RE: using LCA for CAP vs strike and MiG-29K vs LCA, I thought I'd add my $0.02. Any mistakes in understanding are entirely mine.
Carrier air wing sizing is a complicated problem. The primary determinant is the carrier doctrine (in context of the threats and capabilities of the possible foes): everything else follows from that.
The US aircraft carriers are very capable, but large and expensive. They are tailored to cater to the US carrier doctrine, which is expeditionary warfare. The carrier battle groups expect to be able to strike any target on the planet and exercise air dominance over the battlespace. They are also expected to exert sea denial and be able to beat down any naval foe, including in large fleet-on-fleet action.
In contrast the Soviet carrier doctrine was very different, and based on denying access to the US carriers. The primary weapon in this doctrine was the land-based Backfire with its cruise missiles. The Soviet carriers only existed to provide end-game air-support to the Backfires against opposing fleet air defense. As such, they didn't need to be as large or complex as the US carriers.
The new QE and PoW are "strike carriers", whose primary mission is surface strike. Probably similar to our carriers, but consider what it takes to launch a strike mission against a near-peer opponent.
First, one will need several aircraft to be assembled into a strike package. This will include at a minimum the actual strikers, SEAD/DEAD support, air-support escorts, and EW escort. Some platforms can be multi-tasked, but there are limits. E.g. the strikers can't be completely self-escorting, or else they will have to drop their strike munitions at the first sign of trouble and kill the mission.
These aircraft have to be launched and assembled into a package in the air. Without catapults (and sometimes, even with), one would need to launch with limited fuel and top-up from a tanker. In our context, this would mean that additional airplanes will have to be launched first to serve as the buddy tankers. Note that flight paths to the target are often convoluted to (a) avoid enemy air defence, (b) attack from an unexpected axis and (c) not give away the position of the carrier. All this, plus the vagaries of combat mean that actual combat range will be far below brochure numbers. The returning package may have to be met on their way back and refueled for recovery. Finally, any time an aircraft is launched or recovered, the "Angel" SAR helicopter needs to be launched first. All of this might be happening in less than ideal weather and sea-states, so everything might take longer than you expect.
The kinds of targets and the military capabilities of the opponent will determine how large and complicated the strike package needs to be. The launch rate is pretty much fixed - even the US carriers cannot average more than one launch every 2--3 minutes, and they have multiple catapults and launch positions and dedicated organic tanking. Aircraft on a carrier can't be expected to have the same serviceability as land-based aircraft - they don't have access to the same repair depots, spares, etc. So you have to work backwards to determine how big the carrier air group needs to be to fulfill the mission.
As for CAP, the situation is not as easy as it appears either. The carrier's biggest strength is that it is mobile and cannot be located easily. If one is so silly as to set up CAP orbits centered on the carrier, it would be trivial for the opponent to locate the carrier. CAP orbits have to be offset from the carrier to not give its position away. Neither can the CAP simply be placed at a random distance between the carrier and the shore, because that also discloses the threat axis. Additionally, the CAP needs to be able to deal with off-axis attacks as well, which often means multiple CAP orbits when in a high-threat situation. All these factors go into defining the required strength of the air wing.
Air defence missions for carriers are increasingly being taken away from aircraft. Long range stand-off missiles require that the launch platforms themselves are engaged as part of the layered defence. This used to mean requiring an aircraft like the F-14 which could scream away at Mach 2 and engage a platform with AIM-54 before they launched their missiles. However, this is no longer practical. The anti-ship missiles simply have way too much stand-off range for the launch platforms to be practically engaged by carrier based defences. This mission is now better handled by AAW destroyers with their powerful radars and batteries of SAMs, which can persistently maintain station hundreds of miles away from the carrier itself. (The commanding officer for a CBG's air defence is the captain of one of the escort destroyers, and not on the carrier at all.)
So this all comes back to the question: what is the Indian Navy's carrier doctrine? I had the opportunity to meet a retired IN Vice Admiral (who had commanded Viraat), and asked him this question; he was a little shy and gave nothing away. However, he did mention that the navy uses the carrier in very mission-specific task forces whose composition is determined by the mission in question. So they employ carriers very differently than the CBG of the USN. That being said, he did acknowledge that the Indian carriers are undersized, but this is because of funding considerations and lack of experience in building larger ships. Given the navy's track record, they are probably working on a long-term plan for larger carriers, more capable aircraft and larger air arms, and the current situation with the LCA is the first step of a long process. So the stressing about how many LCAs we can pack into the hangar is probably not super relevant.
Hope this wasn't too off-topic.
), Defence Minister Manohar Parrikar, who is visiting the HAL headquarters tomorrow, will hand over the aircraft to the IAF chief Air Marshal Arup Raha. 
