Maths-
General
Easy

Question

The differential equation of all non-vertical lines in a plane is :

  1. fraction numerator d y over denominator d x end fraction equals 0
  2. fraction numerator d x over denominator d y end fraction equals 0
  3. fraction numerator d squared y over denominator d x squared end fraction equals 0
  4. fraction numerator d squared x over denominator d y squared end fraction equals 0

Hint:

In this question, we have to find the differential equation of all non-vertical lines in a plane. First we will find the equation and later differentiate it twice to find the required differential equation.

The correct answer is: fraction numerator d squared y over denominator d x squared end fraction equals 0


    T h e space g e n e r a l space e q u a t i o n space o f space n o n minus v e r t i c a l space l i n e s space i s space a x plus b y equals 1
a x plus b y equals 1
rightwards double arrow b y equals 1 minus a x
rightwards double arrow y equals 1 over b minus fraction numerator a x over denominator b end fraction
d i f f e r e n t i a t i n g space b o t h space s i d e s comma space w e space g e t colon
rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator negative a over denominator b end fraction
A g a i n comma space d i f f e r e n t i a t i n g space comma space w e space g e t colon
rightwards double arrow fraction numerator d squared y over denominator d x squared end fraction equals 0

    Related Questions to study

    General
    Maths-

    The differential equation of all conics with the coordinate axes, is of order

    The differential equation of all conics with the coordinate axes, is of order

    Maths-General
    General
    Maths-

    If the algebraic sum of distances of points (2, 1) (3, 2) and (­-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is

     

    equation of the line passing through the point (x,y) ax+by+c=0
    d i s tan c e space f r o m space t h e space l i n e space t o space p o i n t space open parentheses 2 comma 1 close parentheses equals open vertical bar fraction numerator 2 a plus 1 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
d i s tan c e space f r o m space t h e space i n e space t o space p o i n t space open parentheses 3 comma 2 close parentheses equals open vertical bar fraction numerator 3 a plus 2 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
d i s tan c e space f r o m space t h e space l i n e space t o space p o i n t space open parentheses negative 4 comma 7 close parentheses equals open vertical bar fraction numerator negative 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
A P Q comma
open vertical bar fraction numerator 2 a plus 1 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar plus open vertical bar fraction numerator 3 a plus 2 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar plus open vertical bar fraction numerator negative 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar equals 0
rightwards double arrow fraction numerator 2 a plus b plus c plus 3 a plus 2 b plus c minus 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction equals 0
rightwards double arrow a plus 10 b plus 3 c equals 0
rightwards double arrow 1 third a plus 10 over 3 b plus c equals 0
t h e r e f o r e comma space t h e space l i n e space p a s s e s space t h r o u g h open parentheses 1 third comma 10 over 3 close parentheses.

    If the algebraic sum of distances of points (2, 1) (3, 2) and (­-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is

     

    Maths-General
    equation of the line passing through the point (x,y) ax+by+c=0
    d i s tan c e space f r o m space t h e space l i n e space t o space p o i n t space open parentheses 2 comma 1 close parentheses equals open vertical bar fraction numerator 2 a plus 1 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
d i s tan c e space f r o m space t h e space i n e space t o space p o i n t space open parentheses 3 comma 2 close parentheses equals open vertical bar fraction numerator 3 a plus 2 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
d i s tan c e space f r o m space t h e space l i n e space t o space p o i n t space open parentheses negative 4 comma 7 close parentheses equals open vertical bar fraction numerator negative 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar
A P Q comma
open vertical bar fraction numerator 2 a plus 1 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar plus open vertical bar fraction numerator 3 a plus 2 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar plus open vertical bar fraction numerator negative 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar equals 0
rightwards double arrow fraction numerator 2 a plus b plus c plus 3 a plus 2 b plus c minus 4 a plus 7 b plus c over denominator square root of a squared plus b squared end root end fraction equals 0
rightwards double arrow a plus 10 b plus 3 c equals 0
rightwards double arrow 1 third a plus 10 over 3 b plus c equals 0
t h e r e f o r e comma space t h e space l i n e space p a s s e s space t h r o u g h open parentheses 1 third comma 10 over 3 close parentheses.
    General
    Maths-

