Step 1: Understand the task.
We must find which reformer-institution matches are correct: (J) Theosophical Society with Vivekananda, (K) Ramakrishna Mission with Ram Mohan Roy, (L) Arya Samaj with Dayanand Saraswati, (M) Aligarh Movement with Sir Syed Ahmad Khan.
Step 2: Check pair J.
The Theosophical Society was founded by Blavatsky and Olcott, not Vivekananda, so J is wrong.
Step 3: Check pair K.
The Ramakrishna Mission was founded by Swami Vivekananda, while Ram Mohan Roy founded the Brahmo Samaj, so K is wrong.
Step 4: Check pair L.
Swami Dayanand Saraswati founded the Arya Samaj in 1875, so L is correct.
Step 5: Check pair M.
Sir Syed Ahmad Khan led the Aligarh Movement for modern Muslim education, so M is correct.
Step 6: Select the option.
Only L and M are right, which is option B.
\[ \boxed{\text{L and M only}} \]