ICSE 2009, Mathematics, Sample Question Paper 1, Class XII

Sample Paper – 2009 Class – XII Subject – Mathematics Section A (Question 1 is compulsory) [Total marks 30 ] 1. (a) Give one example each of following diagonal matrix , lower triangular matrix and identity matrix . (b) Calculate the square roots of 3 + 4i. 2. using cramer’s rule solve x – y = 1, x + z = -6 x + y – 2z = 3 3. The slope of one of the straight lines of ax² + 2hxy + by² = 0 is thrice that of the other, show that 3h² = 4ab 4. The parabola with the equation y = x² - 14 x +53 has a tangent at the point P ( 8,5). Find the equation of this tangent 5. Solve tanˉ¹ 2x + tan ˉ¹ 3x = π/4 6. Form the differential equation of the family of curves y = A cos 2x + B sin 2x, where A and B are constants. 7. Calculate the possible values of x when SD of 2, 3, 2x, 11 is 7/2 8.. 9 In how many ways can the letters of ‘LAUGHTER ‘ be arranged so that the vowels are not separated . 10.: Verify Rolle’s Theorem for the following function: f(x) = e2x( sin2x – cos 2x) defined in the interval [ π/8, 5π/8] SECTION B any five (a) Using properties of determinants, find the value of the following determinant │x³ x² x│. y³ y² y z³ z² z (b) If A= [3 -4 ] show that by induction method 1 -1 An = [ 1 + 2n - 4n ] n 1 – 2n a).What do you understand by complex plane ., draw a diagram and plot a + bi there where a and b are natural numbers and explain (b) If find dy/dx (a) Consider f(x) = ( x – 3 ) log x, prove that there is at least one value of x in ( 1 , 3 ) which satisfies x logx (b) A window is in the form of rectangular shape surmounted by a circular opening . The total perimeter of the window is 10 m . Find the dimensions of the windows to admit maximum light through the whole opening (a) Find (b) (a) Find the angle between the pair of st. lines, y² sin² θ -xy sin ²θ+ x² (cos²θ -1) = 1 (b) .Find the area lying above x-axis and included between the circle x² + y²=8x and the parabola y²=4x. (a) Find Spearman's coefficient of rank correlation. between the marks of mathematics and physics obtained by 8 students Math 20 13 18 21 11 12 17 16 Phy 17 12 22 24 20 21 18 10 (b) When two dice are thrown, what would be the probability that one of them will come up less than five? (a) An examination paper consists of 12 questions divided into two parts A and B . Part A contains 7 and part B 5 questions . A candidate is equired to attempt 8 questions ,selectiong atleast 3 from each part . In how many ways can he select the questions (b). Prove that [ 1 ώ² ] [ ώ ώ² ] = [ -1 -1 ] ώ ώ 1 ώ ² -1 2 (a) Using De Moivre's theorem, Simplify (b) Solve cos² x dy/dx+ y = tan x (Section C) Answer any two questions (a) Calculate a suitable price index from the following data Commodity Quantity Price 1996 1997 A 20 2 4 B 15 5 6 C 8 3 2 (b) Calculate the cost of living index number from the following data. Price Items Base year Current year Weight Food 30 45 4 Fuel 10 15 2 Clothing 15 20 1 House Rent 20 15 3 Miscellaneous 25 20 2 a) The marginal cost function of manufacturing x units of a commodity is 3 - 2x - x². If the fixed cost is 200, find the total cost and average cost functions (b)If the marginal revenue for a commodity is MR = 9 - 6x² + 2x, find the total revenue and demand function. (c) What is the average due date of the following installments payable under contract ? OCT 1st → Rs 1600; NOV 1st → Rs 2000; DEC 1st → Rs 1200. (a) Suppose you deposit RS 300 at the end of every three months for 10 years into a bank account paying the annual effective rate of interest 4%. What is the accumulated amount after 10 years? (b) A merchant marks his goods up by 60% and then offers a discount on the marked price. If the final selling price after the discount results in the merchant making no profit or loss, what was the percentage discount offered by the merchant? Paper Submitted by:- Mr. ALOK DEV Email Id:- aloke60@yahoo.co.in Telephone No. 09739052048 http://www.icseguess.com/ -------------------------------------------------------------------------------------------------------www.icseguess.comOther Educational Portalswww.cbseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com