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Which of the following statements are correct? 1. The pair (AB) is controllable implies that the pair (ATBT) is observable. 2. The pair (AB) is controllable implies that the pair (ATBT) is unobservable. 3. The pair (AC) is observable implies that the pair (ATCT) is controllable. 4. The pair (AC) is observable implies that the pair (ATCT) is uncontrollable. where: A, B and C are having their standard meanings
Abhishek ordered 6 pair of red shoes and some pair of books. The price of a pair of red shoes is double than that of a pair of book. While preparing the bill the shopkeeper interchanged the number of pair of shoes and books by mistake which increased the bill by 40%. What was the ratio of the number of pair of red shoes and the number of pair of books in the original order?
In a six-digit number, the digit of thousands place is 4. The digit at ten's place is double that of digit at thousand's place and digit at hundreds places is half of the digit at thousand’s place. The digit at unit's place is half of the digit at hundred's place. Digit at Ten thousand's place is sum of the digits at thousands and hundreds place and digit at lakh's place is half the digit at ten thousands place. What will be the number?
A leading shoe manufacturer produces a pair of Lebron James signature shoes at a labor cost of P 900.00 a pair and a material cost of P 800.00 a pair. The fixed charges on the business are P 5,000,000 a month and the variable costs are P 400.00 a pair. Royalty to Lebron James is P 1,000 per pair of shoes sold. If the shoes sell at P 5,000 a pair, how many pairs must be produced each month for the manufacturer to break-even?
In a five digit number, the digit at ten’s place is 8, digit at units place is one-fourth of the digit at ten’s place, the digit at thousands place is 0, digit at hundreds place is twice that of units place and the digit at ten thousand place is thrice the digit at unit’s place. What is the number?
Suppose you can travel from a place A to a place B by 3 buses, from place Bto place C by 4 buses, from place C to place D by 2 buses and from place D to place E by 3buses. In how many ways can you travel ?from A to E?
What is the Fibonacci sequence, presented in 1202 in this problem: "A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?"
A good costs Rs. 12,000. A customer can choose either of the pairs of successive discounts. Pair A consists of successive discounts of 20% and 30% and pair B consists of 40% and 10%. Customer X chose pair A and customer Y chose pair B. What is the difference in their payment for the good?.
In a five-digit number, the digit at the hundreds place is double of the digit at the unit place and the digit at ten thousand place is double of the digit at the hundreds place. The digit at tens place is the smallest odd prime number and the digit at thousands place is three times the unit digit. If the digit at the unit place is the even prime number, then the number is
Gulshan went to market and bought a pair of gloves for Rs 600 from shop A. When he was returning he saw the same pair of gloves in Shop B being marked at Rs 640 and when he asked the shopkeeper they were ready to give him a discount of 25% on the marked price. Gulshan came up with an idea. He sold the pair of gloves bought from shop A at a loss of 10% and then returned buying the pair of gloves from shop B. How much he saves in this whole transaction?