The correct option is (b).
Explanation
Kathak originated from the storytelling tradition (Kathakars) in North Indian temples and evolved significantly under Mughal patronage and the Bhakti movement. By the nineteenth century, it had developed into a classical dance form with distinct technical and geographical characteristics.
Statement 1 is Incorrect:
By the third quarter of the nineteenth century, Kathak was firmly entrenched as a dance form not only in the courts of Rajasthan (Jaipur) and Lucknow but also in the adjoining areas of present-day Punjab, Haryana, Jammu and Kashmir, Bihar, and Madhya Pradesh. The use of the word "only" makes the statement factually wrong.
Statement 2 is Correct:
The evolution of Kathak, particularly under the patronage of Wajid Ali Shah (the last Nawab of Awadh), placed significant emphasis on intricate and rapid footwork, elaborate costumes, and the dramatic enactment of stories.
Statement 3 is Incorrect:
Kathak did not focus solely on abstract movement. A core element of the dance is the enactment of stories (Abhinaya), often drawing from the legends of Radha-Krishna (Ras Lila) and other mythological narratives, combined with rhythmic gestures.
Key Takeaway:
Kathak is a major North Indian classical dance form defined by rapid footwork, storytelling, and elaborate costumes. By the late 19th century, its practice had spread across North and Central India, beyond just the Jaipur and Lucknow gharanas.