Quiz-1

Explanation:
If heater D is used on the third day, heater B has to be used on the fourth day and A has to be used on the second day. But if A is used on second day, then either B or C has to be used on the first day. But if heater B is used on the first day, then according to the question, the requirement of having different heaters on the first day and fourth days would not be fulfilled. Hence the heater that would be used on the first day is C.

Explanation:
Only ways in which a person can use all the four heaters in a four day period is by the order ADBC. Hence, in total there are four possible permutations of the same.

Explanation:
Considering statement (a)., exactly two tours must depart after. Tour P but before Tour R, and so the departure sequence may be either PSTQR or PSQRT. Although three tours must arrive between Tour P and Tour R, three possible arrival sequence remain, depending on where Tour T fits into the sequence remain, depending on where Tour T fits into the sequence. Considering statement (b). Tour Q must depart immediately after Tour R, with tour T departing last and immediately between Tour Q and Tour S, resulting in only one possible arrival sequence- PSRQT. Similarly, Tour T must arrive third, and Tour R must arrive fifth, resulting in one possible arrival sequence - PQTSR.

Explanation:
If Tour Q departs third, only one possible departure sequence results, and if Tour Q arrives second, two possible arrival sequence result:
Departure Sequence: PSQRT
Arrival Sequence 1: PQTSR
Arrival Sequence 2: PQSTR

Explanation:
Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.

Explanation:
Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.
At least one pear.

Explanation:
Varun may receive no more than five pieces and Tarun may receive no fewer than four pieces. As a result, if Varun receives more pieces than Tarun, then Varun must receive five pieces, and Tarun must receive four pieces. Thus, statement (a) must be true. Since Varun will receive five pieces, none of the other three friends will receive any apple, accordingly, each of the other three friends must receive at least one orange and at least one pear. Thus, statement (b) and (c) must be true.

Explanation:
Ujjwal may receive no more than five pieces, and Tarun may receive no fewer than four pieces. As a result, if Ujjwal receives more pieces than Tarun, then Ujjwal must receive five pieces, and Tarun must receive four pieces. Thus option (a) and (b) must be false Varun will receive three pieces, two apples remaining for the other three friends. Option (c) must be false because each friend must receive must receive at least two different types of fruit.

Explanation:
If heater D is used on the third day, heater B has to be used on the fourth day and A has to be used on the second day. But if A is used on second day, then either B or C has to be used on the first day. But if heater B is used on the first day, then according to the question, the requirement of having different heaters on the first day and fourth days would not be fulfilled. Hence the heater that would be used on the first day is C.

Explanation:
Only ways in which a person can use all the four heaters in a four day period is by the order ADBC. Hence, in total there are four possible permutations of the same.