Title cblemapl03.pdf ✅

CBSE Maths Class 12 Sample Paper 3 Solutions Page 1 Sample Paper 3 Solutions Mathematics (Code-041) Class XII Session 2023-24 Time Allowed: 3 Hours Maximum Marks : 80 General Instructions : 1. This Question Paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are internal choices in some questions. 2. Section A has 18 MCQs and 02 Assertion-Reason based questions of 1 mark each. 3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each. 4. Section C has 6 Short Answer (SA)-type questions of 3 marks each. 5. Section D has 4 Long Answer (LA)-type questions of 5 marks each. 6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub- parts. Section - A Multiple Choice Questions each question carries 1 mark. 1. If = , 1 1x , then at x 2 is (a) 0 (b) 1 (c) (d) Ans : We have y = x Differentiating w.r.t. x , we get x = $ $ x x = x x 2 p p = = p Thus (d) is correct option. 2. The function is (a) decreasing (b) increasing (c) neither decreasing nor increasing (d) none of the above Ans : (a) decreasing Let x On differentiating, we get l Hence, is strictly decreasing function. Thus (a) is correct option. 3. The radius of a cylinder is increasing at the rate of 3m/s and its altitude is decreasing at the rate of 4m/s . The rate of change of volume when radius is 4m and altitude is 6m, is (a) (b) (c) (d) Ans : Let h and r be the height and radius of cylinder. Given that, = and Also, V 2 2 2 $ At r = and h = Thus (a) is correct option. 4. # + is equal to (a) + (b) + (c) + (d) + Ans : # + = # = # Thus (c) is correct option.
Page 2 Sample Paper 3 Solutions CBSE Maths Class 12 5. The value of # is (a) 2 (b) 0 (c) -2 (d) 4 Ans : # # # # # # # # = 4 Thus (d) is correct option. 6. The function , where b and c are real constants, describes (a) one-one mapping (b) onto mapping (c) not one-one but onto mapping (d) neither one-one nor onto mapping Ans : (d) neither one-one nor onto mapping Given function is 2 It is a quadratic equation in x . So, we will get a parabola either downward or upward. Hence, it is many-one mapping and not onto mapping. Hence, it is neither one-one nor onto mapping. Thus (d) is correct option. 7. If x # 1, which of the following four is different from the other three? (a) x - (b) x - (c) - x (d) x - x Ans : Now, x - x x Option (d) is different from the other three. Thus (d) is correct option. 8. If A is # matrix and B is a matrix such that ' and ' are both defined, then B is of the type (a) 4 4 # (b) # (c) # (d) 3 3 # Ans : Given, A is # matrix. So, A' is # matrix. Since, ' is defined, therefore B should be # . Also, ' is defined, so B should be # . Hence, B is the type # . Thus option (b) is correct. 9. If A is a matrix of order 3 such that = , then is equal to (a) 1 (b) 10 (c) 100 (d) I Ans : We have = I = I = 10 = A A = = where n is the order of square matrix A] Thus option (c) is correct. 10. If ! * is continuous at x = 0, then the value of k is (a) (b) (c) (d) Ans : We have ! * Now, " x x x = " x x x" # = = # # p p Also, f = 2k Since, is continuous at x = 0. f = " 2k p & k p = = Thus (b) is correct option. 11. The area of the region bounded by the lines = , x = 1, x = 2 and X -axis is 6 sq units, then m is
CBSE Maths Class 12 Sample Paper 3 Solutions Page 3 equal to (a) 3 (b) 1 (c) 2 (d) 4 Ans : Given, equation of line is = and bounded by x = 1, x = 2 and X -axis. Required area, A = # 6 = 6 m 6 = m = 4 Thus (d) is correct option. 12. Solution of is (a) (b) (c) (d) none of the above Ans : Here, P = x , Q = x = # x x Solution is, + # # # - # Thus (a) is correct option. 13. The equation of the curve, whose slope at any point different from origin is + , is (a) = ! (b) = (c) = (d) Ans : By the given condition 1 1 1 1 y = x y = Thus (a) is correct option. 14. The differential equation representing the family of curve , where c is positive perimeter, is of (a) order 1, degree 3 (b) order 2, degree 2 (c) degree 3, order 1 (d) degree 4, order 4 Ans : y 2 - = y y $ yy = y y Here, degree is 3 and order is 1. Thus (c) is correct option. 15. Let av and b v be two non-parallel unit vectors in a plane. If the vectors v v bisects the internal angle between av and b v, then is equal to (a) 1 (b) 1/2 (c) 4 (d) 2 Ans : Take = 1 v+ v bisects the internal angle between av and b v (Since, av and b v are unit vectors) Thus (a) is correct option. 16. If , , are the angles which a half ray makes with the positive directions of the axes, then + + is equal to (a) 2 (b) 1 (c) 0 (d) -1 Ans : Since, + + = 1 Hence, = 1