Mathematics — 2006 (Set II — Compartment Delhi)
SECTION - A
Q. 1. In a box containing 50 bulbs 5 are defective. What is the probability that a sample of 5 bulbs will have at most 2 defective bulbs?
Q. 14. The two equal sides of an isosceles tri angle with fixed base b cm are decreasing at the rate of 3 cm/sec. How fast is the area decreasing when the two equal sides are equal to the base?
Q. 17. Using matrices, solve the following system of linear equations:
SECTION - B
Q. 19. Using vectors, prove that the perpendicular bisectors of the sides of a triangle are con current.
Q. 21. Driving a train at the speed of 72 km/ .hr a driver noted that he has to stop the train 10 m before the signal which was just 110 m away. Find the retardation and the time taken to stop.
SECTION - C
Q. 20. 2% of the bolts manufactured by a factory are found to be defective. Find the probability that in a packet of 200 bolts not more than 3 bots will come out to be defective.
Q. 22. A bill of exchange drawn on January 4, 2005 at S months was discounted on March 26, 2005 at 3% per annum. If the banker’s discount be Rs. 603.60, find the face value of the bill.
Q. 25. A man borrows Rs. 40,000 at 16% per annum and promises to pay off the loan in 20 annual instalments, beginning at the end of first year. Calculate what annual instalment will clear off the debt. [Use (1.16) -20 = 0.01529]