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

ISC Class XII Notes 2024 : Mathematics (Bombay International School, Mumbai)

10 pages, 106 questions, 0 questions with responses, 0 total responses,

	Aisha	+Fave Message
	Profile Timeline Uploads

Home > kavyaarora > F Also featured on: School Page

Formatting page ...

COMPARTMENT / IMPROVEMENT EXAMINATION 2023 MATHEMATICS --------------------------------------------------------------------------------------------------------------------Maximum Marks: 80 Time Allowed: Three hours (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------This Question Paper consists of three sections A, B and C. Candidates are required to attempt all questions from Section A and all questions EITHER from Section B OR Section C. Section A: Internal choice has been provided in two questions of two marks each, two questions of four marks each and two questions of six marks each. Section B: Internal choice has been provided in one question of two marks and one question of four marks. Section C: Internal choice has been provided in one question of two marks and one question of four marks. All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. --------------------------------------------------------------------------------------------------------------------- SECTION A - 65 MARKS Question 1 In subparts (i) to (x) choose the correct options and in subparts (xi) to (xv), answer the questions as instructed. (i) If ( 1 + 1 3) = 0, then the value of is: (a) [1] 1 3 (b) 3 (c) 1 (d) 0 ---------------------------------------------------------------------------------------------------------------------This Paper consists of 9 printed pages and one blank page. 1223-860-CE/IE Turn over Copyright reserved. (ii) (iii) 2 If the matrix [ 6 (a) 5 (b) 5 (c) 3 (d) 3 If ( ) = { 15 ] is a symmetric matrix, then the value of x will be: 4 1, 5 is continuous at = 5, find the relationship between + 7, > 5 [1] [1] a and b. (iv) (v) (a) = 8 5 (b) + = 8 5 (c) = 5 8 (d) = 5 8 The side of a square sheet is increasing at the rate of 4 cm/min. If the side of the square sheet is 5cm long, at what rate will the area increase? (a) 40 cm2/min (b) 20 cm2/min (c) 100 cm2/min (d) 25 cm2/min The relation R defined on the set of all real numbers such that is: (a) an equivalence relation. (b) reflexive, transitive but not symmetric. (c) symmetric, transitive but not reflexive. (d) neither reflexive nor transitive but symmetric. [1] [1] ---------------------------------------------------------------------------------------------------------------------2 1223-860-CE/IE (vi) (vii) (viii) (ix) Find the point on the curve 2 + 3 = 3 where the tangent is parallel to the line 4 + 5 = 0 (a) ( 6, 11) (b) (6, 11) (c) (6, 11) (d) ( 6, 11) If A is a 3 3 matrix with | | = 5 then the value of | | will be: (a) 5 (b) 1 5 (c) 25 (d) 125 = 2 = 3 then is: (a) 3 2 (b) 2 3 (c) 13t2 (d) 2t Find the interval in which the function ( ) = 5 2 24 + 3 is increasing. [1] [1] [1] [1] 12 ) 5 (a) ( , (b) [ (c) (0, (d) 12 ( , ) 5 12 , ) 5 12 ) 5 ---------------------------------------------------------------------------------------------------------------------3 1223-860-CE/IE Turn over 4 4 Evaluate (x) (a) 0 (b) 1 (c) -1 (d) 1 [1] 3 4 2 1 [1] ( )2 (xi) Evaluate: (xii) Solve the differential equation: (xiii) Evaluate: (xiv) Two cards are drawn randomly from a well shuffled pack of cards. Find the probability that both the cards drawn are either black or aces. (xv) Evaluate: 0 + [1] = (1 + )(1 + ) [1] sin [1] 1 2 Question 2 (i) [1] [2] Let A = R {5} and B = R {1}. If f : A B is a function defined by f (x) = then show that f is a one-one and an onto function. 3 5 OR (ii) Show the relation R defined on the set of all real numbers, such that | | = | | is an equivalence relation. Question 3 [2] Evaluate the following determinant without expanding: | + + | + ---------------------------------------------------------------------------------------------------------------------4 1223-860-CE/IE Question 4 [2] Find the value of p if A and B are independent events such that ( ) = 0 4, ( ) = ( ) = 0 6 Question 5 (i) [2] Solve for : 2 ( 1 5 + 1 ) = 1 OR (ii) cos ( 6 + 1 ( 3 )) Evaluate: Question 6 Evaluate: [2] cos Question 7 Prove that: [4] 1 2 1 5 + 1 5 2 7 1 + 2 1 8 = 4 Question 8 If = ( + ) 3 then prove that [4] 2 2 + 6 + 9 = 0 Question 9 (i) [4] Riya sets an alarm to wake up and reach the examination hall on time. The probability that the alarm will ring is 0 9. If the alarm rings, then the probability of Riya reaching the examination hall on time is 0 8, If the alarm does not ring, then the probability of Riya reaching the examination hall on time is 0 3. Given that she reached the examination hall on time, find the probability that the alarm rang. OR ---------------------------------------------------------------------------------------------------------------------5 1223-860-CE/IE Turn over (ii) Sahil and Rohit throw a die alternatively till one of them gets a three and wins the game. Find their respective probabilities of winning if Sahil throws the die first. Question 10 (i) Solve the differential equation: [4] (1 2 ) = 2 OR (ii) Solve the differential equation: = ( ) Question 11 [6] Solve the following system of linear equations by using matrix method. 