True or False:
In a steamer there are stalls for 12 animals and there are horses, cows and calves ( not less than 12 each) ready to be shipped. They can be loaded in `3^(12)` ways.

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

True or False Each kidney of human measures 10-12 cm in the length and 5-7 cm in width and 2-3 cm in thickness and average weight 120-170 g.

12 boys and 2 girls are to be seated in a row such that there are atleast 3 boys between the 2 girls. The number of ways this can be done is lamdaxx12! . The value of lamda is

These questions consist of two statement each, printed as Assertion and Reason. While answering these questions, you are required to choose any one of the following four responses. A. If both Assertion and Reason are true and Reason is a correct explanation of the Assertion. B. If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion. C. If Assertion is true but Reason is false. D. If both Assertion and Reason are false. Assertion: A duck billed platypus and spiny ant-eater, both are egg-laying animal yet they are grouped under mammlas. Reason: Both of them have seven cervical vertebrae and 12 pairs of cranial nerves.

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope ( see Fig, 12. 11 ). Find (i) the area of that part of the field in which the horse can graze,(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m.(Use pi=3.14 )

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

Number of ways in which 12 different things can be distributed in 3 groups, is

True/false The largest possible right circular cone is cut out of a cube of edge r cm. The volume of the cone is 1/12pir^3 .

Write whether the following statement is True or False ? Justify your answers : The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12 .