/-32 which gives (-8) * (-32) = x * x
This implies: 256 = x^{2} ==> x = √256 = ± 16.
16 or -16 can be the answers but since we are finding the mean proportional between -8 and -32, hence we consider -16 as the answer!
4. The inverse of the function, y = 2x + 9 is:
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Correct answer is option - 4
Explanation: To find the inverse of a function, first switch the ‘x’ and ‘y’ variables with each other.
This gives x = 2y + 9.
Now solving for ‘y’ gives: (x – 9) = 2y
Therefore, y = (x – 9)/2.
5. One piece of pipe 40m long is to be cut into two pieces. If the ratio of the lengths of the pieces is 3: 7, then the lengths of the pieces are:
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Correct answer is option - 1
Explanation: Let the length of the shorter piece of the pipe be = x
Then the length of the other piece is = (40 – x)
The lengths are in the ratio of 3: 7, hence we get 3/7 = x/ (40 – x).
Cross-multiplying gives: 3 * (40 – x) = 7x ==> 120 – 3x = 7x ==> 120 = 10x
Solving for x gives x = 120/10 = 12m, which implies 40 – x = 40 – 12 = 28m.
6. The simplified form of the logarithmic expression, 2log(x) – 3log(x + 5) is?
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Correct answer is option - 5
Explanation:According to the log rule: m * log(a) = log(a^{m}).
This gives: 2log(x) – 3log(x + 5) = log(x^{2}) – log(x + 5)^{3}.
According to the rule: log(a) – log(b) = log(a/b)
Applying the above rule gives: log(x^{2}) – log(x + 5)^{3} = log(x^{2}/(x + 5)^{3})
7. In the figure shown, the coordinates of point ‘P’ are:
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Correct answer is option - 2
Explanation: Here from the figure the radius, r = 6
Hence length of OP = 6.
cos(30°) = (adjacent side)/ (hypotenuse) = x/ OP==> x= OP* cos(30°) = 6cos(30°)= 5.2
sin(30°) = (opposite side)/ (hypotenuse) = y/ OP==> y= OP * sin(30°) = 6 sin(30°) = 3
So the point P = (5.2, 3)