    A particle moves in a straight line with velocity given by fraction numerator d x over denominator d t end fraction equals x plus 1 (x being the distance described). The time taken by the particle to describe 99 meters is:

    fraction numerator d x over denominator d t end fraction equals x plus 1
rightwards double arrow integral subscript 0 superscript 99 fraction numerator d x over denominator x plus 1 end fraction equals integral subscript 0 superscript t d t
rightwards double arrow integral subscript 0 superscript 99 log subscript e open parentheses x plus 1 close parentheses equals t
rightwards double arrow log subscript e open parentheses 100 close parentheses equals t
rightwards double arrow log subscript e open parentheses 10 close parentheses squared equals t
rightwards double arrow 2 log subscript e open parentheses 10 close parentheses equals t

    A particle moves in a straight line with velocity given by fraction numerator d x over denominator d t end fraction equals x plus 1 (x being the distance described). The time taken by the particle to describe 99 meters is:

    Maths-General
    fraction numerator d x over denominator d t end fraction equals x plus 1
rightwards double arrow integral subscript 0 superscript 99 fraction numerator d x over denominator x plus 1 end fraction equals integral subscript 0 superscript t d t
rightwards double arrow integral subscript 0 superscript 99 log subscript e open parentheses x plus 1 close parentheses equals t
rightwards double arrow log subscript e open parentheses 100 close parentheses equals t
rightwards double arrow log subscript e open parentheses 10 close parentheses squared equals t
rightwards double arrow 2 log subscript e open parentheses 10 close parentheses equals t
    parallel
    General
    Maths-

    Integral curve satisfying y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction comma y left parenthesis 1 right parenthesis equals 1 has the slope at the point (1, 0) of the curve, equal to :

    Given,y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction comma y left parenthesis 1 right parenthesis equals 1
    y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction
rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction
rightwards double arrow open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses 1 comma 0 close parentheses end subscript equals fraction numerator 1 squared plus 0 squared over denominator 1 squared minus 0 squared end fraction
space space space space space space space space space space space space space space space space space space space space space space equals 1 over 1 equals 1

    Integral curve satisfying y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction comma y left parenthesis 1 right parenthesis equals 1 has the slope at the point (1, 0) of the curve, equal to :

    Maths-General
    Given,y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction comma y left parenthesis 1 right parenthesis equals 1
    y to the power of straight prime equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction
rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator x squared plus y squared over denominator x squared minus y squared end fraction
rightwards double arrow open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses 1 comma 0 close parentheses end subscript equals fraction numerator 1 squared plus 0 squared over denominator 1 squared minus 0 squared end fraction
space space space space space space space space space space space space space space space space space space space space space space equals 1 over 1 equals 1
    General
    Maths-

    If integrating factor of x open parentheses 1 minus x squared close parentheses d y plus open parentheses 2 x squared y minus y minus a x cubed close parentheses d x is e to the power of JPdx then P is

    integral x open parentheses 1 minus x squared close parentheses d y plus open parentheses 2 x squared y minus y minus a x cubed close parentheses d x equals 0
rightwards double arrow x open parentheses 1 minus x squared close parentheses fraction numerator d y over denominator d x end fraction plus 2 x squared y minus y minus a x cubed equals 0
rightwards double arrow x open parentheses 1 minus x squared close parentheses fraction numerator d y over denominator d x end fraction plus y open parentheses 2 x squared minus 1 close parentheses equals a x cubed
rightwards double arrow fraction numerator d y over denominator d x end fraction plus fraction numerator y open parentheses 2 x squared minus 1 close parentheses over denominator x open parentheses 1 minus x squared close parentheses end fraction equals fraction numerator a x cubed over denominator x open parentheses 1 minus x squared close parentheses end fraction
w h i c h space i s space o f space t h e space f o r m space fraction numerator d y over denominator d x end fraction plus P y equals Q
t h e space i n e t g a r t i n g space f a c t o r space i s space e to the power of integral P space d x end exponent
h e r e comma space P equals fraction numerator 2 x squared minus 1 over denominator x open parentheses 1 minus x squared close parentheses end fraction

    If integrating factor of x open parentheses 1 minus x squared close parentheses d y plus open parentheses 2 x squared y minus y minus a x cubed close parentheses d x is e to the power of JPdx then P is

