Section 253 (4), Rule 47(2) ,Form No 36A deals with filling cross objection . Cross objection has to be filed within 30 days on which receipt of notice of appeal communicated to the assessee or to the Principal Commissioner or Commissioner filed by the opposite party . There is no fees prescribed for filing of cross objection . If there is delay in filing of the Cross objection the Tribunal has the power to condone the delay . The concept of cross objection is borrowed from the appellate provision in Order XLI Rule 22 of the Coode of Civil Procedure , 1908 .

In Atlas Copco (India) Limited v. DCIT (ITA No.649/PUN/2013 &
1726/PUN/2014, AY . 2008-09 & 2009-10 dt. 29-8 2019 ( 2019) 202 TTJ 395 / 184 DTR 73 (Pune)(Trib.) the assessee had through Cross objections raised a legal ground
challenging the validity of assessment order passed u/s.143(3) r.w.s.
144C of the Income-tax Act, 1961. The C.Os were delayed by 1965 days.
The delay was condoned, the C. O. was adjudicated on merits.
In Dy. CIT v. Turquoise Investment & Finance Ltd. (2008) 299 ITR
143 (MP) (HC) it was held that the Appellate Tribunal has power to
entertain any question of law as additional grounds of Appeal, though
the same may not have been raised before any of the authorities below.

There is no difference between an appeal and a cross-objection.
In a cross-objection, a legal issue which has not been raised before
the lower authorities can be raised. The C.O. need not be confined to
the points taken by the opposite party in the main appeal (ACIT v. DHL
Operations (2007 ) 108 TTJ 152 (SB)(Mum) ( Trib ) followed). ITO v. Jasjit Singh [2014] 52 taxmann.com 477 (Delhi ( Trib)

In ACIT v. C. Aswathanarayana (2021) 85 ITR 74 (SN)(Bang) (Trib ):
The Tribunal held that the ground raised in the cross-objections
being a legal ground could be raised by the assessee before the
Tribunal for the first time.

In CIT v. Purrbanchal Paribahan Gosthi ( 1998) 234 ITR 663 ( Gau) (HC) the Court held that section 253 (4) clearly envisages the filing of cross -objections both by assessee as well as by the AO against the order in appeal . Upon filing of such cross objection it has been made obligatory upon the Tribunal too decide such memorandum of cross -objections as if it was an appeal ..

In Ram ji Dass & Co v .CIT ( 2010) 323 ITR 505 ( P& H) (HC) the Tribunal dismissed the revenue’s appeal and not adjudicated the assesses cross objection . The Court held that the cross objection had to be decided by the Tribunal on merits .( Tata Sponge Iron Ltd v. CIT ( 2008) 307 ITR 441 ( Orissa )( HC)

In CIT v Silverline ( 2016) 383 ITR 455 ( Delhi) (HC) held that the respondent can raise an additional ground in cross =objection , there is no distinction between an appeal and cross objection .

In B..R. Ramasi v .CIT ( 1972 ) 83 ITR 223 ( Bom) ( HC) the court held that the powers of the Tribunal are similar to the powers of an Appellate Court under the Civil Procedure Code ,1908

CIT v. New India Assurance Co Ltd ( 1983) 141 ITR 367 ( Bom) (HC) ( 373) , ITO v. Fagoomal Laxxmi Chand ( 1979) 118 ITR 766 ( Mad) (HC) (769) ? Check 149 ITR 457/ 141 ITR 367/ 118 ITR 766

In ACIT v. Ajay Kalia ( 2016) 157 ITD 187 ( Delhi) (Trib) held that even if the appeal of the revenue is dismissed because of low tax effect , the cross objection of the assessee survives it has to be decided on merit.