Correct answer is option - 5 Explanation: The midpoint of a line = [(x1 + x2)/2, (y1 + y1)/2].
This gives the midpoint of the line AB = [(4 + (-3))/ 2, (5 + (-7))/ 2] = (1/2, -2/2).
Hence the midpoint of AB = (0.5, -1).
2. The probability that an unbiased dice produces either a 1 or a 3 is:
1/3
2/3
1/6
4/6
1/2
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Correct answer is option - 1 Explanation: Since there are 6 numbers on a dice, the total number of outcomes which can be produced = 6.
The chances of getting a 1 or a 3 on a dice = 2.
So the probability = 2/6 = 1/3.
3. If (5.6)x = (6.8)y, then x/y is:
1.01
1.11
1.21
1.31
1.41
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Correct answer is option - 2 Explanation: Apply natural logarithms on both sides of the equation: ln(5.6)x = ln(6.8)y.
According to the rule: log(am) = m * log(a).
Applying the above rule gives: x * ln(5.6) = y * ln(6.8) ==> x/y = ln(6.8)/ln(5.6)
This implies ==> x/y = 1.11
4. The mean of 12 integers is 96. When another integer is added, the mean reduces to 92. The new integer added is:
50
62
44
36
75
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Correct answer is option - 3 Explanation: Let the sum of 12 integers be = S.
Then Mean = (Sum of integers)/ (Number of integers) ==> S/12 = 96.
This gives: S = 96 * 12 = 1152.
Let the new integer added be = x.
Then (S + x)/ 13 = 92 ==> S + x = 92 * 13 = 1196.
This gives 1152 + x = 1196 ==> x = 1196 – 1152. Hence, x = 44.
Correct answer is option - 4 Explanation: In the given expression, 6x2 + xy – 12y2, here 6 and -12 are multiplied to get -72.
This -72 can be split as -8 * 9 = -72 and -8 + 9 = 1.
Therefore the given expression is written as: 6x2 + xy – 12y2 = 6x2 + 9xy – 8xy – 12y2
Taking common factors for the first two terms and hence we get:
3x(2x + 3y) – 4x(2x + 3y) = (2x + 3y) (3x – 4y).
6. In triangle ABC, if sin(θ) = 9/15 and the length of the side AB is 9m as shown in the figure, then what is the perimeter of the triangle ABC?
20m
30m
36m
40m
52m
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Correct answer is option - 3 Explanation: sin(θ) = 9/15 = (opposite side)/ (hypotenuse) and given opposite side = AB = 9m.
So hence the hypotenuse = 15m
Using the Pythagorean Theorem, we get AB2 + BC2 = AC2
This gives: 92 + BC2 = 152 ==> 81 + BC2 = 225 ==> BC2 = 225 – 81 = 144
This gives: BC = √144 = 12m.
Perimeter of triangle ABC = AB + BC + AC = 9 + 12 + 15 = 36m.
7. In the parallelogram ABCD, the measure of angle A is (9x – 12) and the measure of angle C is (7x + 6). The measure of angles A, B, C and D respectively are:
Correct answer is option - 3 Explanation: The opposite angles of a parallelogram are equal to each other.
Hence angle A = angle C and angle B = angle D.
This gives 9x -12 = 7x + 6 ==> 2x = 18 ==> x = 9
This gives angle A = 9x – 12 = (9 * 9) – 12 = 81 – 12 = 69°
Hence angle C is also equal to 69°.
Sum of angles in a parallelogram = 360° and let angle B = angle D = y
69° + 69° + y + y = 360° ==> 138° + 2y = 360° ==> 2y = 222 ==> y = 111°.
Therefore angle B = angle D = 111°.
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