2 Marks Questions

Question 12 Marks

Observe the tables given below and in each case find whether $x$ and $y$ are inversely proportional.

$x$	$5$	$9$	$15$	$16$
$y$	$9$	$15$	$21$	$24$

Answer

Clearly, $5\times18=9\times10=15\times6=3\times30$
$=45\times2=90=\text{(consant)}$
Therefore, $x$ and $y$ are not inversely proportional.

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Question 22 Marks

Observe the tables given below and in each one find whether $x$ and $y$ are proportional.

$x$	$2.5$	$4$	$7.5$	$10$	$14$
$y$	$10$	$16$	$30$	$40$	$42$

Answer

Clearly,$\frac{\text{x}}{\text{y}}=\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}=\frac{1}{4},$
while $\frac{14}{42}=\frac{1}{3}$
i.e., $\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}$ is not equal to $\frac{14}{42}$
Therefore, $x$ and $y$ are not proportional.

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Question 32 Marks

Observe the tables given below and in each one find whether $x$ and $y$ are proportional.

$x$	$3$	$5$	$8$	$11$	$26$
$y$	$9$	$15$	$24$	$33$	$78$

Answer

Clearly, $\frac{\text{x}}{\text{y}}= \frac{3}{9}=\frac{5}{15}=\frac{8}{24}=\frac{11}{33}=\frac{26}{78}=\frac{1}{3}$ (constant) Therefore, $x$ and $y$ proportional.

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Question 42 Marks

Observe the tables given below and in each one find whether $x$ and $y$ are proportional.

$x$	$5$	$7$	$9$	$15$	$18$	$25$
$y$	$15$	$21$	$27$	$60$	$72$	$75$

Answer

Clearly, $\frac{\text{x}}{\text{y}}=\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}=\frac{1}{3},$
while $\frac{15}{60}=\frac{18}{72}=\frac{1}{4}$
i.e., $\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}$ is not equal to $\frac{15}{60}$ and $\frac{18}{72}$
Therefore, $x$ and $y$ are not proportional.

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Question 52 Marks

Observe the tables given below and in each case find whether $x$ and $y$ are inversely proportional.

$x$	$6$	$10$	$14$	$16$
$y$	$9$	$15$	$21$	$24$

Answer

Clearly, $6\times9\ne10\times15\ne14\times21\ne16\times24$
Therefore, $x$ and $y$ are not inversely proportional.

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Question 62 Marks

Observe the tables given below and in each case find whether $x$ and $y$ are inversely proportional.

$x$	$9$	$3$	$6$	$36$
$y$	$4$	$12$	$9$	$1$

Answer

Clearly, $9\times4=3\times12=36\times1=36,$
While $6\times9=54$
i.e., $9\times4=3\times12=36\times1\ne6\times9$
Therefore, $x$ and $y$ are not inversely proportional.

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