Tag: maths

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Multiple choice maths pattern patterns in number operations magic squares magic square

Find the number of parallelogram in the figure given below.

  1. 14

  2. 23

  3. 22

  4. 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For parallelograms we can use the formula of rectangles. It is a
$\displaystyle 3 \, \times \, 3 \, gird, \, hence \, \frac{3 \, \times \, 4}{3 \, \times \, 4} \, \times \frac{3 \, \times \, 4}{3 \, \times \, 4} \, = \, 36$ 

Multiple choice maths pattern patterns in number operations magic squares magic square
$12$ $15$ $54$
$37$ $14$ $102$
$71$ $23$ $?$
  1. $168$
  2. $178$
  3. $188$
  4. $190$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Looking at the rows, we can analyze the pattern between the numbers. For the first row, (12 + 15) * 2 = 54. For the second row, (37 + 14) * 2 = 102. Following this rule for the third row, (71 + 23) * 2 = 94 * 2 = 188.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 5'O clock the angle between two hands in a clock is 

  1. ${ 120 }^{ \circ }$
  2. ${ 130 }^{ \circ }$
  3. ${ 140 }^{ \circ }$
  4. ${ 150 }^{ \circ }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
A clock has $12$ equal parts$={360}^{\circ}$
$1$ part$=\dfrac{{360}^{\circ}}{12}={30}^{\circ}$
At $5$O clock the hands will be between $12$ and $5=5$parts
$\therefore 5$ parts$=5\times{30}^{\circ}={150}^{\circ}$
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The centre of a clock is taken as origin At 4.30 pm the equation of line along minute hand is x = 0 Therefore at this istant the equation of line along the hour hand will be 

  1. $x - y = 0$
  2. $x + y = 0$
  3. $\displaystyle y=\sqrt{2x}$
  4. $\displaystyle y=\frac{x}{\sqrt{2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The centre of a clock is taken as origin. At 4:30 pm equation of line along minute hand is $x=0$.
Therefore at this instant the equation of line along the hour hand will be 
$m=-1$ ( as tan 135=-1 )
Therefore equation of line y=mx
or $y=-x$
$y+x=0$.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 4.24 pm, how many degrees has the hour hand of a clock moved from its position at noon?

  1. $132^\circ$
  2. $135^\circ$
  3. $140^\circ$
  4. $145^\circ$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From noon 12 noon to 4:24 total minutes
4*60+24
=240+24
=264
Now in 12 hour angle made by the hour hand= $={ 360^0 } $
so in 1 minute angle made by the hour hand=360/12*60=$= { \frac { 1 }{ 2 }  } $
so in 264 minute angle made by the hour hand=$=264\times \frac { 1 }{ 2 } ={ 132^0 } $

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The minute hand of a clock is 14 cm long
How much distance dose the end of the minute hand
travel in 15 minutes?$\displaystyle \left ( Take \pi  =\frac{22}{7}\right )$

  1. 11 cm

  2. 22 cm

  3. 33 cm

  4. 44 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given minute hand of clock is 14 cm long

Then distance traveled by minute hand in 15 minutes
= one forth of circumference of circle radius 14 cm
=$\left ( \frac{1}{4}\times 2\times \frac{22}{7}\times 14 \right )=22 cm$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 5:20 the angle formed between the two hands of a clock is

  1. obtuse

  2. right

  3. acute

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A clock is a circle, and a circle always contains $360^o$. Since there are 


$60$ minutes on a clock, each minute mark is $6^o.$

$\Rightarrow$  $\dfrac{360^o}{60}=6\,degree$
The minute hand on the clock will point at $20$ minutes, allowing us to calculate it's position on the circle.

$\Rightarrow$  $20\,minutes\times 6=120\,degree$
So the angle made by the hour hand in $5$ hours $20$ minutes $= 5\dfrac{1}{3}hours$ 
                                                                                                    $=\dfrac{16}{3}\times\dfrac {360^o}{12}$ 
                                                                                                    $=160^o$

Hence angle between the hour hand and minute hand at $5:20=160^o-120^o=40^o$

$\therefore$  $40^o$ is less than $90^o$ means its acute angle.

$\therefore$   At $5:20$ the angle formed between the two hands of a clock is $acute.$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 3 o'clock, the angle formed between the two hands of a clock is

  1. right

  2. acute

  3. obtuse

  4. left
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  A clock is a circle made of $360^o$. and that 

$\Rightarrow$  Each number represents an angle and the separation between them is $\dfrac{360}{12}=30^o$. 
$\Rightarrow$  At $2:00$, the minute hand is on the $12$ and the hour hand is on the $3$.  
$\Rightarrow$  The angle between two hands $=3\times 30^o=90^o$
$\Rightarrow$  At $3$ o'clock, the angle formed between the two hands of a clock is $right\,angle.$