Physics-
General
Easy

Question

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is -

  1. 120 to the power of ring operator end exponent    
  2. 60 to the power of ring operator end exponent    
  3. 90 to the power of ring operator end exponent    
  4. 150 to the power of ring operator end exponent    

The correct answer is: 120 to the power of ring operator end exponent

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Here is a velocity - time graph of a motorbike moving in one direction. Calculate the distance covered by it in last two seconds.

Here is a velocity - time graph of a motorbike moving in one direction. Calculate the distance covered by it in last two seconds.

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Here are the graphs of velocity not stretchy rightwards arrow time of two cars A and B, Find the ratio of the acceleration. after time t.

Here are the graphs of velocity not stretchy rightwards arrow time of two cars A and B, Find the ratio of the acceleration. after time t.

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The intercept of the velocity-time graph on the velocity axis gives.

The intercept of the velocity-time graph on the velocity axis gives.

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Slope of the velocity-time graph gives …….. of a moving body

Slope of the velocity-time graph gives …….. of a moving body

physicsGeneral
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Maths-

The domain of the function f left parenthesis x right parenthesis equals square root of cosec space x minus 1 end root text  is  end text

f left parenthesis x right parenthesis equals square root of cos e c space x minus 1 end root
space space space space space space space equals square root of fraction numerator 1 over denominator sin space x end fraction minus 1 end root
space space space space space space equals square root of fraction numerator 1 minus space sin space x over denominator sin space x end fraction end root
D e m o m i n a t o r space greater than space 0
rightwards double arrow sin x space greater than space 0
rightwards double arrow 2 n straight pi less than straight x less than space left parenthesis 2 straight n plus 1 right parenthesis ππ
So comma space the space domain space of space straight f left parenthesis straight x right parenthesis space is space left parenthesis 2 nπ comma left parenthesis 2 straight n plus 1 right parenthesis straight pi right parenthesis.

The domain of the function f left parenthesis x right parenthesis equals square root of cosec space x minus 1 end root text  is  end text

Maths-General
f left parenthesis x right parenthesis equals square root of cos e c space x minus 1 end root
space space space space space space space equals square root of fraction numerator 1 over denominator sin space x end fraction minus 1 end root
space space space space space space equals square root of fraction numerator 1 minus space sin space x over denominator sin space x end fraction end root
D e m o m i n a t o r space greater than space 0
rightwards double arrow sin x space greater than space 0
rightwards double arrow 2 n straight pi less than straight x less than space left parenthesis 2 straight n plus 1 right parenthesis ππ
So comma space the space domain space of space straight f left parenthesis straight x right parenthesis space is space left parenthesis 2 nπ comma left parenthesis 2 straight n plus 1 right parenthesis straight pi right parenthesis.
General
physics

In the figure Velocity (V)not stretchy rightwards arrow position graph is given. Find the true equation.

In the figure Velocity (V)not stretchy rightwards arrow position graph is given. Find the true equation.

physicsGeneral
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physics

Ball A is thrown in upward from the top of a tower of height h. At the same time ball B starts to fall from that point. When A comes to the top of the tower, B reaches the ground. Find the  time to reach maximum height for A.

Ball A is thrown in upward from the top of a tower of height h. At the same time ball B starts to fall from that point. When A comes to the top of the tower, B reaches the ground. Find the  time to reach maximum height for A.

physicsGeneral
General
Maths-

The domain of f left parenthesis x right parenthesis equals fraction numerator 1 over denominator vertical line sin invisible function application x vertical line plus sin invisible function application x end fraction text  is  end text

f left parenthesis x right parenthesis equals fraction numerator 1 over denominator open vertical bar sin space x close vertical bar plus sin space x end fraction
D e n o m i n a t o r not equal to 0
I f space sin space x space greater than 0 comma space space f left parenthesis x right parenthesis space i s space p o s i t i v e.
S o comma space sin space x space plus s i n space x space greater than 0
space space space space space space space space space space space space 2 sin space x space space space space space space space space greater than 0
space space space space space space space space space space space space s i n space x space space space space space space space space space space greater than 0
A s space sin x space greater than space 0 space
S o comma space 2 n straight pi less than straight x less than left parenthesis 2 straight n plus 1 right parenthesis straight pi
So comma space the space d o m a i n space is space U with n element of Z below left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis.

