# II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO ARE APPEARING ANNUAL EXAM-2014

BagalkotDirector & Faculty em Bagalkot

My dear Students, Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014 Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014. wish you all the best Regards, A. NAGARAJ Director-Faculty Shree Susheela Tutorials BAGALKOT-587101 mob: 9845222682

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### II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO ARE APPEARING ANNUAL EXAM-2014

• 1. A. Nagaraj’S II P.U.C.MATHEMATICS- ANNUAL EXAM-2014 Trin : 9845222682 Max. Marks:100 PART-A ANSWER ALL THE QUESTIONS 10X1=10 1. Give example of relation which is symmetric but neither reflexive nor transitive.   1     1   2. Evaluate sin cos −1  −  − sin −1    2 2  cos α  sin α 3. If A =  − sin α  , find the value of α , if A is Identity matrix . cos α   101 102 103 4. Evaluate 104 105 106 107 108 109 without using direct expansion . 5. Differentiate sin [ cos(tan x) ] w.r.t.x 6. Evaluate x2 ∫ 1 + x 2 dx (   ) (   7. Evaluate 3a − 5b • 2a + 7b ) 8. If a line has direction ratios 2 , -1 , -2 , determine its direction cosines . 9. Define “optimal solution “to a linear programming problem. 10. If P ( A) = 1 2 and P ( B ) = 0 then find P ( A | B ) . PART-B Answer any Ten question 10x2=20 ab then find the identity element . 4 11. If ∀a, b ∈ Q and * is defined by a ∗ b =   12. Find the value of sin −1  sin 3π   5  π 13. Solve ta n −1 2 x + ta n −1 3 x = 4 14. If each element of a row ( or a column ) of a determinant is multiplied by a constant K , then show that Its value gets multiplied by K.
• 2. A. Nagaraj’S Trin : 9845222682  x + 3, if x ≤ 2 2 x − 3, if x > 2 15. Find all points of discontinuity of f ,where f is defined by f ( x ) =  3 16. Verify Mean Value Theorem for the function f ( x) = x 2 in the interval [ 2, 4] 17. Find the equation of the tangent to the curve y = 18. Evaluate 3 x − 2 which is  to line 4 x − 2 y + 5 = 0 ∫ xSinxCosx dx e log x 2 19. Evaluate ∫ dx x 1 2 20. Find the order and degree of D . E d2 y dy  dy  xy 2 + x   − y = 0 dx dx  dx  ( ) ˆ ˆ 21. If the position vectors of the points A and B respectively are i + 2 ˆ − 3k and j ( ˆj − kˆ ) find the direction cosines of AB. ˆ ˆ j 22. Find a vector of magnitude 8 units in the direction of the vector, 5i − ˆ + 2k  ˆ 9 ˆ 23. Find the distance of the point ( 2, 3, -5 ) from the plane r.(i + 2 ˆ − 2k ) = j 24. A Die marked 1, 2, 3 in Red and 4,5,6 in Green is tossed. Let A be the event “ the number is even “ and B be the event “ the number is Red “. Are “ A and B “ independent . Answer any Ten questions. 10x3=30 25. On Z * is detined by a* b = a-b , determine whether * is Commutative or Associative 26. Show that ta n −1 1 1 1 1 π + ta n −1 + ta n −1 + ta n −1 = 5 7 3 8 4 1 3   2 7 27. Using elementary transformation, find inverse of  28. If e x + e y = y ,then show that e x+ dy = −e y − x . dx dy  1  29. If y = s ec −1  2  , 0 < x < 1/ 2 then find dx  2x − 1  30. Use differential to find approximate value of 31. Evaluate ∫ tan 4 x dx 36.6
• 3. A. Nagaraj’S Trin : 9845222682 3 32. Evaluate x ∫ (1 + x )dx 2 2 33. Find the Area of the region bounded by the curve y 2 = x and the lines= 1, x 4 and the x-axis. x = 34. From the Differential equation of the family of circles having centre on Y- axis and radius 3 units. ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ ˆ 35. Show that the points A −2i + 3 ˆ + 5k , B i + 2 ˆ + 3k , &C 7i − k are collinear. j j       36. If= 3, b 4, c 5 and each one of them being ⊥ to the other two , find a + b + c a = = 37. Find the vector and the Cartesian equations of the line through the point (5,2,-4) and which is parallel to ˆ ˆ the vector 3i + 2 ˆ − 8k j 38. From a lot of 30 bulbs which includes 6 defectives, a sample of 4 bulbs is drawn at random with Replacement. Find the probability distribution of the number of defective bulbs. 6×5 = 30 PART - D Answer any SIX questions 39. Let f : R → R be defined by f ( x) 3 x − 7 . show that f is invertible. Find f −1 : R → R = 40. If A 1 2 −3 =  5 0 2  , B 1 −1 1     3 −1 2  4 2 5 & C =   2 −0 3    4 1 2  0 3 2  verify that A + ( B − C ) = ( A + B) − C .   1 −2 3    41.Solve by using Matrix method: 3 x − 2 y + 3= 8, 2 x + y − = 1& 4 x − 3 y + 2= 4 z z z 42.If y ae mx + be nx ,then Show that y2 − (m + n) y1 + mny = 0 = 43. A Man of height 2mt walks at a uniform speed 5km/h away from a Lamp post which is 6mt high.Find the rate at which the length of his shadow increases. 44. Prove that ∫ 1 x dx = sin −1   + C and hence evaluate a a2 − x2 ∫ sec 2 x 4 − tan 2 x dx . 45. Find the Area of the circle x 2 + y 2 =by integration method. a2 46. Derive the equation of a plane in Normal form (both in vector and Cartesian form). 47. Solve the differential equation, x dy + 2y = e . x 2 log x dx 48. If a Fair coin is tossed 10 times .Find the Probability of a) exactly 6 heads most 6 heads. b) At least 6 heads c) At
• 4. A. Nagaraj’S Trin : 9845222682 Part- E Answer any One question 1x10=10 49. (a) An Aero plane can carry a maximum of 200 passengers, A Profit of Rs.1000 is made on each executive class ticket and a profit of Rs.600 is made on each economy class ticket.The Airline reserves at least 20 seats for executive class. However at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the Profit for the airline .What is the Maximum Profit?  x + 2, if x < 1  (b) Find all the points of discontinuity of the function f defined by f ( x ) = 0, if x = 1  x − 2, if x > 1  a 50. (a) Prove that f ( x) ∫= 0 π a ∫ f (a − x) dx , xSinx ∫ (1 + Cos x )dx . hence evaluate 2 0 0 a 2 + 1 ab ac 2 (b) Prove that ab b + 1 bc = + a 2 + b 2 + c 2 ` 1 2 ca bc 1+ c ----------- ----------------- -------------------- -------------------------- -------------------- ------------------- Attention!!!!. Vacation classes (For I puc to II puc moving students) 10-March-2014 & start from 20-march-14( 2nd Batch) ------------We wish you all the best for your Annual Exams-----From: A. Nagaraj Shree susheela tutorials, Trin:9845222682 Email: edulation@gmail.com C E T COACHING CLASSES START FROM 02-APRIL-14 AND CLOSES ON 01-MAY-2014. We wish you All the best in your Annual & C E T Exams- 2014.
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