CBSE Guess > Papers > Question Papers > Class XII > 2004 > Maths > Compartment Outside Delhi SetI
MATHS (Set I—Compartment Outside Delhi)
Or
Using differentials, find the approximate value of correct upto three decimal places.
Q. 13. Evaluate:
Q. 14. Evaluate:
Q. 15. Evaluate:
Q. 16. Using matrices, solve the following system of equations:
Q. 17. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is of the volume of the sphere.
Or
Prove that the curves cut at right angles if 8k^{2}=1.
Q. 18. Using integration, find the area of the region in the first quadrant enclosed by the xaxis, the line and the circle
SECTION  B
Q. 19. For what value of are the vectors coplanar?
Or
For what value of are the four points A (3, 2, 1) B (4, , 5 ), C (4, 2,2) and D (6, 5,1) coplanar?
Q. 20. Using vectors prove that an angle in a semicircle is a right angle.
Q. 21. Show that the sphere touches the plane
Q. 22. Find the equation of the line through the point (1, 2, 3) which is perpendicular to the lines .
Q. 23. Prove that the equation of the plane making intercepts a, b and c on the coordinate axes, is of the form
Q. 24. A body of weight 5 kg is suspended by two strings 7 cm and 24 cm long. Their other ends being fastened to the end points of a rod of length 25 cm. If the rod be so held that the body hangs immediately below its midpoint, find the tension in the strings. Q. 25. Two forces, when acting at right angles, have their resultant of magnitude and when they act at , the magnitude of the resultant is Find the magnitude of the two forces.
Q. 26. A particle is projected upwards with a velocity of 4 m/sec and after t seconds, another particle is projected upwards from the same point with the same velocity. Prove that the particles will meet at a height of after a time period of seconds start.
Or
A particle is projected so as to graze the tops of two walls, each of height 10 m at distances of 10 m and 60 m respectively from the point of projection. Find the angles of projection.
SECTION  C
Q. 19. Find the face value of a ball discounted at 6% per annum 146 days before the legally due date, if the bankers gain is Rs. 18.
Or
The difference between Bankers discount and True Discount on a bill legally due 3 months hence at 5 %per annum is Rs. 50. Find the face value, Bankers Discount and True Discount.
Q. 20. A bill of exchange drawn on May 1, 2003 for Rs. 73,200 for 6 months was discounted by a bank at 6% per annum for Rs. 72,443,20. On what day was the bill discounted?
Q. 21. A box contains 2 gold and 3 silver coins. Another box contains 3 gold and 3 silver coins. A box is chosen sat random and a coin is drawn from it. If the selected coin is a gold coin. Find the probability that it was drawn from the second box.
Q. 22. 10% of the tools produced by a machine are defective. Find the probability distribution of the number of defective tools in a sample of 3 drawn at random.
Q. 23. Two partners A and B invest Rs. 20.000 and Rs. 30.000 respectively in a business. They decided to distribute 50% of the total profit equally and her remaining in the ratio of their investments. If B receives Rs. 3,000 more than A, find the total profit and profit received by each.
Q. 24. What equivalent payments made at the beginning of each month for 8 years will pay for a house priced at Rs. 5.00.000, If money is worth 12% per annum, compounded monthly? [Use (1.01)^{95} =0.3904] Q. 25. If the Cost function C (x) is given by , where x is the output
Prove that
Also find the marginal Cost when 50 units are produces.
Q. 26. A housewife wishes to mix two kinds of foods X an Y in such a way that the mixture contains at least 10 units of Vitamin A, 12 units of Vitamin B and 8 units of Vitamin C. The vitamin contents of one kg of each food is given below.

Vitamin A 
Vitamin B 
Vitamin C 
Food 
1 
2 
3 
Food 
1 
2 
1 
One kg of Food X and Food Y respectively cost Rs.6 and Rs.10. Find the least cost of mixture graphically, making it a linear programming problem.
Or
A man has Rs. 1,500 for purchase of rice and wheat. A bag of rice and a bag of wheat cost Rs. 180 and Rs. 120 respectively. He has a storage capacity of 10 bags only. He earns a profit of Rs. 11 and Rs. 9 respectively per bag of rice and wheat. Formulate it as a linear programming problem and solve it graphically for maximum profit.
CBSE 2004 Question Papers Class XII
