Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

A circular wire of radius $7$ cm is cut and bend again into an arc of a circle of radius $12$ cm. The angle subtended by the arc at the centre is

  1. $50^\circ$
  2. $210^\circ$
  3. $100^\circ$
  4. $60^\circ$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, radius of circular wire $= 7$ cm

Circumference of wire $= 2 \pi r = 2 \pi (7) = 14 \pi$
Radius of arc $= 12$ cm

Angle subtended by the arc $= \dfrac{\text{arc}}{\text{radius}} = \dfrac{14 \pi}{12} = \dfrac{7 \pi}{6}$

Angle subtended by arc $=\cfrac{7\pi}{6}\times \cfrac{180}{\pi}= 210^{\circ}$

Multiple choice maths basic geometrical concepts and shapes construction of line segment and circle of given radius construction related to lines constructing line segment

Four distinct points $(2K , 3K), (1 , 0), (0 , 1)$ and $(0 , 0)$ lie on a circle when

  1. all values of $K$ are integral
  2. $0 < K < 1$
  3. $K < 0$
  4. For one values of $K$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A = $(0,0)$ , B$(0,1)$ , C$(2k,3k)$ , D$(1,0)$

As we can see

$AD \perp AB$

$\angle A = 90$

$\angle C = 90$

$\implies m _{BC} \times m _{DC} = -1$

$\dfrac{3k - 1}{2k} \times {3k}{2k - 1} = -1$

$\implies k(9k - 3) = -(4k - 2)k$

$k = 0 , 9k + 4k = 2+ 3 \implies 13k = 5 \implies k = \dfrac{5}{13}$

But if $k = 0$, C will be $(0,0)$ which is A

$k = \dfrac{5}{13} $ only one point.

Multiple choice maths basic geometrical concepts and shapes construction of line segment and circle of given radius construction related to lines constructing line segment

A ray of light passing through the point A$(1, 2, 3)$, strikes the plane $x + y + z = 12$ at B on reflection passes through point C$(3, 5, 9)$. The coordinates of point B are 

  1. $(2, 5, 5)$
  2. $(-4, 6, 10)$
  3. $(-7, 0, 19)$
  4. $(0, -5, 17)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let image of point $A(1,2,3)$ about $x+y+z=12$ be $D(p,q,r)$ then,
$\cfrac{p-1}{1}=\cfrac{q-2}{1}=\cfrac{r-3}{1}=-2\cfrac{1+2+3-12}{1^2+1^2+1^2} \\ D(p,q,r)=D(5,6,7) $

Line joining $CD$
$\cfrac{x-5}{2}=\cfrac{y-6}{1}=\cfrac{z-7}{-2}=\lambda$
Coordinate of $B(2\lambda+5,\lambda+6,-2\lambda+7)$
This lies on plane $2\lambda+5+\lambda+6-2\lambda+7=12 \Rightarrow \lambda=-6$
$B(2\lambda+5,\lambda+6,-2\lambda+7)=B(-7,0,19)$
Multiple choice maths numbers international place value system international system of numeration use of commas and comparison and number systems

Thirty one crore fifty-five lakh thirty-two thousand eight hundred in numerals is written as

  1. $31,55,32,800$
  2. $3,01,55,32,800$
  3. $3,15,05,32,800$
  4. $3,15,53,02,800$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In Indian System, the numeral is Thirty one crore, fifty-five lakh thirty-two thousand eight hundred can be written as $31,55,32,800$.

Multiple choice maths numbers international place value system international system of numeration use of commas and comparison and number systems

Kiran had $85$ currency notes in all, some of which were of Rs. $100$ denomination and the remaining of Rs. $50$ denomination. The total amount of all these currency notes was Rs. $5000$. How much amount did she have in the denomination of Rs. $50$?

  1. Rs. $2725$
  2. Rs. $3500$
  3. Rs. $1500$
  4. Rs. $2800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let $100$ Rs note be $x$ and $50$ Rs note be $y$

Total number of notes =$x+y=85$................(1)
Total amount of these currency notes + $5000=100x+50y$.............(2)
Multiplying equation 1 with $50$
therefore we get $50x+50y=4250$.......(3)
Subtracting equation 3 from equation 2, we get
$50x=750$
$x=15$
Substituting $x=15$ in equation 1, weget $y=70$
Amount in dominnation of $50$ Rs=$70\times 50=3500$

Multiple choice maths pair of straight lines bisection of angle pair of bisectors of angles bisector of angle between lines

If the line y = mx is one of the bisector of the lines $x^2 + 4xy - y^2 = 0$, then the value of no ___________.

  1. $\frac{\sqrt{5} - 1}{2}$
  2. $\frac{\sqrt{5} + 1}{2}$
  3. $-(\frac{\sqrt{5} + 1}{2})$
  4. $-(\frac{\sqrt{5} -1}{2})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angle bisectors of the pair of lines ax^2 + 2hxy + by^2 = 0 are given by (x^2 - y^2)/(a - b) = xy/h. Substituting the coefficients from x^2 + 4xy - y^2 = 0, we find the slopes of the bisectors.

Multiple choice maths pair of straight lines bisection of angle pair of bisectors of angles bisector of angle between lines

The Straight lines represented by the equation $135{ x }^{ 2 }-136xy+33{ y }^{ 2 }=0$ are equally inclined to the line 

  1. $x-2y=7$
  2. $x+2y=7$
  3. $x-2y=4$
  4. $3x+2y=4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Give pair of lines is $135{ x }^{ 2 }-136xy+33{ y }^{ 2 }=0$   ...(1)


The equation of bisector of angles between pair of lines (1) is

$\displaystyle \frac { { x }^{ 2 }-{ y }^{ 2 } }{ a-b } =\frac { xy }{ h } \Rightarrow \frac { { x }^{ 2 }-{ y }^{ 2 } }{ 135-33 } =\frac { xy }{ -68 } $

$\Rightarrow 2{ x }^{ 2 }+3xy-2{ y }^{ 2 }=0\Rightarrow \left( x+2y \right) \left( 2x-y \right) =0$

One of the bisectors is $x+2y=0$ which is parallel to the line $x+2y=7$.

Hence, the line $x+2y=7$ is equally inclined to the given lines.