Tag: maths

Questions Related to maths

Two boys P and Q walk at 6 km/hr and 6 km/hr respectively. If Q covers a certain distance in 10 minutes less than P. What is the time taken by Q to cover the same distance (in minutes)?
time speed and distance problems involving speed word problems on speed time and distance time and distance word problems on simultaneous equations applications of simultameous equations unitary method idea of speed distance and time speed math time work and distance ratio and proportions linear equations in two variables maths

  1. 40

  2. 60

  3. 30

  4. 70

Show answer
Correct Option: A

A can run 1 km in 4 min 54 sec and B in 5 min. How many metres start can A can give B in a km race so that the race may end in a dead heat ?
time speed and distance problems involving speed word problems on speed time and distance time and distance word problems on simultaneous equations applications of simultameous equations unitary method idea of speed distance and time speed math time work and distance ratio and proportions linear equations in two variables maths

  1. 16 m

  2. 18 m

  3. 20 m

  4. 22 m

Show answer
Correct Option: C
Explanation:

Distance covered by B in 6 sec $= \dfrac{(1000}{300}×6)=20 m$

If a car travels 150 km in 5 hours then its speed is
ime speed and distance problems involving speed word problems on speed time and distance time and distance word problems on simultaneous equations applications of simultameous equations unitary method idea of speed distance and time speed math time work and distance ratio and proportions linear equations in two variables maths

  1. 150 km/hr

  2. 30 km/hr

  3. 50 km/hr

  4. 10 km/hr

Show answer
Correct Option: B
Explanation:

$Speed=\dfrac{distance}{time}=\dfrac{150}{5}$ $=30 km/hr$

The intercepts of the plane $2x-3y+5z-30=0$ are 

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. $15,-10,6$

  2. $5,10,6$

  3. $1/8,-1/6,1/4$

  4. $3,-4,6$

Show answer
Correct Option: A
Explanation:

We have,

$\begin{array}{l} 2x-3y+5z=30 \ \frac { x }{ { 15 } } +\frac { y }{ { -10 } } +\frac { z }{ 6 } =1 \end{array}$
Intercept we $(15,-10,6)$
Then,
OPtion $A$ is correct answer.

If $A=(3,1,-2) , B=(-1,0,1)$ and $l, m$ are the projections of AB on the y-axis, zx plane respectively then $3l^2-m+1$=

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. 0

  2. 1

  3. 11

  4. 27

Show answer
Correct Option: A

A plane $
\pi
 $ makes intercept 3 and 4 respectively on z-axis and x-axis. If $
\pi
 $ is parallel to y-axis, then its equation is


maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. 3x+4z=12

  2. 3z+4x=12

  3. 3y+4z=12

  4. 3z+4y=12

Show answer
Correct Option: A
Explanation:
$X-$intercept $a=4$
and $Z-$intercept $c=3$
Required equation $\dfrac{x}{4}+\dfrac{z}{3}=1$
or $3x+4z=12$

The lengths of the intercepts on the co-ordinate axes made by the plane $5x+2y+z-13=0$ are

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. $5, 2, 1$ unit

  2. $\dfrac{13}{5}, \dfrac{13}{2}, 13$ unit

  3. $\dfrac{5}{13}, \dfrac{2}{13}, \dfrac{1}{13}$ unit

  4. $1, 2, 5$ unit

Show answer
Correct Option: B
Explanation:

Solution:

Given that:
$5x+2y+z-13=0$ 
or, $\cfrac{x}{\frac{13}{5}}+\cfrac{y}{\frac{13}{2}}+\cfrac{z}{13}=1$
$\therefore$ Lengths of intercepts are $\cfrac{13}5,\cfrac{13}2$ and $13.$
Hence, B is the correct option.

Equation of a plane making X-intercept $4$, Y-intercept ($-6$), Z-intercept $3$ is _______.

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. $3x-4y+6z=12$

  2. $3x-2y+4z=12$

  3. $4x-6y+3z=1$

  4. $4x-3y+2z=12$

Show answer
Correct Option: B
Explanation:

Equation of a plane which cuts intercepts $4,-6,3$ on axes is
$\cfrac { x }{ 4 } +\cfrac { y }{ (-6) } +\cfrac { z }{ 3 } =1$
$\therefore$ $3x-2y+4z=12$

Two system of rectangular axes have the same origin. If a plane cuts them at distances, $a$, $b$, $c$ and ${a} _{1}$,${b} _{1}$ , ${c} _{1}$ from the origin, then

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. $\dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } +\dfrac { 1 }{ { c }^{ 2 } } =\dfrac { 1 }{ { a } _{ 1 }^{ 2 } } +\dfrac { 1 }{ { b } _{ 1 }^{ 2 } } +\dfrac { 1 }{ { c } _{ 1 }^{ 2 } }$

  2. $\dfrac { 1 }{ { a }^{ 2 } } -\dfrac { 1 }{ { b }^{ 2 } } +\dfrac { 1 }{ { c }^{ 2 } } =\dfrac { 1 }{ { a } _{ 1 }^{ 2 } } -\dfrac { 1 }{ { b } _{ 1 }^{ 2 } } +\dfrac { 1 }{ { c } _{ 1 }^{ 2 } }$

  3. ${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }={ a } _{ 1 }^{ 2 }+{ b } _{ 1 }^{ 2 }+{ c } _{ 1 }^{ 2 }$

  4. ${ a }^{ 2 }-{ b }^{ 2 }+{ c }^{ 2 }={ a } _{ 1 }^{ 2 }-{ b } _{ 1 }^{ 2 }+{ c } _{ 1 }^{ 2 }$

Show answer
Correct Option: A
Explanation:
Let the equation of the plane be
$\dfrac { x }{ a } +\dfrac { y }{ b } +\dfrac { z }{ c } =1$  and $\dfrac { x }{ a _1 } +\dfrac { y }{ b _1 } +\dfrac { z }{ c _1 } =1$
$ax+by+cz+d=0\quad perpendicular\quad distance\quad from\quad origin\quad is\quad \dfrac { \left| d \right|  }{ \sqrt { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }  } $
as they have the same origin their perpendicular distance is constant.
$\dfrac { 1 }{ \sqrt { \dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } +\dfrac { 1 }{ { c }^{ 2 } }  }  } =\dfrac { 1 }{ \sqrt { \dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } +\dfrac { 1 }{ { c }^{ 2 } }  }  }$
$\dfrac { 1 }{ { a _1}^{ 2 } } +\dfrac { 1 }{ { b _1 }^{ 2 } } +\dfrac { 1 }{ { c _1 }^{ 2 } } =\dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } +\dfrac { 1 }{ { c }^{ 2 } } $


A plane $x-3y+5z=d$ passes through the point $(1,2,4)$. Intercepts on the axes are

maths the plane equation of a plane in intercept form equation of a plane in different forms different forms of equation of a plane

  1. $15,-5,3$

  2. $1,-5,3$

  3. $-15,5,-3$

  4. $1,-6,20$

Show answer
Correct Option: A
Explanation:

$(1, 2, 4)$ must satisfy this plane

$(1)(1) - (3)(2) + (5)(4) = d$ 
$\Rightarrow $ plane $\Rightarrow x - 3y + 5z = 15$
$x$ intercept $\Rightarrow x - 0 + 0 = 15 \Rightarrow 15 = x \, ml$
$y$ intercept $\Rightarrow 0 - 3y + 0 = 15 \Rightarrow y \, int = -5$
$z$ intercept $\Rightarrow 0 - 0 + 52 = 15 \Rightarrow z \, int . = 3$
$\therefore A = (15, -5 , 3)$