Trending ▼   ResFinder  

Class 12 ISC Pre board 2015 : Mathematics

3 pages, 38 questions, 28 questions with responses, 35 total responses,    0    0
saviopala
   		+Fave Message
ProfileTimelineUploads
 Home > saviopala >   F Also featured on: saksham87 isc

Formatting page ...

-4Question 9. (a) Find the particular solution of the differential equation: e given y (0) = 3. (b) If z = dy dx = x + 1, [5] 13 5i , using De Moivre s theorem prove that z 6 = 8i. [5] 4 9i SECTION B [Any TWO] Question 10. (a) In any triangle ABC, prove by vector method that [2x10=20] c = a cos B + b cos A. (b) Find vector equation of the line passing through the point (2,3, 2) and r r r r r r parallel to the line r = 2i + 3 j + (2i 3j + 6k). Also find the distance between them. Question 11. (a) Find the length and the foot of the perpendicular from the point (7,14,5) to the plane 2 x + 4 y z = 2. (b) Find the cartesian equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes x + 2 y + 3 z 7 = 0 and 2x 3 y + 4z = 0 . Question 12. (a) The overall percentage of passes in a certain examination is 75. If five candidates from a certain town appear in the examination, what is the probability that at least four pass in the examination? (b) A consulting firm rents cars from three agencies such that 20% of the cars are rented from agency A, 30% from agency B and 50% from agency C. It is known that 70% of the cars from A, 80% of the cars from B and 90% of the cars from C are in good condition. If a car taken on rent is in good condition, what is the probability that it is from agency B? PRE BOARD EXAMINATION CLASS XII MATHEMATICS Marks: 100 Time: 3 Hours (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) Section A - Answer Question 1 (compulsory) and any other five questions. Section B and Section C - Answer any two questions from either Section B or Section C. All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer. SECTION A Question 1. [10x3=30] 2 2 2 and A = kA, then find the value of k. 2 2 1. If A = 2. Using suitable substitution, express in the simplest form: 1 + x2 1 tan 1 . x 3. Find the value of k so that the line y = 2 x + k touches the ellipse 3 x 2 + 5 y 2 = 15. 4. Evaluate: 5. Evaluate: Lim ( 1 tan x ) sec 2 x x 4 log x ( 1 + log x ) 2 dx a 6. Using properties of definite integrals, evaluate: 0 x dx x + a x 7. A die is thrown three times. If the first outcome is a four, find the probability of getting 15 as a sum. 8. You are given the following two regression lines. Find the regression line of Y on X & that of X on Y. Justify your answer. 3 x + 4 y = 8; 4 x + 2 y = 10. 9. If is a cube root of unity, then find the value of ( 2 ) ( 2 2 ) ( 2 10 ) ( 2 11 ) . -2- 10.Solve: dy y + = x2 dx x given y = 1 when x = 1. Simplify the expression and construct the switching circuit for the simplified expression. Question 2. -3- (a) Using matrix method, solve the following system of linear equations: [5] x + 2 y = 5, y + 2 z = 8, z + 2 x = 5. x (b) If x, y , z are all different and y z x 2 1 + x3 y 2 1 + y 3 = 0 then using z2 1 + z3 properties of determinants prove that xyz = 1. Questions 5. ( (a) If y = x + x 1 Question 3. 5 2x . (a) Verify Rolle s theorem for f ( x ) = e ( sin 2 x cos 2 x ) in , 8 8 Question 6. [5] Question 4. cos 1 x cos 1 y = . 3 x + sin x 1 + cos x dx (b) Find the altitude of the right circular cylinder of maximum volume that can be inscribed in a sphere of radius r. [5] (b) Find the equation of the parabola whose vertex is (3, 2) and focus is 1 1 (a) Solve the following simultaneous equations: sin x + sin y = 2 dy , prove that ( x 1) = m 2 y 2 . dx 2 lines x = 0 and x = a. (a) Evaluate: (6, 2). ) m (b) Find the area under the curve y = a 2 x 2 included between the [5] Find the point in the interval where the derivative vanishes. 2 2 , 3 [5] (b) Write the Boolean expression corresponding to the switching circuit given below. Question 7. (a) The marks obtained by 10 students in English and Hindi are given below. Calculate Spearman s Rank Correlation coefficient. English 10 25 13 25 22 11 12 25 21 20 Hindi 12 22 16 15 18 18 17 23 24 17 (b) Fit a straight line to the following data, treating y as independent variable: x 1 12 13 1 12 4 4 y 22 23 22 24 24 Question 8. (a) Ten cards numbered 1 to 10 are placed in a box and one card is drawn randomly. If it is known that the number on the card drawn is more than 3, what is the probability that it is an even number? (b) In a bag there are 6 white and 4 red balls. In bag B, there are 7 white and 8 red balls. In bag C, there are 4 white and 3 red balls. One ball is taken out at random from each bag. Find the probability that all the three balls are of the same colour. (b) A bill of Rs 28050 is drawn on 22 April 1990 at 11 months and is discounted on 11 January, 1991. Find the Banker s gain if the rate of interest is 10%. -5SECTION C [Any TWO] -6[2x10=20] Question 13. (a) A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling one chair is Rs 30 while by selling one table, the profit is Rs 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximize profit? Formulate the problem as an L.P.P. and solve it graphically. (b) A man borrowed some money and paid it back in three equal quarterly installments of Rs 9261 each. If the first installment is to be paid one year after the date of borrowing and the rate of interest charged was 20% per annum compounded quarterly, find the sum borrowed. Also find the total interest charged. Question 14. (a) The cost of manufacturing a certain item involves Rs 1600 as overheads, Rs 30 per item as the cost of the material and the labour costs Rs x2 for x items produced. How many items must be produced 100 to have a minimum average cost? Question 15. (a) Construct the price index number for 2006 on the basis of 1996 by the weighted average of price relatives for the following data: Commodity Weight A B 4 25 0 Price/unit (1996) 16 4 0 Price/unit (2006) 20 60 C 5 D 20 E 10 0.50 5.12 2 0.50 6.25 1.50 (b) Calculate the four quarterly yearly moving averages of the data given below: Year Jan-Mar Apr-Jun Jul-Sep 1980 45 56 39 1981 39 49 45 1982 46 56 49 Oct -Dec 30 41 40

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)


Thanu Shree
(14)

American Badass
(7)

Tuba Khaled
(5)

Anonymous
(4)

Formatting page ...

 

  Print intermediate debugging step

Show debugging info


 

 

© 2010 - 2025 ResPaper. Terms of ServiceContact Us Advertise with us

 

saviopala chat