Vacating the stay granted by a single-judge bench, a division bench comprising Justices Pranab Chattopadhyay and T K Das directed that the tests can be held as per schedule.
The tests are scheduled to begin from December 23.
The bench also said that though the recruitment process can be held as per schedule, jobs of those recruited would depend on the final outcome of the hearing of the main petition before the court of Justice Debasish Kar Gupta.
The hearing of the main petition is set to begin three weeks after the end of winter vacation.
The state counsel had moved an appeal against the single bench's order. It had submitted that there are 34,559 vacancies in primary schools and only around 11,000 trained candidates available for them.
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After offering jobs to successful aspirants from among the trained candidates, jobs would be offered to the successful candidates from untrained category for the posts left, the counsel submitted.
All candidates, both trained and untrained, would have to appear for the recruitment test.
Justice Debasish Kar Gupta had on December 13 stayed the recruitment process for primary teachers following petitions by several candidates.