On comparing the ratios  find out whether the following pair o

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 Multiple Choice QuestionsLong Answer Type

1.

Aftab tells his daughter, 'Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be'. (Isn’t this interesting?) Represent this situation algebraically and graphically.

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2. The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Represent this situation algebraically and graphically.
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3. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and geometrically.
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4.

(i) 10 students of Class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

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5. 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
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 Multiple Choice QuestionsShort Answer Type

6. On comparing the ratios  straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.

5x - 4y + 8 = 0, 7x + 6y - 9 = 0
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7. On comparing the ratios  straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.

9x + 3y + 12 = 0, 18x + 6y + 24 = 0
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8. On comparing the ratios  straight a subscript 1 over straight a subscript 2 comma space straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.

6x - 3y + 10 = 0, 2x - y + 9 = 0.
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9. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

3x + 2y = 5; 2x - 3y = 7
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10. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

2x - 3y = 8; 4x - 6y = 9


2x - 3y = 8; 4x - 6y = 9

Here comma space space straight a subscript 1 equals 2 comma space straight b subscript 1 equals 3 comma space straight c subscript 1 equals 8
space space space space space space space space space space straight a subscript 2 equals 4 comma space straight b subscript 2 equals negative 6 comma space straight c subscript 2 equals 9
therefore space space straight a subscript 1 over straight a subscript 2 equals 2 over 4 equals 1 half equals straight b subscript 1 over straight b subscript 2 equals fraction numerator negative 3 over denominator negative 6 end fraction equals 1 half comma space and space straight c subscript 1 over straight c subscript 2 equals 8 over 9
Clearly comma space straight a subscript 1 over straight a subscript 2 equals straight b subscript 1 over straight b subscript 2 not equal to straight c subscript 1 over straight c subscript 2

Hence, the given lines are parallel. So, the given pair of linear equation it has no solution and therefore it is inconsistent.


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