5 Marks Questions

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Question 15 Marks

If m is a whole number less than $5,$ complete the table and by inspection of the table, find the solution of the equation $2m - 5 = -1:$

$m$
$2m - 5$

Answer

Since, m is a whole number which is less than $5,$ then solution of the equation is given by putting the value ofm $= 0, 1, 2, 3, 4, ...$
Now, put $m = 0,$ then
$= 2m - 5 = 2 \times 0 - 5$
$= -5$
Put $m = 1,$ then
$= 2m - 5 = 2 \times 1 - 5$
$= -3$
Put $m = 2,$ then
$= 2m - 5 = 2 \times 2 - 5 = 4 - 5$
$= -1$
Put $m = 3,$ then
$= 2m - 5 = 2 \times 3 - 5 = 6 - 5$
$= 1$
Put $m = 4,$ then
$= 2m - 5 = 2 \times 4 - 5$
$= 3$
Hence, table is:

$m$	$0$	$1$	$2$	$3$	$4$
$2m - 5$	$-5$	$-3$	$-1$	$1$	$3$

and given equation is $2m - 5 = -1$
$\Rightarrow 2m = -1 + 5 [$transposing $-5$ to $RHS]$
$\Rightarrow 2m = 4$
$\Rightarrow\frac{2\text{m}}{2}=\frac{4}{2} [$dividing both sides by $2]$
$\Rightarrow m = 2$

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Question 25 Marks

Let Kanika’s present age be $x$ years. Complete the following table, showing ages of her relatives:

	Situation $($described in ordinary language$)$	Expressions
$(i)$	Her brother is $2$ years younger.
$(ii)$	Her father’s age exceeds her age by $35$ years.
$(iii)$	Mother’s age is $3$ years less than that of her father.
$(iv)$	Her grand father’s age is 8 times of her age.

Answer

Given, Kanika’s present age $= x\ yr$
$i.\ $Her brother’s age $= x - 2\ yr [v$ her brother is $2$ years younger$]$
$ii.\ $Kanika’s present age $= x\ yr$
Father’s age $=$ Kanika’s present age $+\ 35 = x + 35yr$
$iii.\ $Kanika’s present age $= x\ yr$
Father’s age $= (x + 35)yr [$from part $(ii)]$
and Mother’s age $=$ Father’s age $-\ 3 = x + 35 - 3$
$= (x + 32)yr$
$iv.\ $Kanika’s present age $= x\ yr$
Now, grandfather’s age $= 8 $times of Kanika’s age $= 8 × x = 8x\ yr$

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Question 35 Marks

Match the items of Column $I$ with that of Column $II:$

	Column $I$		Column $II$
$(i)$	The number of corners of a quadrilateral	$(A)$	$=$
$(ii)$	The variable in the equation $2p + 3 = 5$	$(B)$	constant
$(iii)$	The solution of the equation $x + 2 = 3$	$(C)$	$+1$
$(iv)$	Solution of the equation $2p + 3 = 5$	$(D)$	$-1$
$(v)$	A sign used in an equation	$(E)$	$p$
		$(F)$	$x$

Answer

	Column $I$		Column $II$
$(i)$	The number of corners of a quadrilateral	$(B)$	constant
$(ii)$	The variable in the equation $2p + 3 = 5$	$(E)$	$p$
$(iii)$	The solution of the equation $x + 2 = 3$	$(C)$	$+1$
$(iv)$	Solution of the equation $2p + 3 = 5$	$(C)$	$+1$
$(v)$	A sign used in an equation	$(A)$	$=$

The number of corners of a quadrilateral are $4,$ which is a constant.
$i.\ $Giver, equation is $2p + 3 = 5$
Here, variable $= p$
$ii.\ $Given, equation is $x + 2 = 3$
$\Rightarrow x = 3 - 2 [$transposing $+2$ to $RHS]$
$\Rightarrow x = 1$
$iii.\ $Given, equation is $2p + 3 = 5$
$\Rightarrow 2p = 5 - 3 [$transposing $+3$ to $RHS]$
$\Rightarrow 2p = 2$
$\Rightarrow\frac{2\text{p}}{2}=\frac{2}{2} [$dividing both sides by $2]$
$\Rightarrow p = 1$
$iv.\ $Equal $(=)$ sign is used in an equation.

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