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

ISC Class XII Board Exam 2026 : Mathematics

8 pages, 89 questions, 0 questions with responses, 0 total responses,

Abc
G. D. Birla Centre for Education (GDB), Kolkata
XII

+Fave Message

Profile Timeline Uploads

Home > sukanya0805 >

Formatting page ...

GLB/ Pre-Board Examination-2024 CLASS XII. F.M - 80 SUBJECT: MATHEMATICS. TIME 3HOURS. ... This question paper consist of three sections A, B and C. Candidate are required to attempt all questions from Section A and all questions either from Section B or C. Section A: Internal choice has been provided in two questions of two marks each, two questions four marks each and two questions 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, must be clearly shown and must be done on the same sheet as the rest of the answer. The intended marks for the questions or parts of questions are given in bracket [ ]. SECTION A [65 MARKS] Question 1 [1 15 = 15] In subparts, (i) to (x) choose the correct options and in subparts (xi) to (xv), answer the questions as instructed. (i) Assersion (A): Let A = 0 0 0 0 0 0 exists , it is also diagonal matrix. , then Reason (R) : If A is the diagonal matrix , then = (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (ii) The value of dx equals ( ) log + C (b) ( ) + C (c) ( ) + C (d) log ( ) ( ) + C (iii) If A and B are two independent events with P(A) = 0.3 and P(B) = 0.6, then find P(neither A nor B) (a) 0.28 (b) 0.34 (c) 0.25 (d) 0.37 4 3 3 (iv) The value of k , = is 0 1 4 (a) 4 (b) 4 (c) 3 (d) 0 | | |4 |=k| | (v) If A is a square matrix of order 3, 0 and , find k. (a) 27 (b) 9 (c) 64 (d) 16 (vi) If P(A) = , P(B) = and P(A B) = , find P Page 1 of 8 (a) (b) (c) (d) (vii) Matrix P is a skew symmetric matrix of odd order. Assertion (A): The inverse of matrix P does not exist. Reason (R): The determinant of matrix P is zero. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (viii) The value of (a) -2 (b) 0 if y= + at x=3 is: (c)2 (d) 4 (ix) Let a function f: N N be defined by f(x) = + x +1. Statement I: f is one one. Statement II: f is onto. (a) Both the Statements are true and Statement II is the correction explanation of Statement I. (b)Both the Statements are true and Statement II is not the correction explanation of StatementI. (c) Statement I is true, Statement II is false. (d) Statement I is false, Statement II is true. (x) A bag contains 4 red, 2 white and 3 blue balls. If three balls are drawn one by one (without replacement), then what is the probability that all three balls are red ? (a) (b) (c) (d) (xi) Given below are the graphs of f(x) along with the statements. Which one of the following statements is NOT correct about the graphs? (a) f(x) is neither continuous nor differentiable at x = 0 (b) f(x) is continuous and but not differentiable at x = 1 (c) f(x) is not continuous and differentiable at x = -1 (d) f(x) is neither continuous nor differentiable at x = 1 (xii) If f(x) = sin sin + sec , find (x) (xiii) Find the domain of the function: ( ) = sin + sin Page 2 of 8 (xiv) The function f : X Y is not invertible. State the reason. (xv) If + = 0, then find the value of x. Question 2. (a) The table below shows some of the values of differentiable functions u and v and their derivatives. [2] x u(x) ( ) v(x) ( ) 1 0 2 -1 5 2 4 5 3 2 3 2 -1 3 0 If r(x) = u(v(x)) , find ( ). OR (b) If + = 1 and 1, prove that Question 3. (a) Evaluate: (b) Evaluate : = [2] dx OR Question 4. [2] The equation of tangent at (2, 3) on the curve = a + b is y = 4x 5. Find the values of a and b. Question 5. [2] Prove that the function f : N N defined by f(x) = is one - one but not onto.. Question 6. [2] Solve the differential equation: = 1 + x + y + xy Question 7. [4] (a) Let, f(x) = + + + If and are the maximum and minimum values of f(x) then find ( + ) OR Page 3 of 8 (b) If = ( ), then prove that + tanx + y cos2x = 0 Question 8. If [4] . + + . + = S , then find S. OR -1 Solve for x: tan (x+1) + tan-1(x-1) = tan-1 Question 9. [4] ( ) (a) Evaluate: dx ( ) Question 10. [4] What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face? Question 11. [6] The sum of three numbers is 6. If we multiply third number by 3 and add second to it, we get 11. By adding first and third numbers, we get double the second number. Represent it algebraically and find the numbers using matrix method. Question 12. [6] (a) Evaluate: : dx OR (b) Solve the differential equation: [6] ( + ) = 4 2xy Question 13. The length of the perimeter of a slice of a pizza in the form of a sector of a circle is 20 cm. r be the radius of the circle, sectorial angle be radian and l be the length of the arc . Based on the above