    Maths-General
    integral x open parentheses 1 minus x squared close parentheses d y plus open parentheses 2 x squared y minus y minus a x cubed close parentheses d x equals 0
rightwards double arrow x open parentheses 1 minus x squared close parentheses fraction numerator d y over denominator d x end fraction plus 2 x squared y minus y minus a x cubed equals 0
rightwards double arrow x open parentheses 1 minus x squared close parentheses fraction numerator d y over denominator d x end fraction plus y open parentheses 2 x squared minus 1 close parentheses equals a x cubed
rightwards double arrow fraction numerator d y over denominator d x end fraction plus fraction numerator y open parentheses 2 x squared minus 1 close parentheses over denominator x open parentheses 1 minus x squared close parentheses end fraction equals fraction numerator a x cubed over denominator x open parentheses 1 minus x squared close parentheses end fraction
w h i c h space i s space o f space t h e space f o r m space fraction numerator d y over denominator d x end fraction plus P y equals Q
t h e space i n e t g a r t i n g space f a c t o r space i s space e to the power of integral P space d x end exponent
h e r e comma space P equals fraction numerator 2 x squared minus 1 over denominator x open parentheses 1 minus x squared close parentheses end fraction
    General
    physics-

    Cathode rays are made to pass between the poles of a magnet as shown in figure The effect of magnetic field is

    Cathode rays are made to pass between the poles of a magnet as shown in figure The effect of magnetic field is

    physics-General
    parallel
    General
    physics-

    A neutron, a proton, an electron and an alpha particle enter a region of constant magnetic field with equal velocities The magnetic field is along the inward normal to the plane of the paper The tracks of the particles are labled in the figure The electron follows ____ track and alpha particle follows track ______

    A neutron, a proton, an electron and an alpha particle enter a region of constant magnetic field with equal velocities The magnetic field is along the inward normal to the plane of the paper The tracks of the particles are labled in the figure The electron follows ____ track and alpha particle follows track ______

    physics-General
    General
    physics-

    A graph regarding photoeletric effect is shown between the maximum kinetic energy of electrons and the frequency of the incident light On the basis of data as shown in the graph, calculate the work function

    A graph regarding photoeletric effect is shown between the maximum kinetic energy of electrons and the frequency of the incident light On the basis of data as shown in the graph, calculate the work function

    physics-General
    General
    physics-

    The graph between the stopiing potential open parentheses V subscript 0 end subscript close parenthesesand left parenthesis 1 divided by lambda right parenthesis is shown in figure, ϕ subscript 1 end subscript comma ϕ subscript 2 end subscriptand ϕ subscript 3 end subscript are work functions Which of the following is

    The graph between the stopiing potential open parentheses V subscript 0 end subscript close parenthesesand left parenthesis 1 divided by lambda right parenthesis is shown in figure, ϕ subscript 1 end subscript comma ϕ subscript 2 end subscriptand ϕ subscript 3 end subscript are work functions Which of the following is

    physics-General
    parallel
    General
    Maths-

    The equation of circle which touches the line 5x + 12 y =1 and which has its centre at (3, 4) is:

    The equation of circle which touches the line 5x + 12 y =1 and which has its centre at (3, 4) is:

    Maths-General
    General
    physics-

    1.
    2.
    3.
    4.
    Identify the wrong description of the above figures

    1.
    2.
    3.
    4.
    Identify the wrong description of the above figures

    physics-General
    General
    physics-

    Match the List I with the List II from the combinations shown

    Match the List I with the List II from the combinations shown

    physics-General
    parallel
    General
    physics-

    The resolving limit of healthy eye is about

    Resolving limit of eye is one minute (1').

    The resolving limit of healthy eye is about

    physics-General
    Resolving limit of eye is one minute (1').
    General
    physics-

    A person is suffering from myopic defect. He is able to see clear objects placed at 15 cm. What type and of what focal length of lens he should use to see clearly the object placed 60 cm away

    For viewing far objects, concave lenses are used and for concave lens
    u = wants to see equals negative 60 c m; v = can seeequals negative 15 c m
    so from fraction numerator 1 over denominator f end fraction equals fraction numerator 1 over denominator v end fraction minus fraction numerator 1 over denominator u end fraction rightwards double arrow f equals negative 20 c m.

    A person is suffering from myopic defect. He is able to see clear objects placed at 15 cm. What type and of what focal length of lens he should use to see clearly the object placed 60 cm away

    physics-General
    For viewing far objects, concave lenses are used and for concave lens
    u = wants to see equals negative 60 c m; v = can seeequals negative 15 c m
    so from fraction numerator 1 over denominator f end fraction equals fraction numerator 1 over denominator v end fraction minus fraction numerator 1 over denominator u end fraction rightwards double arrow f equals negative 20 c m.
    General
    physics-

    A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true

    In minimum deviation position refracted ray inside the prism is parallel to the base of the prism

    A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true

    physics-General
    In minimum deviation position refracted ray inside the prism is parallel to the base of the prism
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.