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Time : 3 Hours 15 Minutes
Max. Marks : 100
i) The question paper consists of five Parts – A, B, C, D and E. Answer all the Parts.
ii) Part – A carries 10 marks, Part – B carries 20 marks, Part – C carries 40 marks, Part – D carries 20 marks and Part – E carries 10 marks.
iii) Write the question numbers properly as indicated in the question paper.
PART – A :
Answer all the ten questions : 10 × 1 = 10
1. Negate “If questions are easy then the students are happy”.
2. If n C 5 = n C 7 , find n C 11 .
4. The average height of 10 boys is 4 ft. Find the sum of their heights.
5. A bill was drawn on 05. 05. 2005 for 3 months. When will the bill fall legally due ?
6. Write the learning curve equation.
7. Find the centre of the circle x 2 + y 2 – 4x – 6y + 1 = 0.
9. Find the derivative of x e + e x w.r.t. x.
PART – B :
Answer any ten questions : 10 × 2 = 20
11. If p ? ( q V ~ r ) is false, find the truth values of p, q and r.
12. In how many ways 6 boys and 5 girls be arranged in a row so that no two boys are together ?
16. The ratio of the age of father to that of his son is 5 : 3. After 10 years, the ratio of their ages will be 3 : 2. Find their present ages.
17. If y 2 = 12 x, find the focus and length of latus rectum.
PART – C :
I. Answer any three questions : 3 × 5 = 15
23. Construct a truth table for ( ~ p V q ) ? ( p V q ).
24. a) A jar contains 2 white balls, 3 green balls and 4 red balls. A ball is drawn at random. Find
i) the probability of getting a white ball
ii) the probability that the ball drawn is not white
iii) the probability that the ball drawn is red. 3
b) There are 14 points in a plane, out of which 4 are collinear.
How many straight lines can be drawn ? 2
26. Solve the following equations by matrix method :
x – y + 2z = 5
2x + y + z = 7
3x – 2y + 2z = 5.
II. Answer any two questions : 2 × 5 = 10
27. Monthly incomes of Ram and Shyam are in the ratio 2 : 3. Their monthly expenditure are in the ratio 3 : 5. If each saves
Rs. 1,000 per month, Find the monthly incomes of Ram and Shyam.
28. a) How much should be invested in 14·25% stock at 98 to produce the same income as would be obtained by investing Rs. 9,975 in 15% stock at 105 ? 3
b) Find the mean proportional to 8 and 18. 2
29. The first sample batch of 50 units of a product took 80 hours. The company now wishes to produce a total of 350 units. Find the total labour hours to produce 350 units and labour cost at Rs. 20 per hour. The company has 80% learning effect.
30. Solve graphically the following L.P.P.:
Maximize Z = 9x + 15y
subject to x + 2y = 2000
x + y = 1500
x, y = 0
III. Answer any three questions : 3 × 5 = 15
31. Find the equation of a circle passing through ( 2, 0 ), ( – 1, 3 ) and ( – 2, 0 ).
32. a) Find the equation of the parabola whose vertex is ( 4, 3 ) and focus is ( 2, 3 ). 3
b) If s = 3t 2 + 4t + 5, find (i) velocity, (ii) acceleration at t = 2 seconds. 2
33. Differentiate e 5x with respect to x by first principle.
PART – D :
Answer any two questions : 2 × 10 = 20
35. a) A committee of 8 has to be formed out of 6 men and 7 women. In how many ways can this be done if the committee contains
i) at least 3 women and at least 3 men ?
ii) exactly 2 men ? 5
36. a) The volume of a spherical ball is increasing at the rate of 4p c.c./sec. Find the rate of increase of radius and that of surface area when the radius = 6 cm. 5
37. a) Find the area between the parabola y 2 = 4x and the line y = x. 5
b) A bill for 14,600 drawn for 3 months was discounted on November 20th for Rs. 14,544. If the rate of discount is 14% p.a., on what date was the bill drawn ? 5
b) Find the vertex, focus, axis, equation of directrix and length of latus rectum of the parabola : ( y – 5 ) 2 = 20 ( x + 2 ). 5
PART – E :
Answer any one question : 1 × 10 = 10
39. a) A company manufactures two types of bulbs A and B by using 2 machines M 1 and M 2 . One bulb of type A requires 2 hours at machine M 1 and 1 hour at machine M 2 . One bulb of type B requires 1 hour at M 1 and 2 hours at M 2 . The profit from each bulb of type A is Rs. 3·00 and the profit from each of type B is Rs. 2·00. The number of hours available per week on machine M 1 and M 2 are 20 hours and 30 hours. Formulate the above as L.P.P. to maximize the profit ( only equations ).
b) A dealer purchased certain number of leather bags at an average cost of Rs. 190 per bag. The average cost of 10 bags was Rs. 175. That of the remaining was Rs. 200. Find the total number of bags purchased. 4
c) Find the value of ( 1·02 ) 3 using binomial theorem. 2
40. a) Prove that P ( A U B ) = P ( A ) + P ( B ) – P ( A I B ), where A and B are two mutually non-exclusive events. 4
b) What is true discount and Banker’s discount on a bill of Rs. 415 due 9 months hence at 15% p.a. ? 4
c) If M.R. = 16 – x 2 , find the total revenue and average revenue if fixed revenue = 50. 2
Full List of Basic Mathematics Questions refer the PDF Link : http://www.indianjobtalks.in/uploads/9423-75.pdf