Title SAMPLE PAPER(2025) - 7.pdf ✅

Page 1 Sample Paper 07 CBSE Mathematics Class 12 Sample Paper 07 Class - 12th Exam - 2024 - 25 Mathematics (Code-041) Time : 3 Hours Max. Marks : 80 General Instructions : Read the following instructions very carefully and strictly follow them : 1. This Question paper contains 38 questions. All questions are compulsory. 2. This Question paper is divided into five Sections - A, B, C, D and E. 3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and 20 are Assertion-Reason based questions of 1 mark each. 4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks each. 5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each. 6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each. 7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each. 8. There is no overall choice. However, an internal choice has been provided some questions. 9. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. The function f x x x2 2 ^ h = − is increasing in the interval (a) x !- 1 (b) x $- 1 (c) x ! 1 (d) x $ 1 2. If x t at 1 2 = 3 + and ( ) y t at 1 2 3 2 2 = + , then dx dy is equal to (a) ax (b) a x2 2 (c) a x (d) a x 2 3. Which of the following is correct for the function f x( ) = sin2 1 x − at the point x = 0 and x π = (a) Continuous at x = 0, π (b) Discontinuous at x = 0 but continuous at x π = (c) Continuous at x = 0 but discontinuous at x π = (d) Discontinuous at x = 0, π 4. The minimum value of f x^ h= sin c x x os is (a) 2 1 (b) 2 1 - (c) 0 (d) 5
Page 2 Sample Paper 07 CBSE Mathematics Class 12 5. If R = {(33 66 , ), ( , ), (9 9, ), (12 12 , ), (6 1, )2 39 3 , ( , ), ( , ) 12 , (3 6, )} is a relation on the set A = { , 3 6, , 9 12}. Then, the relation is (a) an equivalence relation (b) reflexive and symmetric (c) reflexive and symmetric (d) only reflexive 6. If P A^ h = 0 5. , P B^ h = 0 4. and P A^ h k B = 0 3. , then ' P B A b l is equal to (a) 3 1 (b) 2 1 (c) 3 2 (d) 4 3 7. The value of sin cos2 5 1 3 - - ; E b l is (a) 25 24 (b) 25 24 - (c) 25 7 (d) none of these 8. sin cos sin x x x dx 2 2 2 2 + # is equal to (a) log s ( ) 1 in x C 2 − + + (b) log c ( ) 1 os x C 2 + + (c) log c ( ) 1 os x C 2 − + + (d) log t ( ) 1 an x C 2 + + 9. cos x dx 2 1 2 0 π + # is equal to (a) 0 (b) 2 (c) 4 (d) -2 10. If AB = A and BA = B , then B2 is equal to (a) B (b) A (c) -B (d) B3 11. The solution of e x 1 0 , ( y ) 3 dy dx / = + = , is (a) y x = log x x − + 2 (b) y x = ( )( ) + + 1 1 log x x − + 3 (c) y x = ( )( ) + + 1 1 log x x + + 3 (d) y x = log x x + + 3 12. The area of enclosed by y x = 3 5 − , y = 0, x = 3 and x = 5 is (a) 12 sq units (b) 13 sq units (c) 13 2 1 sq units (d) 14 sq units 13. ( ) x xy dy x( ) y dx 2 2 2 + = + is (a) log l x x og( )y x y = − + + c (b) log l x x og( )y x y = 2 − + + c (c) log l x x og( )y y x = − + + c (d) none of the above
Page 3 Sample Paper 07 CBSE Mathematics Class 12 14. The general solution of the differential equation x y ( ) 1 1 dx y x ( )dy 0 2 2 + + + = is (a) ( ) 1 1 x y ( ) 0 2 2 + + = (b) ( ) 1 1 x y ( ) c 2 2 + + = (c) ( ) 1 1 y c( ) x 2 2 + = + (d) ( ) 1 1 x c( ) y 2 2 + = + 15. If av and b v are position vectors of A and B respectively, then the position vector of a point C in AB produced such that AC = 3AB , is (a) 3a b v- v (b) 3b a v- v (c) 3 2 a b v- v (d) 3 2 b a v- v 16. If a i v = t t + j b, v = 2tj k − t and r a v v # # = b a, v v r b v# v= a b v# v, then r r v v is equal to (a) i j k 11 1 + − 3 t t t ` j (b) i j k 11 1 − + 3 t t t ` j (c) i j k 3 1 t t − + t ` j (d) none of these 17. The foot of the perpendicular from (0, 2, 3) to the line x y z 5 3 2 1 3 + 4 = = = + is (a) ( , - 2 3, )4 (b) ( , 2 1 - , )3 (c) ( , 2 3, ) - 1 (d) ( , 3 2, ) - 1 18. A mapping f n: " N , where N is the set of natural numbers is define as f n( ) , , for odd for even n n n 2 1 n 2 = + * for n N d . Then, f is (a) Surjective but not injective (b) Injective but not surjective (c) Bijective (d) neither injective nor surjective 19. Let A and B be two events associated with an experiment such that P A( ) k B = PAPB ( ) ( ) Assertion: P A( | B)= P A( ) and P B( | A P ) ( = B) Reason: P A( ) j B P = ( ) A P + ( ) B (a) Assertion is true, Reason is true; Reason is a correct explanation for Assertion. (b) Assertion is true, Reason is true; Reason is not a correct explanation for Assertion. (c) Assertion is true; Reason is false. (d) Assertion is false; Reason is true. 20. For any square matrix A with real number entries consider the following statements. Assertion: A A + l is a symmetric matrix. Reason: A A - l is a skew-symmetric matrix. (a) Assertion is true, Reason is true; Reason is a correct explanation for Assertion. (b) Assertion is true, Reason is true; Reason is not a correct explanation for Assertion. (c) Assertion is true; Reason is false. (d) Assertion is false; Reason is true.
Page 4 Sample Paper 07 CBSE Mathematics Class 12 Section - B This section comprises of very short answer type-questions (VSA) of 2 marks each. 21. What are the direction consines of a line which makes equal angles with the coordinate axes? 22. If A B = = { , 1 2, }3 4 , { , , 5 6, }7 and f = {(1 4, ), (2 5, ), (3 6, )} is a function from A to B . State whether f is one-one or not. 23. Two groups are computing for the positions of the Board of Directors of a corporation. The probabilities that the first and second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product introduced way by the second group. 24. Find a vector in the direction of vector 2 3 i j − + 6k t t t which has magnitude of 21 units. O Find the angle between X -axis and the vector i j + + k t t t. 25. Evaluate cos s( ) in x dx -1 # . O Write the anti-derivative of x x 3 1 c m + . Section - C This section comprises of short answer type questions (SA) of 3 marks each. 26. Find the area of a parallelogram whose adjacent sides represented by the vectors 2 3 i k t- t and 4 2 i k t+ t. 27. Using the principal values, write the value of cos sin 2 1 2 2 1 1 1 + − − b b l l. 28. If y x sin ( ) 6 1 9x 1 2 = − − , x 3 2 1 3 2 1 1 1 - , then find dx dy . O If ( ) cos c x y ( ) os y x = , then find dx dy . 29. If sin cos x sin cos x 1 x θ 1 8 θ θ θ − − = , write the value of x . 30. The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm. O Show that the function f x( ) 4 1 x x8 27 7 x 3 2 = − + − is always increasing on R.