information, answer the following questions. (a) Express the radius of the sector is expressed in terms of sectorial angle be . (b) Let A be the area of the slice. Then express A in terms of r. (c) For the maximum value of A, find the value of the sectorial angle. (d) Find the maximum area of the slice of the pizza . OR (b) A printed page is to have a total area of 80 sq.cm with a margin of 1 cm at the top and on each side and a margin of 1.5 cm at the bottom. What should be the dimensions of the page so that the printed area will be maximum? Question 14. [6] Page 4 of 8 An insurance company insured 1500 scooter drivers, 2500 car drivers and 4500 truck drivers. The probability of a scooter, a car and a truck driver meeting with an accident is 0.01, 0.02 and 0.04 respectively. If one of the insured persons meets an accident, then find the probability that he is a scooter driver. SECTION B [15 MARKS] Question 15. [5] In subparts, (i) to (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. (i) Find the angle between the vectors If = and = - (a) (b) (c) (d) 120 60 90 None of these. (ii) If , and are the direction angles of a line, then find the value of (Sin2 + Sin2 + Sin2 ) (a) (b) (c) (d) 2 1 0 None of these. (iii) If and are perpendicular vectors, | | = 5 and + =13, find the value of (iv) Find the area of the parallelogram whose adjacent sides are given by the vectors = + 3 and = + . (v) If the distance of the point (k, 3, -5) to the plane x + 2y - 2z = 9 is 3, then find the value(s) of k. Question 16. [2] (a) If = + + , = 2 - + 3 and = - + , then find unit vectors parallel to the vector 2 - +3 OR (b) Find a vector of magnitude 5 units and parallel to the resultant of the vectors = 2 + - and = - 2 + Page 5 of 8 Question 17. [4] (a) The adjoining figure shows an air plant holder which is in the shape of a tetrahedron. Let A(1, 1, 1) , B(2, 1, 3) ,C(3, 2, 2) and D(3, 3, 4) be the vertices of air plant holder. Based on the above information, answer the following questions: (i) Find the area of the triangle ABC. (ii) Find the unit vector along . Question 18. Find the area of the region bounded by the curve x = 4y - and the y-axis. SECTION C [15 MARKS] Question 19. In subparts, (i) to (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. (i) (ii) (iii) [4] [5] If cost function for a certain commodity is C(x) = 3 + 4x - x2 , find the average variable cost when 4 items are produced (a) 4 (b) 1 (c) 3 (d) None of above Find the break-even points when R(x) = 50x x2 and C(x) = 5x + 350. (a) 15 or 5 (b) 10 or 35 (c) 20 or 10 (d) None of these. If the cost function of a firm given by C(x) = 3x2 - 2x + 50, where x is the output. Find the marginal cost for x = 2. (iv) If the two coefficients of regression are - and , find the coefficient of correlation. (v) Out of two regression lines, find the line of regression of Y on X: 3x + 12y = 8 and 9x + 3y = 5 Question 20. [2] (a) The total cost function for a production is given by C(x) = -7x +27. Find the number of units produced for which M.C = A.C OR Page 6 of 8 (b) The revenue function is given by R(x) = 100x - - . Find (i) the demand function (ii) the marginal revenue function. Question 21. [4] You are given the following data: x y Arithmetic Mean 36 85 Standard Deviation 11 8 Calculate (i) two regression coefficients (ii) two regression equations (iii) the most likely value of y when x = 10. Given correlation coefficient between x and y is 0.66 Question 22. [4] (a) A manufacturer manufactures two types of tea cups, A and B. Three machines are needed for their manufacturing and the time (in minutes) required for each cup on the machines is given below: Type of Cup Time in minutes Machine I Machine II Machine III A 12 18 6 B 6 0 9 Each machine is available for a maximum of 6 hours per day. If the profit on each cup of type A is Rs.1.50 and on each cup of type B is Rs.1.00. Show that 15 cups of type A and 30 cups of type B should be manufactured per day to get maximum profit. OR (b) The feasible region for an L.P.P is shown in the given figure below: Based on the given information, answer the following questions: (i) The equation of the line AD. (ii) The equation of the line BC. (iii) The constraints for the L.P.P. (iv) The maximum value of the objective function, Z = 3x +4y. Page 7 of 8 Page 8 of 8

Formatting page ...

Related ResPapers
ISC Class XII Board Exam 2023 : Mathematics
by mathematics28

ISC Class XII Board Exam 2025 : Mathematics
by preety15

ISC Class XII Board Exam 2019 : Mathematics
by fatherstretchmyhand

ISC Class XII Board Specimen 2024 : Mathematics
by fatherstretchmyhand

Formatting page ...

sukanya0805 chat

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