Directions (1-5): The following pie-chart shows the population of six cities of MP who is going to cost their votes in Assembly election of MP 2018. Study the graph carefully and answer the questions that follow:
Note: - Some data are missing in chart, find them if it is required in any question and then proceed.
Also, some data are in degree and some data are in absolute value.
Q1. If no. of voters in Rewa make a central angle of 12° then total no. of voters in Indore is what percent more than the total no. of voters in Satna if ratio of voters in Indore and Satna is 20 : 9?
Q2. If ratio of no. of voters of Rewa, Indore and Satna is 4 : 20 : 9, then total no. of voters in Indore is what percent of total no. of voters in Ujjain?
Q3. What is the average no. of voters in Bhopal, Ujjain and Rewa together? If voters from Rewa makes central angle of 120.
Q4. No. of voters in Jabalpur and Satna together is what percent more or less than the number of voters in Indore and Rewa together? If ratio of no. of voters of Rewa, Indore and Satna is 4 : 20 : 9.
Q5. If 40% voters of Ujjain are in the age group of (20–30) years and 25% are in the age group of (31–40) years and the ratio of voters of age group of above 40 years and below 20 years is 4 : 3, then what is the total no. of voters who are below 20 years in Ujjain? If Rewa makes central angle of 120.
Q6. Nitya’s weight is 140% of Tripti’s weight. Maithili’s weight is 90% of Lawanya’s weight. Lawanya weighs twice as much as Tripti. If Nitya’s weight is x% of Maithili’s weight, then x is equal to:
Q7. In how many ways the five boys can be seated among six girls in such a way that no two boys sit together?
Q8. A shopkeeper sold an article for Rs 750 after giving 20% discount on the labeled price and made 40% profit on the cost price. What would have been the approximate percentage profit, had he not given the discount?
Q9. If the area of a circle is 616 cm², what would be the total surface area of a hemisphere having the same radius as the circle?
Q10. Tap A fills a tank in 10 hours and B can fill it in 15 hours. Both are opened simultaneously. Sometimes later tap B was closed and time taken to fill the whole tank was 8 hours. After how many hours B was closed?
Directions (11-15): In each of the following questions two equations are given. You have to solve the equations and
Give answer —
Q11. I. 9x² – 36x + 35 = 0
II. 2y² – 15y – 17 = 0
⇒ 9x² - 21x – 15x + 35 = 0
⇒ 3x (3x – 7) -5 (3x – 7) = 0
⇒ (3x- 7) (3x – 5) = 0
⇒ x=5/3,7/3
II. 2y² – 15y – 17 = 0
⇒ 2y² - 17y + 2y – 17 = 0
⇒ (y + 1) (2y – 17) = 0
⇒ y= -1, 17/2
No relation
Q12. I. 2x² – 7x + 3 = 0
II. 2y² – 7y + 6 = 0
⇒ 2x² - 6x – x +3 = 0
⇒ (x – 3) (2x – 1) = 0
⇒ x = 3, 1/2,
II. 2y² - 7y +6 = 0
⇒ 2y² - 4y – 3y + 6 = 0
⇒ (y – 2) (2y – 3) = 0
⇒ y = 2, 3/2
No relation
Q13. I. 4x² + 16x + 15 = 0
II. 2y² + 3y + 1 = 0
⇒ 4x² + 10x + 6x + 15 = 0
⇒ 2x (2x + 5) + 3 (2x + 5) = 0
⇒ (2x + 5) (2x + 3) = 0
⇒ x= -5/2, -3/2
II. 2y² + 3y + 1 = 0
⇒ 2y² + 2y + y + 1 = 0
⇒ (y + 1) (2y + 1) = 0
⇒ y = -1, -1/2
y > x
Q14. I. 9x² – 45x + 56 = 0
II. 4y² – 17y + 18 = 0
⇒ 9x² - 24x – 21x + 56 = 0
⇒ 3x (3x – 8) – 7 (3x – 8) = 0
⇒ (3x – 8) (3x – 7) = 0
⇒ x = 8/3, 7/3
II. 4y² - 17y + 18 = 0
⇒ 4y² - 8y – 9y + 18 = 0
⇒ (y – 2) (4y – 9) = 0
⇒ y = 2, 9/4
x>y
Q15. I. 2x² + 11x + 14 = 0
II. 2y² + 15y + 28 = 0
⇒ 2x² + 4x + 7x + 14= 0
⇒ (x + 2) (2x + 7) = 0
⇒ x = -2, -7/2
II. 2y² + 15y + 28= 0
⇒ 2y² + 8y + 7y + 28 = 0
⇒ (y + 4) (2y + 7) = 0
⇒ y = -4, -7/2
⇒ x ≥ y
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