CBSE Guess > Papers > Question Papers > Class XII > 2004 > Maths > Outside Delhi SetI
MATHS (Set I—Outside Delhi)
SECTION  A
Q. 1. If
Or Prove that
Q. 2. Using properties of determinants, Prove that
Q. 3. From a bag containing 20 tickets, numbered from 1 to 20 two tickets are drawn at random. Find the probability that
(i) Both the tickets have prime numbers on them;
(ii) On one there is prime number and on the other there is a multiple of 4.
Q. 4. Two dice are tossed once. Find the probability of getting an even number on the first dice or a total of 8.
Or
From a lot of 30 bulbs, which includes 6 defective bulbs, a sample of 3 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
Q. 5. Evaluate:
Q. 6. Evaluate:
Q. 7. Solve the differentia equation:
Q. 8. Solve the differential equation:
Given that
Q. 9. For each x in a Boolean Algebra B, prove that
Q. 10. Evaluate:
Or
Evaluate:
Q. 11. Differentiate
Q. 12. Differentiate from first principles.
Q. 13. The volume of a spherical balloon is increasing at the rate of 25cm 3 /sec. Find the rate of changer of its surface area at the instant when its radius is 5cm.
Q. 14. Evaluate:
Q. 15. Prove that:
Or
Prove that:
Q. 16. Using matrix method solve the following system of linear equations:
Or
If
Prove that: Hence find A^{1} .
Q. 17. Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius
Q. 18. Find the area bounded by the circle and the line in the first quadrant.
SECTION  B
Q. 19. If the vectors are coplanar, find the value of
Q. 20. Prove that
Or
The volume of the parallelopiped whose edges are is 546 cubic units, find the value of .
Q. 21. The Cartesian equations of a line are .Find the fixed point through which it passes its direction ration ratios and also its vector equation.
Q. 22. Find the equation of the plane passing through the points (0,1, 0), (1,1,1,) and (3,3,0).
Q. 23. Prove that the plane intersects the sphere in a circle of radius unity. Also the centre of the circle.
Q. 24. Three forces act along O A, OB and OC, where O is the orthocenter of the . If the forces be in equilibrium, prove that
Q. 25. The resultant of two like parallel forces acting at A and B, 8 cm apart is 40 N. If the resultant passes through C, where AC=3 cm, find the magnitude of the forces.
Q. 26. A particle moving in a straight line with uniform acceleration describes successive equal distance in times
Prove that
Or
A stone is projected at an angle with the horizontal. Given its velocity when it attains half of the maximum height (it can attain) is times of the velocity at the maximum height, prove that
SECTION  C
Q. 19. The true discount and banker's gain on a certain bill of exchange due after a certain period of time are respectively Rs. 700 and Rs. 17.50. Find the face of the bill.
Q. 20. A bill of Rs. 1,000 drawn on May 7, 2003 for six months was discounted on August 29, 2003 for a cash payment of Rs. 988. Find the rate of interest charged by the bank.
Q. 21. A company has two plants to manufacture T. V. s. The plant manufactures 70% of the T.V.s. and the rest are manufactures by the other plant. 80% of the T.V.s. manufactured by the first plant are rated of standard quality, while that of the second plant only 70% are of standard quality. If a T.V. chosen at random is found to be of standard quality, find the probability that it was produced by the first plant.
Q. 22. A pair of dice is thrown 7 times. If getting the total 7 is considered a success find the probability of (i) no success, (ii) at least 6 succes.
Or
If the probability that an individual suffers from reaction by an injection is , find the probability that out of 5000 individuals given that injection (i) exactly 5 will suffer from reaction, (ii) no one will suffer reaction. Given that
Q. 23. X and Y entered into a joint business with their capitals in the ratio 3 : 2. At the end of 3 months, X took out onethird of his capital, but after another 3 months Y put in a sum equal to what X had taken out. If at the end of the year y gets Rs. 11,000 more than what X got as profit find
(i) the total profit in the business;
(ii) the profit share of X in the business.
Q. 24. A television set is available for Rs. 20, 000 cash or Rs. 5,000 as cash down payment followed by 6 equal annual instalments, the first to be paid one year after the date of purchase. If the rate of interest under the instalment plan is 10% per annum, determine the amount of instalment.
Q. 25. If the cost function of an article manufactured by a company is given by
find the output at which
(i) The marginal cost is minimum;
(ii) The average cost is minimum.
Q. 26. A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 calories. Two folds X and Y are available at a cost of Rs. 4 and Rs. 3 per unit respectively. One unit of the food X contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas one unit of food Y contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of X and Y should be used to have least cost, satisfying the requirements.
Or
Solve the following linear programming problem graphically:
CBSE 2004 Question Papers Class XII
