Tag: maths

Questions Related to maths

With a given centre and a given radius,only one circle can be drawn.

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. True

  2. False

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Correct Option: A

If angle of sector is $x^o$, then formula used to calculate area is

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $\dfrac{x^o}{360}\times \pi r^2$

  2. $2\dfrac{x^o}{360}\times \pi r$

  3. $\dfrac{x^o}{180}\times \pi r^2$

  4. $2\dfrac{x^o}{360}\times r^2$

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Correct Option: A
Explanation:

If angle of sector is $x^o$ then formula used to calculate is $\dfrac{x^o}{360}\times \pi r^2$.

If the circumference of a circle is $8$ units and arc length of major sector is $5$ units then find the length of minor sector.

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $3$ units

  2. $5$ units

  3. $7$ units

  4. None of these

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Correct Option: A
Explanation:

Length of major arc + Length of minor arc = Circumference

Length of Minor arc $= 8 – 5 = 3$ units 

The angle subtended at the centre of a circle of radius $3cm$ by an arc of length $1cm$ is:

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $\cfrac { { 30 }^{ o } }{ \pi } $

  2. $\cfrac { { 60 }^{ o } }{ \pi } $

  3. ${ 60 }^{ o }$

  4. None of the above

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Correct Option: B
Explanation:

Angle subtended at the centre  of circle is $\theta =\dfrac { l }{ r }$ 

$\Rightarrow \theta =\dfrac { 1 }{ 3 }$  
Now, $\pi$ radian $ =180^{o}$ 
$\Rightarrow \frac { 1 }{ 3 }$ radian $=180^{o}\times \dfrac { 1 }{ 3\pi  } =\dfrac { 60^{o} }{ \pi  }$ 
Hence, option B is correct.

Write True or False:

The tangent to the circumcircle of an isosceles $\triangle ABC$ at A, in which $AB = AC$, is parallel to BC.

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. True

  2. False

  3. Ambiguous

  4. Data insufficient

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Correct Option: A
Explanation:

Given-

PQ is a tangent to a circle at a point A when the circle is a circumcircle of the isosceles $\Delta ABC$.
$ AB=AC.$ 
To find out -
The statement, $PQ\parallel BC$, is true or not.
Justification-
In $\Delta ABC$ we have,
$ AB=AC.$ 
$\therefore  \angle ABC=\angle ACB$    ...(base angles of an isosceles triangle)    ........(i)
Again, PQ is the tangent to the circle at A & AB is a chord drawn from A. 
And AB subtends \angle ACB to the corresponding alternate segment of the circle.
$ \therefore  \angle PAB=$ corresponding alt. segment $\angle ACB$ ......(ii)
So, from (i) & (ii), 
$\angle PAB=\angle ABC.$ 
But they are alternate angles $\Longrightarrow  PQ\parallel BC$ 
$\therefore$ The statement, $PQ\parallel BC$, is true.

In $\bigodot (P, 6)$, the length of an arc is $\pi$. Then the arc subtends an angle of measure ___at the center.

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. 30

  2. 60

  3. 90

  4. 120

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Correct Option: A
Explanation:

Given : $r=6$

$l=\pi $
We know that $l=r\theta $
$\Rightarrow \cfrac { \pi  }{ 6 } =\theta $
$\theta ={ 30 }^{ 0 }$
$\therefore$ The arc subtends ${ 30 }^{ 0 }$ at $P$.

Absolute value of $-58$ is 

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $+58$

  2. $-58$

  3. $58$

  4. $0$

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Correct Option: C
Explanation:

Absolute value of a number is its numerical value without any sign.

Absolute value of $+131$ is equal to

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $- 16$

  2. $0$

  3. $+16$

  4. $131$

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Correct Option: D
Explanation:

Absolute value of $x$ is given by
$|x|=x, x\ge0 \text{ or} -x, x<0 $
Since $131>0$
$\therefore |131|=131$
Option $D$ is correct.

The value of $ \displaystyle \left | 3-10 \right |$ is equal to

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $7$

  2. $-7$

  3. $3+10$

  4. $3-10$

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Correct Option: A
Explanation:

$|x|=x$  when  $x>0$
$|x|=-x$  when  $x<0$
That means it always gives positive quantity.
Now,
$|3-10|=|-7|=7$

The absolute value of $0$ is 

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $-1$

  2. $1$

  3. $0$

  4. not defined

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Correct Option: C
Explanation:

The absolute value of $0$ is $|0|=0.$