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Q1 / 25
2.00 marks
Simplify the following. (x-3y) 3 + 27(y 3 −xy 2 ) + (2x+y) 3 -3xy(x+2y)
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Q2 / 25
2.00 marks
Two chords PQ and MN of lengths 5 cm and 1 1 cm respectively are parallel and are on the same side of centre O of a circle. If the distance between the chords is 3 cm, then what is the radius of the circle?
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Q3 / 25
2.00 marks
A, B and C start a business. A invests 33(1/3) % of the total capital. B invests 25% of the remaining and C, the rest. A and C left the business after first and second quarter respectively. If the total profit at the end of the year is Rs. 2,16 ,000 then B’s share is:
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Q4 / 25
2.00 marks
The radii of the two circular faces of the frustum of a case are 5 cm and 4 cm. If the heig ht of the frustum is 21cm, find the volume [ in cm 3 ] and lateral surface area [in cm 2 ] of the frustum.
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Q5 / 25
2.00 marks
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Q6 / 25
2.00 marks
If 3x+2y-5z = 11, 2x-3y+9z = 14 and y-4z = 15 then find the value of x/2.
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Q7 / 25
2.00 marks
What is the value of sin30 cos15 +sin15 cos30 ?
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Q8 / 25
2.00 marks
How many spherical lead shots each of diameter 8.4 cm can be obtained from a rectangular solid of lead with dimension 88cm, 63cm, 42 cm ?
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Q9 / 25
2.00 marks
A garment shop sells a shirt for Rs A, in curring a loss of 5%. During an end-of-season sal e, they mark up the same shirt a t Rs 1.2A. At the sale, they provide a fl at discount of 10% on this mark ed price. What will be the percentage profit or loss for the garment shop on that shirt during the sale?
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Q10 / 25
2.00 marks
A laptop is priced at Rs.40,000. At customer gets a discount of Rs. 4,000 on it. After the discount, the customer buys a mouse marked for Rs. 1,500 at a 20% discount. What is the total amount the customer spends on both items?
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Q11 / 25
2.00 marks
The ratio of the time taken by P and Q to complete a task is 3:2. If Q can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?
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Q12 / 25
2.00 marks
In a class, the ratio of boys to girls is 5 : 3. In an exam, 20% of the boys and 40% of the girls were absent. Among the students who were present, 40% of the boys and 60% of the girls passed the exam. Find the ratio of boys to girls who appeared in the exam and failed.
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Q13 / 25
2.00 marks
Which of these number sets is NOT a subset of the Real Numbers?
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Q14 / 25
2.00 marks
A sum of money is invested at a compound interest rate of 8% p.a. for the first year and 10% p.a. for the second year. If th e total interest earned is Rs. 4512 , what was the original principal?
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Q15 / 25
2.00 marks
It the side of a regular hexagon is 12cm. Find the inradius of the circle inscribed in it.
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Q16 / 25
2.00 marks
A policeman started following a thief who was 1200 metres ahead of him. The thief is running at 2.5 km/h, while the speed of the policeman is 3.75 km/h. Find the distance covered by the thief in metres just when he was caught.
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Q17 / 25
2.00 marks
The average of 15 numbers is 80. The average of the first 6 numbers is 72. The average of the next 6 nu m bers is 25% more than the average of the first 6 numbers. The 13 th number is 8 more than the 15 th number, and the 14 th number is 10 less than the 15 th number. What is the average of the 13 th and 14 th ?
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Q18 / 25
2.00 marks
Find the difference between mean and mode of the following data: 22, 24, 10.5, 27.5, 22, 24, 25, 23.5, 24, 21 .5
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Q19 / 25
2.00 marks
The annual instalment (in ₹) to discharge a debt of ₹8,432 due in 4 years at 16% simple interest per annum is:
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Q20 / 25
2.00 marks
At present, Himanshu is younger than Bi pin by 8 years. If 4 years ago, ages of Himanshu, Bipin and Ranjeet were in the ratio 1:2 :3 then what is the present age of Ranjeet in years?
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Q21 / 25
2.00 marks
The following data set is given: 8, 12, 15, 13, 12, 12, 14, 10 Which of the following statements is correct regarding the distribution?
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Q22 / 25
2.00 marks
P and Q together can do a piece of work in 20 days. They worked for 8 days, and M completed the remaining in 4 days. How long will M alone take to do the whole work?
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Q23 / 25
2.00 marks
A man rows a boat to a point 45 km upstream and returns to the starting point. The total time ta ken for the entire journey is 14 hours. The speed of the stream is 2 km/h. if the stream speed increases by 1 km/h, how much additional time (in hours) will the man take to complete the same journey
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Q24 / 25
2.00 marks
Find a single discount equivalent to the successive discount of 20%, 24%, and 32%.
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Q25 / 25
2.00 marks
A mixture containing 72% oil is mixed with another mixture containing 48% oil in the ratio 6:16. What is the percentage of oil in the mixture formed?
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