M.C.Q. [1 Marks Each]

MCQ 11 Mark

The side of a square is $10\ cm$. How many times will the new perimeter become if the side of the square is doubled?

✓
$2$ times
B
$4$ times
C
$6$ times
D
$8$ times

Answer

Correct option: A.

$2$ times

Given, side of a square $= 10\ cm$
We know that, perimeter of a square $= 4 \times $ Side $= 4 \times 10$
$= 40\ cm$
$\therefore$ Perimeter of old square $= 40\ cm$
Now, according to the question, side of the square is doubled.
New side$ = 2 \times 10 = 20\ cm$
Again, perimeter of new square = 4 \times Side
$= 4 \times 20 = 80\ cm$
$\therefore$ New perimeter
$= 2 \times $ (Old perimeter)
$= 2 \times 40 = 80\ cm$
Hence, the new perimeter is $2$ times of the old perimeter.

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MCQ 21 Mark

A square shaped park $ABCD$ of side 100m has two equal rectangular flower beds each of size $10m \times 5m$ Length of the boundary of the remaining park is:

A
$360m$
✓
$400m$
C
$340m$
D
$460m$

Answer

Correct option: B.

$400m$

In order to find the length of the boundary of the remaining park, we add two flower beds each of length $10m$ and breadth $5m$, then remaining park is shown below:

Now, length of the boundary of the remaining park = Perimeter of remaining park $= (90 + 5 + 10 + 95 + 90 + 5 + 10 + 95)m = 400m$

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MCQ 31 Mark

Following figures are formed by joining six unit squares. Which figure has the smallest perimeter in Fig.?

A
$(ii)$
B
$(iii)$
C
$(iv)$
✓
$(i)$

Answer

Correct option: D.

$(i)$

$i.$ Let the square $\Box = 1$ unit

Then, perimeter = Sum of all sides
$= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
$= 10$ units
$ii.$ Perimeter $=$ Sum of all sides

$= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
$= 12$ units
$iii.$ Perimeter $=$ Sum of all sides

$= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1 + 1 + 1 + 1$
$= 14$ units
$iv.$ Perimeter $=$ Sum of all sides

$= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1 + 1 + 1 + 1$
$= 14$ units
Hence, smallest perimeter $= 10$ units
which is the perimeter of figure $(i).$

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MCQ 41 Mark

Two regular Hexagons of perimeter $30\ cm$ each are joined as shown in Fig. The perimeter of the new figure is:

A
$65\ cm$
B
$60\ cm$
C
$55\ cm$
✓
$50\ cm$

Answer

Correct option: D.

$50\ cm$

Given, perimeter of hexagon $= 30\ cm$
and number of sides in hexagon $= 6$
$\therefore$ Length of one side $=\frac{\text{Perimeter of hexagon}}{\text{Total number of sides}}$
$=\frac{30}{6}$
$=5\text{cm}$

Now, two hexagons are joined then perimeter = Sum of all sides
$= AB + BC + CD + DE + EF + FG + GH + HI + IJ + JA$
$= 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5$
$= 50\ cm$

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MCQ 51 Mark

In Fig. which of the following is a regular polygon? All have equal side except $(i)$

A
$(i)$
✓
$(ii)$
C
$(iii)$
D
$(iv)$

Answer

Correct option: B.

$(ii)$

In regular polygon, all sides and angles are equal.
According to the question,
In figure $(i)$, all sides are not equal.
So, it is not a regular polygon.
In figure $(ii)$, it is a square and in square all sides are equal and all angles are of $90^\circ .$
So, it is a regular polygon.
In figure $(iii)$, it is a parallelogram and in parallelogram opposite sides are equal and
opposite angles are equal.
So, it is not a regular polygon.
In figure $(iv),$ all sides are not equal. So, it is not a regular polygon.

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MATHS M.C.Q. [1 Marks Each]

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