Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Choose the correct answer from the alternatives given.
Water is flowing at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank which is $50$ m long, $44$ m wide. The time taken (in hours) for the rise in the level of water in the tank to be $7$ cm is

  1. $2$
  2. $1\dfrac{1}{2}$
  3. $3$
  4. $2\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Water
flowed by the pipe in lh = $\pi r^2h$
= $\dfrac{22}{7} \times$ $\dfrac{7\times 7}{100\times100}$ $\times 5000 m^3 =77m^3$
Volume
of expected water in the tank = $\frac{50 \times 44 \times 7}{100} = 154
m^3$ 
Required
time= $154/77 = 2 hrs$.

Multiple choice maths introduction to three dimensional geometry midpoint of line segment mid point formula mid-point of a line segment

If $z = \cos \dfrac{\pi }{6} + i\sin \dfrac{\pi }{6}$, then

  1. $\left| z \right| = 1,\arg z = \dfrac{\pi }{4}$
  2. $\left| z \right| = 1,\arg z = \dfrac{\pi }{6}$
  3. $\left| z \right| = \dfrac{{\sqrt 3 }}{2},\arg z = \dfrac{{5\pi }}{{24}}$
  4. $\left| z \right| = \dfrac{{\sqrt 3 }}{2},\arg z = {\tan ^{ - 1}}\dfrac{1}{{\sqrt 2 }}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

if $z=\cos \left(\dfrac{\pi}{6}\right)+i\sin \left(\dfrac{\pi}{6}\right)$ then.

As $z=|z|e^{i arq (z)}$
$\therefore z=\cos \left(\dfrac{\pi}{6}\right)+i\sin \left(\dfrac{\pi}{6}\right)=e^{i\left(\pi/6\right)}\quad [\because e^{i\theta}=\cos\theta+i\sin \theta]$
$\Rightarrow |z|=1,  arq=\dfrac{\pi}{6}$

Multiple choice maths section and mid-point formula midpoint of line segment mid point formula mid-point of a line segment

STATEMENT - 1 : The coordinates of the point P(x, y) which divides the line segment joining the points A$(x _1,  y _1)$ and B$(x _2,  y _2)$ internally in the ration $m _1$  :  $m _2$ are $\left ( \dfrac{m _1 x _2 -m _2 x _1}{m _1 + m _2} ,  \dfrac{m _1 y _2 - m _2 y _1}{m _1 + m _2}\right )$


STATEMENT - 2 : The mid-point of the line segment joining the points P $(p _1 y _1)$ and Q$(x _2, y _2)$ is $\left ( \dfrac{x _1+x _2}{2} , \dfrac{y _1 + y _2}{2} \right )$

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement -1 is false,

As the formula is not for the internally it is when point divides externally.
Statement -2 is true.

Multiple choice maths section and mid-point formula midpoint of line segment mid point formula mid-point of a line segment

Consider points $A(-1,3), B(-1,2)$. Find point $P$ which divides $AB$ externally in $\dfrac{5}{4}$.

  1. $(9,-22)$
  2. $(-1,2)$
  3. $(-1,-2)$
  4. $(9,22)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let point P be (x,y)
$x=\cfrac { 5\times (-1)-4\times (-1) }{ 5-4 } \\ x=\cfrac { -5+4 }{ 1 } \\ x=-1\\ y=\cfrac { 5\times (2)-4\times (3) }{ 5-4 } \\ y=\cfrac { 10-12 }{ 1 } \\ y=-2\\ \therefore P=(-1,-2)$
Multiple choice maths triangles relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

In the sides $BC,CA,AB$ of a triangle $ABC$, three points $D,E,F$ are taken such that each of $BD,CE,AE$ is equal to one-third of the corresponding side, then
$\triangle DEF=\dfrac {1}{2}\triangle ABC$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If D, E, F divide the sides in 1:2 ratio, the area of triangle DEF is (1 - 3*(1/3)*(2/3)) = 1/3 of the area of triangle ABC. The statement that it is 1/2 is false.

Multiple choice maths triangles relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR$, respectivetly where $\triangle ABC \sim \triangle PQR$, then  $\dfrac {AB}{PR}=\dfrac {AC}{PM}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For similar triangles, the ratio of corresponding medians is equal to the ratio of corresponding sides (AB/PQ = AD/PM). The provided ratio AB/PR = AC/PM is not a standard property of similar triangles.

Multiple choice maths perimeter and area of rectilinear figures region enclosed by a plane figure area of square and rectangle mensuration-i (area)

The standard unit of volume is in

  1. $m$
  2. $m^2$
  3. $m^3$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For eg., a cube is a $3D$ object.

$\therefore$ volume of a cuboid $=$ $l \times b \times h$
All the three dimensions are measures in "meter".
Hence, the unit of measure measurement of volume is in cubic meter or $m^3$.
So, option C is correct.