Correct answer is option  5 Explanation: The midpoint of a line = [(x_{1} + x_{2})/2, (y_{1} + y_{1})/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
Show me the answers!
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
Show me the answers!
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(a^{m}) = 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
Show me the answers!
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.
5. The factors of the expression, 6x^{2} + xy 12y^{2}?
Correct answer is option  4 Explanation: In the given expression, 6x^{2} + xy – 12y^{2}, 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: 6x^{2} + xy – 12y^{2} = 6x^{2} + 9xy – 8xy – 12y^{2}
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
Show me the answers!
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 AB^{2} + BC^{2} = AC^{2}
This gives: 9^{2} + BC^{2} = 15^{2} ==> 81 + BC^{2} = 225 ==> BC^{2} = 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°.
HAVE A QUESTION?
Chat With Our Tutoring Experts Now
I just want you to know how great Brinda has been in tutoring me on probability. She is patient and very knowledgeable in all concepts. I look forward to many more sessions with her. I appreciate her help and the great work that Tutor Pace is doing.

9th Grade, from Barbara
Thank you for your excellent tutoring services. It has surely made a lot of difference in our child's academic performance.

9th Grader, from Venkat (father of Sai)
I have enjoyed my session with Aparna and it was helpful. I will hope to see her as my Math tutor in future sessions as well.

10th Grade, from Senia Revayo
Your tutor has been such an inspiration to me as I have difficulty getting some of the physics concepts down and truly understanding them. She takes the time to fully explain each and every aspect of any problem I might ask for help and always with encouragement and humor.