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MATHS 5 Marks Questions

Algebra · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 3 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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