The domain of f left parenthesis x right parenthesis equals fraction numerator 1 over denominator vertical line sin invisible function application x vertical line plus sin invisible function application x end fraction text  is  end text

Maths-General
f left parenthesis x right parenthesis equals fraction numerator 1 over denominator open vertical bar sin space x close vertical bar plus sin space x end fraction
D e n o m i n a t o r not equal to 0
I f space sin space x space greater than 0 comma space space f left parenthesis x right parenthesis space i s space p o s i t i v e.
S o comma space sin space x space plus s i n space x space greater than 0
space space space space space space space space space space space space 2 sin space x space space space space space space space space greater than 0
space space space space space space space space space space space space s i n space x space space space space space space space space space space greater than 0
A s space sin x space greater than space 0 space
S o comma space 2 n straight pi less than straight x less than left parenthesis 2 straight n plus 1 right parenthesis straight pi
So comma space the space d o m a i n space is space U with n element of Z below left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis.
General
physics

A particle is thrown in upward direction with initial velocity V0 It crosses point P at height  h at time t1 and t2 so t1 t2 ……..

A particle is thrown in upward direction with initial velocity V0 It crosses point P at height  h at time t1 and t2 so t1 t2 ……..

physicsGeneral
General
Maths-

2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals

2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals

Maths-General
General
Maths-

The domain of the function  f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text  is  end text

f left parenthesis x right parenthesis equals fraction numerator tan space 2 x over denominator 6 cos space x plus 2 space sin space 2 x space end fraction
A s space tan space i s space u n d e f i n e d space a t space o d d space i n t e g r a l space m u l t i p l e space o f straight pi over 2.
2 x space not equal to space straight pi over 2 left parenthesis 2 straight n plus 1 right parenthesis
straight x space space not equal to fraction numerator straight pi left parenthesis 2 straight n plus 1 right parenthesis over denominator 4 end fraction

Now comma space for space denominator comma space
6 cos space straight x space plus 2 space sin 2 straight x space not equal to 0
6 space cos space straight x space plus 2.2 space sin space straight x space cos space straight x space not equal to 0
2 space cos space straight x left parenthesis 3 plus 2 sin space straight x right parenthesis not equal to 0
2 space cos space straight x space not equal to 0 space space space space 0 straight r space 3 plus 2 sin space straight x space not equal to 0
For comma 2 space cos space straight x space not equal to 0 rightwards double arrow cos space straight x not equal to 0
For comma space 3 plus 2 sin space straight x not equal to 0 rightwards double arrow 2 sin space straight x not equal to negative 3 rightwards double arrow sinx space not equal to fraction numerator negative 3 over denominator 2 end fraction
minimum space value space of space sin space straight x space is space minus 1 space.
cos space not equal to 0 comma space cos space is space 0 space at space odd space integral space multiple space of space straight pi over 2.
so comma space straight x not equal to fraction numerator left parenthesis 2 straight n plus 1 right parenthesis straight pi over denominator 2 end fraction
so comma d o m a i n space o f space f left parenthesis x right parenthesis space i s space R minus open curly brackets left parenthesis 2 n plus 1 right parenthesis pi over 2 colon n element of Z close curly brackets

The domain of the function  f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text  is  end text

Maths-General
f left parenthesis x right parenthesis equals fraction numerator tan space 2 x over denominator 6 cos space x plus 2 space sin space 2 x space end fraction
A s space tan space i s space u n d e f i n e d space a t space o d d space i n t e g r a l space m u l t i p l e space o f straight pi over 2.
2 x space not equal to space straight pi over 2 left parenthesis 2 straight n plus 1 right parenthesis
straight x space space not equal to fraction numerator straight pi left parenthesis 2 straight n plus 1 right parenthesis over denominator 4 end fraction

