
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

12th Maths Sectionwise paper - 04 (Vectors, 3D, Probability, LP)

3 pages, 52 questions, 0 questions with responses, 0 total responses,

	Jen -, .	+Fave Message
	Profile Timeline Uploads

Home > the_unknown >

Formatting page ...

MATHEMATICS Class II Pre-Uni Plus 2016-17 Topics Board Section-wise Test - 04 Vector Algebra, Probability, Three dimensional Geometry, Linear programming Max. Marks 100 Duration Date 3 hrs 15 min 03-01-2017 Instructions 1. Do not overwrite. 2. Draw a line using pen at the end of each answer. 3. Steps adopted in solving problems should be clearly shown. 4. In case of violation of the above conditions, the answer scripts will not be considered for valuation. PART - A I. Answer all the ten questions [10 1 = 10] 1. Find the unit vector in the direction of a b given that a 2i 2 j 5k and b 4i 2 j 3k . 2. Find the projection of a 5i 2 j 3k on b 4i 2 j 5k . 3. If the vectors i 2 j k and i 3j 2k are orthogonal. Find . 4. Find the vector equation of the line passing through the origin and the point (1, 3, 2). 5. Find the distance of the point (1, 2, 3) from the plane r 2i 3j 4k 5 . 6. Find the equation of the plane through the point (2, 3, 4) and parallel to the plane 5x 6y + 5z = 6. 7. If P A 0.7, P B 0.6 and P(B | A) 0.5 find P(A B). 8. A family has two children. What is the probability that both the children are girls given that at least one of them is a girl? 9. Define feasible region in a linear programming problem. 10. Define optimal solution of a linear programming problem. PART - B II. Answer any TEN of the following questions [10 2 = 20] 11. If a and b are unit vectors inclined at an angle . Show that a b 2cos . 2 12. If a 2, 3, 1 and b 3, 2,5 find a b 2a b . 13. If a, b, c are unit vectors such that a b c 0 . Find the value of a b b c c a . 14. For any two vectors a and b show that a b a b . 15. Find the area of parallelogram whose 3i j 5k and 2i 4 j 3k . adjacent sides are represented by the k i . 16. Evaluate i j, j k, 17. If cos , cos , cos are the direction cosines of a line, show that sin 2 sin 2 sin 2 2 . 18. Find the direction cosines of the line passing through the points ( 3, 1, 2) and (2, 3, 5). 2P1617M(B)SWT4 1 vectors 19. Find the intercepts cut-off by the plane 3x 2y + z = 7 with the coordinate axes. 20. Find the equation of a plane which is at a distance of 6 units from the origin and is perpendicular to 3i 2 j 4k , directed towards the plane. 21. Find the angle between the planes r i j 1 and r j k 3 . 22. The random variable x has a probability distribution P(X) of the following form where k is some number X 0 1 2 P(X) K 2K 3K Find (1) K (2) P(X 2) 23. Find the mean and variance for the following probability distribution. X 0 1 2 3 3 1 P(X) 1 1 6 2 10 30 24. An unbiased coin is tossed 6 times. Find the probability of obtaining atleast 5 heads. PART - C III. Answer any TEN of the following questions [10 3 = 30] 25. Find the angle between the diagonals of a cube. 26. Find the distance between the lines given by r i 2 j 4k 2i 3j 6k and r 3i 3j 5k 2i 3j 6k . 27. Find the angle between the lines x 1 y 2 x 2 x 1 y 4 z 3 and . 2 3 4 3 1 5 28. Find the equation of the plane passing through the intersection of the planes r i 3j k 0 and r j 2k 0 and the point (2, 1, 1). 29. For any three vectors a, b and c prove that vectors a b, b c and c a are coplanar. 30. Find the area of the triangle with vertices A(1, 2, 3), B(2, 1, 1) and C(1, 2, 4). 31. If a 5, b 2 and a b 8 find a b . 32. If a 1,1, 1 , b 1, 2,1 and c 1, 2, 1 . Find the unit vector perpendicular to both a b and b c . 33. Obtain an expression for the area of a parallelogram whose diagonals are represented by d1 and d 2 . 34. Find the sine of the angle between the vectors i 2 j 2k and 3i 2 j 6k . 35. Box-I contains 2 gold coins, while another Box-II contains 1 gold and 1 silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold? 36. State and prove multiplication theorem on probability. 37. If A and B are two independent events with P(A) = 0.4 and P(B) = 0.5. Find (1) P(A B), (2) P A B (3) P A B . 38. Two persons throw a dice alternately till one of them gets a three and wins the game. Find their probabilities of winning. 2P1617M(B)SWT4 2 PART - D IV. Answer any SIX of the following questions [6 5 = 30] 39. Derive the equation of a plane perpendicular to a given vector and passing through a given point both in vector form and Cartesian form. 40. Find the shortest distance between the lines r 2i j k 3i j k and r i 2 j 3k 2i 3j 2k . 41. Show that the points (0, 1, 1), ( 4, 4, 4), (4, 5, 1) and (3, 9, 4) are coplanar. 42. Maximize z = 5x + 3y subject to the constraints x + y 50; 2x + y 80, x 0 and y 0. 43. Minimize z = 5x + 4y subject to the constraints x + 4y 20; x + y 10, x 0 and y 0. 44. One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredient. Used in making the cakes. 45. A man is known to speak truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. 46. If 5 males out of 200 and 20 females out of 1000 are good orators. An orator is chosen at random. Find the probability that a male person is chosen. Assume that there are equal number of males and females. 47. Six dice are thrown 729 times. How many times do you expect at least 3 dice to show 5 or 6? 1 . Find the probability that out of 5 students (i) atleast 5 four are swimmers and (ii) atmost three are swimmers. 48. The probability that a student is not a swimmer is PART - E IV. Answer any ONE of the following questions [1 10 = 10] 49. (a) Minimize and maximize z = 5x + 10y subject to the constraints x + 2y 120; x + y 60, x 2y 0 x 0 and y 0 by graphical method. [6] x 1 y 2 z 3 x 2 y 2 z 6 (b) Show that the lines and are coplanar. [4] 2 2 1 3 2 4 50. (a) A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit? If he operates his machines for atmost 12 hours a day? [6] 3 . How many minimum numbers of times must he 4 shoot so that the probability of hitting the target atleast once is more than 0.99? [4] (b) The probability of a shooter hitting a target is *** 2P1617M(B)SWT4 3

Formatting page ...

the_unknown chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: