Maths-
General
Easy

Question

Let f : [-10, 10] →R, where f(x) = sin x + open square brackets fraction numerator x to the power of 2 end exponent over denominator a end fraction close square brackets be an odd function. Then set of values of parameter a is/are

  1. (-10, 10) – {0}    
  2. (0, 10)    
  3. [100, ¥)    
  4. (100, ¥)    

The correct answer is: (100, ¥)

Book A Free Demo

+91

Grade*

Related Questions to study

General
physics-

Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than

Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than

physics-General
General
maths-

If the function not stretchy integral subscript 0 end subscript superscript x end superscript blankf(x) dt → 5 as |x| → I, then the value of ‘a’ so that the equation 2x + not stretchy integral subscript 0 end subscript superscript x end superscript blankf(t) dt = a has at least two roots of opposite signs in (-1, 1) is

If the function not stretchy integral subscript 0 end subscript superscript x end superscript blankf(x) dt → 5 as |x| → I, then the value of ‘a’ so that the equation 2x + not stretchy integral subscript 0 end subscript superscript x end superscript blankf(t) dt = a has at least two roots of opposite signs in (-1, 1) is

maths-General
General
Maths-

In straight triangle A B C comma fraction numerator a left parenthesis cos invisible function application B plus cos invisible function application C right parenthesis over denominator 2 left parenthesis b plus c right parenthesis end fraction equals

In straight triangle A B C comma fraction numerator a left parenthesis cos invisible function application B plus cos invisible function application C right parenthesis over denominator 2 left parenthesis b plus c right parenthesis end fraction equals

Maths-General
General
chemistry-

On Bohr’s stationary orbits -

On Bohr’s stationary orbits -

chemistry-General
General
chemistry-

For a valid Bohr orbit, its cicumfrence should be -

For a valid Bohr orbit, its cicumfrence should be -

chemistry-General
General
chemistry-

Arrange the following particles in increasing order of values of e/m ratio: Electron (e), proton (p), neutron (n) and α-particle (α) -

Arrange the following particles in increasing order of values of e/m ratio: Electron (e), proton (p), neutron (n) and α-particle (α) -

chemistry-General
General
Maths-

In straight triangle A B C comma open parentheses fraction numerator b minus c over denominator a end fraction close parentheses sin invisible function application open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses equals

In straight triangle A B C comma open parentheses fraction numerator b minus c over denominator a end fraction close parentheses sin invisible function application open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses equals

Maths-General
General
physics-

An antenna behaves as resonant circuit only when its length is

An antenna behaves as resonant circuit only when its length is

physics-General
General
Maths-

If A equals 60 to the power of ring operator text  then the value of  end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals

If A equals 60 to the power of ring operator text  then the value of  end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals
open parentheses fraction numerator c plus a plus b over denominator c end fraction close parentheses open parentheses fraction numerator b plus c minus a over denominator b end fraction close parentheses
equals fraction numerator b c plus c squared minus a c plus a b plus a c minus a squared plus b squared plus b c minus a b over denominator c b end fraction
equals fraction numerator 2 b c plus c squared plus b squared minus a squared over denominator c b end fraction
equals fraction numerator 2 b c plus 2 b c space cos space A over denominator b c end fraction space space left parenthesis b y space cos i n e space f o r m u l a comma space a squared equals b squared plus c squared minus 2 b c space cos A right parenthesis
equals 2 plus 2 space cos A
p u t t i n g space A equals 60 degree
equals 2 plus 2 space cos space 60 degree
equals 2 plus 2 cross times 1 half
equals 2 plus 1
equals 3

If A equals 60 to the power of ring operator text  then the value of  end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals

Maths-General
If A equals 60 to the power of ring operator text  then the value of  end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals
open parentheses fraction numerator c plus a plus b over denominator c end fraction close parentheses open parentheses fraction numerator b plus c minus a over denominator b end fraction close parentheses
equals fraction numerator b c plus c squared minus a c plus a b plus a c minus a squared plus b squared plus b c minus a b over denominator c b end fraction
equals fraction numerator 2 b c plus c squared plus b squared minus a squared over denominator c b end fraction
equals fraction numerator 2 b c plus 2 b c space cos space A over denominator b c end fraction space space left parenthesis b y space cos i n e space f o r m u l a comma space a squared equals b squared plus c squared minus 2 b c space cos A right parenthesis
equals 2 plus 2 space cos A
p u t t i n g space A equals 60 degree
equals 2 plus 2 space cos space 60 degree
equals 2 plus 2 cross times 1 half
equals 2 plus 1
equals 3
General
physics-

In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (mu equals 1) will be equal to

In the case of refraction if CD is the refracted wave front and v1 and v2 are the speed of light in the two media, then in the time the wavelets from B reaches C, the wavelet from A will reach D, such that

t equals fraction numerator B C over denominator v subscript a end subscript end fraction equals fraction numerator A D over denominator v subscript g end subscript end fraction rightwards double arrow fraction numerator B C over denominator A D end fraction equals fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction .....(i)
But in capital delta A C B comma B C equals A C sin invisible function application theta .....(ii)
while in capital delta A C D comma A D equals A C sin invisible function application phi to the power of ´ end exponent .....(iii)
From equations (i), (ii) and (iii) fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction
Also mu proportional to fraction numerator 1 over denominator v end fraction rightwards double arrow fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator mu subscript g end subscript over denominator mu subscript a end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction rightwards double arrow mu subscript g end subscript equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction

In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (mu equals 1) will be equal to

physics-General
In the case of refraction if CD is the refracted wave front and v1 and v2 are the speed of light in the two media, then in the time the wavelets from B reaches C, the wavelet from A will reach D, such that

t equals fraction numerator B C over denominator v subscript a end subscript end fraction equals fraction numerator A D over denominator v subscript g end subscript end fraction rightwards double arrow fraction numerator B C over denominator A D end fraction equals fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction .....(i)
But in capital delta A C B comma B C equals A C sin invisible function application theta .....(ii)
while in capital delta A C D comma A D equals A C sin invisible function application phi to the power of ´ end exponent .....(iii)
From equations (i), (ii) and (iii) fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction
Also mu proportional to fraction numerator 1 over denominator v end fraction rightwards double arrow fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator mu subscript g end subscript over denominator mu subscript a end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction rightwards double arrow mu subscript g end subscript equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction
General
chemistry-

Whicstatemeninocorrect for n=5,m=2:

Whicstatemeninocorrect for n=5,m=2:

chemistry-General
General
chemistry-

In P-atom find out the no. of paired electrons for l=1 and m =0-

In P-atom find out the no. of paired electrons for l=1 and m =0-

chemistry-General
General
chemistry-

For H- atomthenergrequired fothremoval electrofrovariousub-shelligiveaunder:
The order of the energies would be:

For H- atomthenergrequired fothremoval electrofrovariousub-shelligiveaunder:
The order of the energies would be:

chemistry-General
General
physics-

Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in

Refractive index of liquid C is same as that of glass piece. So it will not be visible in liquid C.

Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in

physics-General
Refractive index of liquid C is same as that of glass piece. So it will not be visible in liquid C.
General
maths-

Values of stretchy integral subscript negative 1 divided by 2 end subscript superscript plus 1 divided by 2 end superscript   c o s invisible function application x l o g invisible function application fraction numerator 1 plus x over denominator 1 minus x end fraction is :

Values of stretchy integral subscript negative 1 divided by 2 end subscript superscript plus 1 divided by 2 end superscript   c o s invisible function application x l o g invisible function application fraction numerator 1 plus x over denominator 1 minus x end fraction is :

maths-General