Let us use C major scale notes for finding the swaras in each mode of the major scale.

First mode – Ionian – the major scale

C major scale : C D E F G A B C
Swaras and notes starting from C note:

C
C#
D
D#
E
F
F#
G
G#
A
A#
B
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3

Swaras for each note in the major scale:

C
D
E
F
G
A
B
Sa
Ri2
Ga3
Ma1
Pa
Dha2
Ni3

The major scale notes correspond to the swaras of Raga Shankarabharanam.

Second mode – Dorian

The second mode of the C major scale starts from the second note (D) of the C major scale. The dorian mode of the C major scale uses the exact same notes as the major scale, though from a different starting point.

D dorian scale : D E F G A B C D

Swaras and notes starting from D

D
D#
E
F
F#
G
G#
A
A#
B
C
C#
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3
 

Swaras for each note of the Dorian scale starting from D:

D
E
F
G
A
B
C
Sa
Ri2
Ga2
Ma1
Pa
Dha2
Ni2

The notes of the dorian scale, which is the 2nd mode of the major scale,  correspond to the swaras of Raga Kharaharapriya.

Third mode – Phrygian

Phrygian mode of the C major scale starts from the note E. It has the same notes as the C major scale, but starts from E instead of C.
E phrygian scale : E F G A B C D E
Swaras and notes starting from E

E
F
F#
G
G#
A
A#
B
C
C#
D
D#
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3

Swaras for each note of the Phrygian scale starting from E:

E
F
G
A
B
C
D
Sa
Ri1
Ga2
Ma1
Pa
Dha1
Ni2

The swaras of the phrygian mode correspond to that of Raga Hanumatodi.

Fourth mode – Lydian

Lydian mode of the C major scale starts from the note F. It has the same notes as the C major scale, but starts from F, the 4th note of the C major scale.
F lydian scale : F G A B C D E F
Swaras and notes starting from F

F
F#
G
G#
A
A#
B
C
C#
D
D#
E
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3

Swaras for each note of the Lydian scale starting from F:

F
G
A
B
C
D
E
Sa
Ri2
Ga3
Ma2
Pa
Dha2
Ni3

Swaras corresponding to the notes of the Lydian scale are that of the Raga Kalyani.

Fifth mode – Mixolydian

Mixolydian mode of the C major scale starts from the note G. It has the same notes as the C major scale, but starts from G, the 5th note of the C major scale.
G mixolydian scale : G A B C D E F G
Swaras and notes starting from G

G
G#
A
A#
B
C
C#
D
D#
E
F
F#
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3

Swaras for each note of the Mixolydian scale starting from G:

G
A
B
C
D
E
F
Sa
Ri2
Ga3
Ma1
Pa
Dha2
Ni2

Swaras corresponding to the notes of the Mixolydian scale are that of the Raga Harikamboji.

Sixth mode – Aeolian (natural minor scale)

Aeolian mode, the 6th mode of the C major scale starts from the 6th note A of the C major scale. It has the same notes as the C major scale, but starts from note A instead of note C.
A aeolian scale : A B C D E F G A
Swaras and notes starting from A

A
A#
B
C
C#
D
D#
E
F
F#
G
G#
Sa
Ri1
Ri2/ Ga1
Ri3/ Ga2
Ga3
Ma1
Ma2
Pa
Dha1
Dha2/ Ni1
Dha3/ Ni2
Ni3

Swaras for each note of the Aeolian scale starting from A:

A
B
C
D
E
F
G
Sa
Ri2
Ga2
Ma1
Pa
Dha1
Ni2

Swaras corresponding to the notes of the Mixolydian scale are that of the Raga Natabhairavi.

Summary: Ragas corresponding to each mode of the major scale:

1.    Raga shankara bharanam – ionian (major scale)
2.    Raga kharaharapriya – dorian
3.    Raga hanumatodi – phrygian
4.    Raga kalyani – lydian
5.    Raga harikamboji – mixolydian
6.    Raga natabhairavi – aeolian
7.    (locrian scale without pa – not a melakarta raga)

More ragas and chords