2 1 3 3 3 + = 10 1 1 + + = 10 1 2 + = 13 Question 12 (i) [6] A right circular cylinder of maximum volume is inscribed in a sphere of radius 2 3 units. Find the altitude and the maximum volume of the cylinder. OR (ii) If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is . 3 Question 13 [6] Five defective screw pieces are mixed with twenty good pieces. Four screw pieces are then drawn at random from this lot. If denotes the number of defective pieces, then find the probability distribution for the number of defective screw pieces. Also find the mean and the variance of X. ---------------------------------------------------------------------------------------------------------------------6 1223-860-CE/IE Question 14 (i) [6] Evaluate: +sin 1+cos OR (ii) Evaluate: 2 +2 1 4 + 2 +1 SECTION B - 15 MARKS Question 15 [5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. (i) (ii) The vector with initial and terminal points P(2, 5, 0) and Q( 3, 8, 4) respectively then the position vector of will be: (a) + 12 + 4 (b) 5 + 3 4 (c) 5 + 3 + 4 (d) + + The distance of the point (2, 3, 4) from the plane . (3 6 + 2 ) = 11 is: (a) 1 unit (b) 2 units (c) 3 units (d) 15 7 units (iii) Find the value of such that the vectors 2 and + + 5 are perpendicular. (iv) Find when = + 3 + and = + 2 + 5 (v) Find the equation of a line passing through the point (2, 3, 0) and having direction 1 4 6 cosines 7 , 7 , 7 ---------------------------------------------------------------------------------------------------------------------7 1223-860-CE/IE Turn over Question 16 (i) [2] Find the angle between the two planes 2 + = 6 + + 2 = 7 OR (ii) Find the vector projection of 2 + on the vector 2 + 2 Question 17 (i) [4] Find the co-ordinates of the point where the line passing through the points (3, 4, 1) (5, 1, 6) crosses the plane. OR (ii) Find the length of the foot of the perpendicular from the point (7, 14, 5) to the plane 2 + 4 = 2 Question 18 [4] Using integration, find the area of the region included between the curve 4 = 3 2 and the line 2 = 3 + 12 SECTION C - 15 MARKS Question 19 [5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. (i) The total revenue generated from the sale of x units of an item is given by ( ) = 36 + 3 2 + 5 . The actual revenue generated from the sale of the 50th item is: (a) 330 (b) 334 (c) 336 (d) 333 ---------------------------------------------------------------------------------------------------------------------8 1223-860-CE/IE (ii) For the given regression lines 3x 2y = 5 and x 4y = 7, the coefficient of correlation is: (a) 6 6 6 (b) 6 (c) (d) 6 6 6 6 (iii) The cost of manufacturing of a television set includes 1600 as overhead, 30 per 2 unit as the cost of material and (100) as the cost of labour for x units produced. Find the marginal cost function. (iv) If 4 5 + 33 = 0 and 20 9 107 = 0 are two lines of regression and respectively, then calculate the value of when = 10. (v) If the demand function is = 300 3 , where is the number of units demanded and is the price per unit, find the Marginal Revenue (MR). Question 20 (i) [2] The total cost function for a commodity is given by ( ) = 2 + 5 + 36 in terms of output . Find the range of values of the output , for which Average Cost (AC) is increasing. OR (ii) If ( ) = 5 + 350 and ( ) = 50 2 are the total cost and revenue functions for a company that produces and sells x units of a product, then find the value of x that produces profit. Question 21 (i) [4] Find the line of regression of on from the following table: 0 1 2 3 4 5 6 2 1 3 2 4 3 5 OR ---------------------------------------------------------------------------------------------------------------------9 1223-860-CE/IE Turn over (ii) In a partially destroyed chemical laboratory, following is the only correlation data available for analysis: Regression equations, 8 10 + 66 = 0, 40 18 = 214 and Variance of = 9 Calculate the following: (a) Values of and (b) Standard deviation of (c) Coefficient of correlation between and Question 22 [4] Solve the following Linear Programming Problem graphically. Minimize Z = 20 + 10 subject to + 2 40, 3 + 30, 4 + 3 60, . 0 ---------------------------------------------------------------------------------------------------------------------10 1223-860-CE/IE

Formatting page ...

kavyaarora chat

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