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Linear Inequalities

Short Answer Type

31. Find all pairs of consecutive odd natural numbers, both of which are larger than 5, such that their sum is less than 20.

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32. Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.

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33. Ravi obtained 70 and 75 marks in first two unit tests. Find the number of minimum marks he should get in the third test to have an average of at least 60 marks.

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34. To receive grade ‘A’ in a course, one must obtain an average of 85 marks or more in four examinations (each of 100 marks). If Keshav’s marks in first three examinations are 82, 80, 91. Find the minimum marks that Keshav must obtain in the fourth examination to get grade ‘A’ in the course.

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35. A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree celsius (C), if the conversion formula is given by

$straight F equals open parentheses 9 over 5 straight C plus 32 close parentheses ?$

Solution not provided.

Ans. $20 degree straight C space to space 25 degree straight C$

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36.

The company manufactures cassettes and its cost equation for a week is C = 300 + 1.5x and its revenue equation is R = 2x. where x is the number of cassettes sold in a week. Find the least number of cassettes that must be sold for the company to realize a profit.

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37. Find all pairs of positive integers, such that their sum is less than 8 and their difference is 2.

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38. In drilling world’s deepest hole, it was found that the temperature T in degree celsius, x km below the surface of earth was given by:

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At what depth will the temperature be between

150 degree straight C

and

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39. A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

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40.

Solve the following inequality:

$30 straight x space less or equal than space 200 space space For space left parenthesis straight i right parenthesis space straight x space element of space straight N space left parenthesis ii right parenthesis space straight x space element of space straight Z space left parenthesis iii right parenthesis space straight x space element of space straight R$

176 Views