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In △ABC, D and E are the points on sides AB and AC, respectively, such that DE ll BC. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, then (AB + EC) is equal to (all measurements in cm):
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The correct answer is option 4 i.e. 9.
Since DE || BC, AD/DB = AE/EC
x/(x - 2) = (x + 2)/(x - 1)
⇒ x2 - x = x2 - 4
⇒ -x = -4
⇒ x = 4
AB = AD + DB = x + (x - 2) = 4 + 2 = 6 cm
EC = x - 1 = 3 cm
AB + EC = 6 + 3 = 9 cm
When a positive integer 'n' is divided by 12, the remainder is 5. What will be the remainder if 8n2 + 7 is divided by 22?
The correct answer is option 3 i.e. 3.
n / 12 → Remainder = 5
(8n2 + 7)/ 12 = [(8 × 52) + 7] / 12
= 207 / 12 → Remainder = 3
A class of 66 students made a mean score of 62 marks, and another class of 34 students made it exactly 51.5. What is the overall mean score?
The correct answer is option 4 i.e. 58.43
Mean = Sum of the terms/Number of terms
The mean score of 66 students = 62
The total score of 66 students = 62 × 66 = 4092
The mean score of 34 students = 51.5
The total score of 34 students = 51.5 × 34 = 1751
The total number of students = 66 + 34 = 100
The mean score of all students = (4092 + 1751)/100 = 5843/100 = 58.43
Therefore, the overall mean score is 58.43
Two positive numbers differ by 2134. When the greater number is divided by the smaller number, the quotient is 2 and the remainder is 147. What is the HCF of the greater of the two given numbers and 4225?
The correct answer is Option 4 i.e. 13.
Let the bigger number be a
Smaller number = b
⇒ a - b = 2134
⇒ a = 2b + 147
⇒ b = 1987
⇒ a = 4121
HCF(4121, 4225) = 13
The following pie chart shows the percentage quantity of fruits at two fruit shops A and B.
If the price of guava is ₹12 per kg, that of mango is ₹30 per kg, that of apple is ₹40 per kg, that of orange is ₹20 per kg, and that of banana is ₹15 per kg.
Then what is the total cost of all the fruits at Shop B?
The correct answer is Option 2 i.e. ₹28,992.
The total cost of fruits from shop B = [1200 × (8/100) × 12] + [1200 × (18/100) × 30] + [1200 × (22/100) × 40] + [1200 × (24/100) × 20] + [1200 × (28/100) × 15]
= 1200(0.96 + 5.4 + 8.8 + 4.8 + 4.2)
= 1200 × 24.16
= 28992
What must be subtracted from x3 - 3x2y + 3xy2 - y3 to get x3 - y3?
The correct answer is Option 3 i.e. -3x2y + 3xy2.
(x3 - 3x2y + 3xy2 - y3) - (x3 - y3)
= x3 - 3x2y + 3xy2 - y3 - x3 + y3
= - 3x2y + 3xy2
Directions For Questions
Directions: Study the given pie chart and answer the question that follows.
The pie chart shows the expenditure of a family on different items and their savings throughout the year 2021.
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If the total income of the family was Rs 1,00,000, how much money (in Rs) was spent on the education of the children?
The correct answer is option 2 i.e. 12,000.
According to the given pie-chart,
Total income of the family = Rs 1,00,000
Percentage spent on children's education = 12%
The amount was spent on the education of the children = 100000 × 12/100 = 12000
The correct answer is Option 2 i.e. 5.
secθ = 13/5
Triangle sides: 5, 12, 13
tanθ = 12/5; cosecθ = 13/12; sinθ = 12/13
= [(10 × 12/5 + 24 × 13/12)/(39 × 12/13 - 10 × 13/5)]
= [(24 + 26)/(36 - 26)]
= 50/10
= 5
G is the centroid of the equilateral ΔABC. If AB = 8√3 cm, then the length of AG is equal to:
The correct answer is Option 4 i.e. 8 cm.
Height of triangle = (√3/2) × 8√3 = 12 cm
AG = 2/3 of Height = (2/3) × 12 = 8 cm
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