Now comma space for space denominator comma space
6 cos space straight x space plus 2 space sin 2 straight x space not equal to 0
6 space cos space straight x space plus 2.2 space sin space straight x space cos space straight x space not equal to 0
2 space cos space straight x left parenthesis 3 plus 2 sin space straight x right parenthesis not equal to 0
2 space cos space straight x space not equal to 0 space space space space 0 straight r space 3 plus 2 sin space straight x space not equal to 0
For comma 2 space cos space straight x space not equal to 0 rightwards double arrow cos space straight x not equal to 0
For comma space 3 plus 2 sin space straight x not equal to 0 rightwards double arrow 2 sin space straight x not equal to negative 3 rightwards double arrow sinx space not equal to fraction numerator negative 3 over denominator 2 end fraction
minimum space value space of space sin space straight x space is space minus 1 space.
cos space not equal to 0 comma space cos space is space 0 space at space odd space integral space multiple space of space straight pi over 2.
so comma space straight x not equal to fraction numerator left parenthesis 2 straight n plus 1 right parenthesis straight pi over denominator 2 end fraction
so comma d o m a i n space o f space f left parenthesis x right parenthesis space i s space R minus open curly brackets left parenthesis 2 n plus 1 right parenthesis pi over 2 colon n element of Z close curly brackets
General
Maths-

Let f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket is given byf left parenthesis x right parenthesis equals 4 x cubed minus 3 x text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text  is given by  end text

f left parenthesis x right parenthesis equals 4 x cubed minus 3 x
w h e r e comma space f open square brackets 1 half comma 1 close square brackets rightwards arrow open square brackets negative 1 comma 1 close square brackets
L e t space x equals space cos space theta space a n d space y equals cos space 3 theta
f left parenthesis cos space theta right parenthesis equals 4 cos cubed theta minus 3 space cos space theta
space space space space space space space space space space space space space equals space cos space 3 space theta
a s space 3 theta space equals cos to the power of negative 1 end exponent y
space space space space space space space space space space theta equals 1 third cos to the power of negative 1 end exponent y
f to the power of negative 1 end exponent left parenthesis cos space 3 theta right parenthesis equals cos space theta
a s space y space equals space f left parenthesis x right parenthesis rightwards double arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis equals x
f to the power of negative 1 end exponent left parenthesis cos space 3 theta right parenthesis space equals space cos space theta
f to the power of negative 1 end exponent left parenthesis y right parenthesis space equals space cos space open parentheses 1 third cos to the power of negative 1 end exponent y close parentheses
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals cos open parentheses 1 third cos to the power of negative 1 end exponent x close parentheses

Let f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket is given byf left parenthesis x right parenthesis equals 4 x cubed minus 3 x text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text  is given by  end text

Maths-General
f left parenthesis x right parenthesis equals 4 x cubed minus 3 x
w h e r e comma space f open square brackets 1 half comma 1 close square brackets rightwards arrow open square brackets negative 1 comma 1 close square brackets
L e t space x equals space cos space theta space a n d space y equals cos space 3 theta
f left parenthesis cos space theta right parenthesis equals 4 cos cubed theta minus 3 space cos space theta
space space space space space space space space space space space space space equals space cos space 3 space theta
a s space 3 theta space equals cos to the power of negative 1 end exponent y
space space space space space space space space space space theta equals 1 third cos to the power of negative 1 end exponent y
f to the power of negative 1 end exponent left parenthesis cos space 3 theta right parenthesis equals cos space theta
a s space y space equals space f left parenthesis x right parenthesis rightwards double arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis equals x
f to the power of negative 1 end exponent left parenthesis cos space 3 theta right parenthesis space equals space cos space theta
f to the power of negative 1 end exponent left parenthesis y right parenthesis space equals space cos space open parentheses 1 third cos to the power of negative 1 end exponent y close parentheses
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals cos open parentheses 1 third cos to the power of negative 1 end exponent x close parentheses
General
Maths-

