All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The competitions on T.V or elsewhere are permissible if the purpose for arranging them is to urge people to achieve good knowledge or to engage in good activities. If they are held for this purpose, then participating in such programs and receiving their prizes is also permissible on two conditions:
One, the prizes should be offered by a volunteer donor.
Second, the donor should not make it as a commercial act to gain material benefits.
Whenever a sponsor of these competitions desires any material profit through them, all the programs turn to be a pure act of gambling.
As long as the opportunity of answering is restricted to those who make calls using a specific phone line, as mentioned in your question, it is apparent that the one who owns the phone line and the one who sponsors the show are both involved in gambling, along with the one who makes the call. This is evident since the answering call is restricted to a given phone number, which is expensive, so if the purpose of the show was only to serve people or to bring benefits to them, then the charge of the calls would be normal.
Muslim scholars define gambling as a deal in which one party gains profits while the other party loses. In this case, the one who makes the call either gets a prize, gaining a large amount of money against something which is not equal to the profit at all, or loses the charge of the phone call which is unusually high.
Allah mentioned gambling along with drinking wine, seeking fortune through arrows, and sacrificing to stones to emphasize its wickedness.
Allah Says (what means): {O you who have believed, indeed, intoxicants, gambling, [sacrificing on] stone alters [to other than Allah], and divining arrows are but defilement from the work of Satan, so avoid it that you may be successful.} [Quran 5:90]
Finally, it is not permissible for a Muslim to pay something for participating in a risky competition where he might gain something or lose something; in this case, he commits a sin whether he wins or loses.
We advise our Muslim brothers who present these shows to fear Allah and abstain from advertising such forbidden shows. They have to find legal ways to develop their sources of income.
Allah knows best.