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ISC Class XII Sample / Model Paper 2024 : Mathematics

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Vamika bhati
St. Joseph's School, Greater Noida

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St. Joseph's School, Greater Noida First Term Examination 2024-25 Subject: Mathematics Class: XII TIME:3 HRS MM: 80 (Candidates are allowed additional 15 minutes for only reading the question paper. They must NOT start writing during this time) The Question Paper consist of three sections A, Band C. Candidates ates are a required to attempt all questions Irom Section A and ail questions EITHER from Section B OR Section ( SECTION A: Internal choice has been provided in two questions of 2marks each, two questions of 4 marks cach and two questions of 6 marks each. SECTION B: Internal choice has been provided in one questions of 2marks and one questions of 4 marks. SECTIONC: Internal choice has been provided in one questions of 2marks and one questions of 4 marks. All working including rough work should be done on same sheet. The intended marks for questions or parts of question are given in brackets. SECTION A- (65 MARKS| O 1. In sub parts (i) to (x) choose the correct option and sub- parts (xi) to (XV), answer the questions as instnucted i [Ixl5-15] If as 2sin x + cos a) a=-/2, S = /2 <ii> tan7/9 +tan xsBthen b) a=0, =n c) a=-3n/2, S = /2 d) a=n/2, S =n 1/8 is equal to a) tan' 65/72 b) tan- 63/65 c) n/4 d}n/2 <iii> the function f(x) =x] is continuous at a) 4 <|V> d c) 1.5 The set of points were the function f given by f(x) =|2x a)R <V> b) -2 b) R-(1/2}c) 1|lcosx Is differential is : (0,co) d) none of these ,y=t then d'y/dx' is c) 3/2t aj3/2 b)3/4t Ifx= d) % <Vi> Ify = sec(tan x), then dy/dx at x=1 is equal to alv2 b)1/V2)1 d) 1 <Vi> Which of the following function is decreasing on (0,r/2) a sin2x b) tanx cosX d) cos3X <vii> Ify =t' and t= x +3, then dy/dx = <iX> bl 2(x+3) c) 2t a) (x+3)* For the curve y'=2x -7,the slope of normal at (2,3) is a) 4 b) c -4 d) 2(x+3) -1/4 The rate of change of a square is 40 cm/s. what will be the Change of side if the side is 10cm a 2cm/s b) 4cm/s c) 6cm/s d) <xi> Trigonometric and Inverse Trigonometric function differential in Their <xii> lalr+dr= <xiij> Sx-5|dx = <XiV> Sf)dx =2f f(a)dr if fiarx)= <XV> The integrating factor of+ ytanx- secx=0 is--- 8cm/s [2 Find the value of sin(2tan 1/3) + cos(tan2V2). Q2. Or b) Q3. then find the value of cot+coty. If tanx+tan y= ifx < 1 Explain f(x) =s if x> 1 [2) is continuous at x=2 or not. Or Examinethe differentiability of f(x)=-) if0sxs2 if2<s3 Q4. Find an angle 8 , where 0< <n/2, which increase twice as fast as its sine. (2] Q 5. If x-35r dx = k. 5r +c, then find the value of k. Ify px +/a'p'+b , where p =,then fid the sum of degree and order. dy [2 (21 Q7. if tan Q8. [4) a, prove that x' =sin2 a. a) Find the intervals in which f(x) = Strictly increasing (4] x-5x + 24x + 12 is ii) strictly decreasing b) Find the equation of tangent and normal to the curve Vx +tJy=a at (a'/4,a/4). O9. Evaluate , [4] [(4] dx Or Evaluate ,dx Q10. Solve the differential equation x(* -1)-1. [4) Q11. Shovw that the height of aclosed right circular cylinder ofgiven surface area and maximum volume equal to diameter of base. (6) Prove that the perimeter of a right angled triangle of given hypotanious is maximum when the triangle is isosceles. Q12, Evaluate Vtantd). [6] Q13. Evaluate loglsinx|dx. [6 Q 14. Solve the differential equation =owhen x=0, y=2. (1+sinz) (6] Or Show that the differential equation 2y e"'dx +(y -2xe")dy =0 is homogenous and find its solution ;given that x=0 when y=1. SECTIONB Q 15. Choose correct answer of and <ii> and give appropriate Answer from <ii> to <v>, a) <ii: (1X5=5] The area enclosed by y =x, y =1,y =3, and y-axis is: 2 b) 9/2 4 d) 3/2 The area enclosed by y=Cos X,-n/2s x< n/2 and x-axis is: a 1 b) 4 c) 2 d) <ii> What do you understand by oblique line. <iy> The area enclosed between the curves y=ax and x = ay (a>0) is 1, Then What is the value of a Find the coordinates of the point where y=|x + 4| meets the y-axis. Q 16. A) b) Determine the area enclosed between the curve y =4x -x and X-axis. Find the area of the curve y = x-5x + 6 and X- axis. (2) Q 18. Find the area enclosed by 4y = 3x and the line 2y =3x + 12. a) [4) Using integration,find the area bounded by the curvey - |x 1|And y =3- |x|. [4) Or b) Find the area of the region (x.y): y's4x and 4x' +4y's 9 ). Using the method of integration. SECTIONC Q 19. Choose correct answer of and <ii> and give appropriate Answer from to <y>. 3 c) Amonopolist's demand function is x = 60- p/5. What is the average revenue function: a) 300- 5x/2 b) 300 -5xc) 300-5x? <iij> Average profit P(*) x <0V> What is Break event point. d) 300x - 5/2 C(*) What does the given graph depicts. Quantity Q 20. a) In a factory it is found that total number of 'x' units produce in a day depend upon the number of workers 'n' and is obtained by the relation x= 5n Vn+5 .the demand function [2 of the productp=+x. determine marginal revenue function when X= 20. Or b) Given the M.C. and A.C. are equal. show that the total cost C is linear function of number of units (x) produced. Q21. The demand function of a particular commodity is p=15eW for Osxs8, where pis the price per unit and x is the number of units demanded. Determine the price and quantity for which total [4 revenue is maximum. Q 22. a) A product can be manufactured at a total cost C(x)=+100x +40. Where x is the number of units produced. the price at which each unit. Can be sold is p = (200 Determine the oroduction level x at which The profit is maximum. what is the price unit and total profit at the level of production? [4) Or b) The total cost of a product is C= a +bx + cx', where a, b 20 and c>0. Show that the average and marginal cost are equal at minimum average cost.

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