If f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals

f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction equals y
rightwards double arrow fraction numerator 10 to the power of x left parenthesis 10 to the power of 2 x end exponent minus 1 right parenthesis over denominator 10 to the power of x left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis end fraction equals y
rightwards double arrow fraction numerator left parenthesis 10 to the power of 2 x end exponent minus 1 right parenthesis over denominator left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis end fraction equals y
rightwards double arrow 10 to the power of 2 x end exponent minus 1 space equals y left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis
rightwards double arrow 10 to the power of 2 x end exponent minus 1 equals y.10 to the power of 2 x end exponent plus y
rightwards double arrow 10 to the power of 2 x end exponent minus y.10 to the power of 2 x end exponent equals y plus 1
rightwards double arrow 10 to the power of 2 x end exponent left parenthesis 1 minus y right parenthesis equals 1 plus y
rightwards double arrow 10 to the power of 2 x end exponent equals fraction numerator 1 plus y over denominator 1 minus y end fraction
P u t t i n g space log space o n space b o t h space t h e space s i d e s comma
rightwards double arrow log space 10 to the power of 2 x end exponent space equals log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow 2 x space log space 10 space equals log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow 2 x space equals fraction numerator log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses over denominator log space 10 end fraction
rightwards double arrow x space equals 1 half log subscript 10 open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals space 1 half log subscript 10 open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses

If f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals

Maths-General
f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction equals y
rightwards double arrow fraction numerator 10 to the power of x left parenthesis 10 to the power of 2 x end exponent minus 1 right parenthesis over denominator 10 to the power of x left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis end fraction equals y
rightwards double arrow fraction numerator left parenthesis 10 to the power of 2 x end exponent minus 1 right parenthesis over denominator left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis end fraction equals y
rightwards double arrow 10 to the power of 2 x end exponent minus 1 space equals y left parenthesis 10 to the power of 2 x end exponent plus 1 right parenthesis
rightwards double arrow 10 to the power of 2 x end exponent minus 1 equals y.10 to the power of 2 x end exponent plus y
rightwards double arrow 10 to the power of 2 x end exponent minus y.10 to the power of 2 x end exponent equals y plus 1
rightwards double arrow 10 to the power of 2 x end exponent left parenthesis 1 minus y right parenthesis equals 1 plus y
rightwards double arrow 10 to the power of 2 x end exponent equals fraction numerator 1 plus y over denominator 1 minus y end fraction
P u t t i n g space log space o n space b o t h space t h e space s i d e s comma
rightwards double arrow log space 10 to the power of 2 x end exponent space equals log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow 2 x space log space 10 space equals log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow 2 x space equals fraction numerator log space open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses over denominator log space 10 end fraction
rightwards double arrow x space equals 1 half log subscript 10 open parentheses fraction numerator 1 plus y over denominator 1 minus y end fraction close parentheses
rightwards double arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals space 1 half log subscript 10 open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses
General
Maths-

If f left parenthesis x right parenthesis equals fraction numerator e to the power of x plus e to the power of negative x end exponent over denominator 2 end fraction ,then the inverse function of f left parenthesis x right parenthesis text  is  end text

If f left parenthesis x right parenthesis equals fraction numerator e to the power of x plus e to the power of negative x end exponent over denominator 2 end fraction ,then the inverse function of f left parenthesis x right parenthesis text  is  end text

Maths-General
General
maths-

If f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1 observe the following
text  l)  end text delta f equals 2.11
text  II)  end text d f equals 2.1
text  III) Relative error in  end text x text  is  end text 1
The true statements are

If f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1 observe the following
text  l)  end text delta f equals 2.11
text  II)  end text d f equals 2.1
text  III) Relative error in  end text x text  is  end text 1
The true statements are

maths-General