3<\/sup>\/sec. Find the rate at which the radius of the balloon is increasing when its radius is 15 cm.<\/p>\nQuestion 8. \nIf the function f(x) is differentiable at x = 2, then find the value of a and b. \n <\/p>\n
Question 9. \nFind the vector and the cartesian equation of the line that passes through the origin and (5, -2, 3).<\/p>\n
Question 10. \nIf P(A) = 0.8, P(B) = 0.5, P(B|A) = 0.4, then find P(A \u222a B).<\/p>\n
Question 11. \nOne kind of cake requires 200 gm of flour and 25 gm of fat and another kind of cake requires 100 gm of flour and 50 gm of fat. Make an LPP to find the maximum number of cakes made from 5 kg of flour and 1 kg of fat.<\/p>\n
Question 12. \nEvaluate \\(\\int _{ 0 }^{ 2 }{ { \\left[ x \\right] }^{ 2 } } dx\\)<\/p>\n
SECTION C<\/strong><\/p>\nQuestion 13. \n <\/p>\n
Question 14. \n <\/p>\n
Question 15. \nDifferentiate (xcosx)x + (xsinx)1\/x<\/sup> w.r.t. x.<\/p>\nQuestion 16. \n <\/p>\n
Question 17. \n <\/p>\n
Question 18. \n <\/p>\n
Question 19. \n <\/p>\n
Question 20. \n <\/p>\n
Question 21. \nTwo persons A and B thrown die alternately till one of them gets a ‘three’ and wins the game. Find their respective probability of winning if A begins.<\/p>\n
Question 22. \n12 cards numbered 1 to 12 are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number. Write any two values which are reflected in the bright students, report card?<\/p>\n
Question 23. \nSolve the following L.P.P. graphically. \nMaximise profit Z = \u20b9 (80x + 120y) \nSubject to constraints are \n9x + 12y \u2264 180 \n1x + 3y \u2264 30 \nx, y \u2265 0<\/p>\n
SECTION D<\/strong><\/p>\nQuestion 24. \nLet L be the set of all lines in the XY plane and R be the relation on L defined as R = {(L1<\/sub>, L2<\/sub>) : L1<\/sub> is parallel to L2<\/sub>}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4. \nOR<\/strong> \nLet * be the binary operation on N given by a * b = LCM of a and b. Find \n(i) 5 * 7 \n(if) 20 * 16 \n(Hi) Is * commutative? \n(iv) Is * associative? \n(v) Find the identity of * in N. \n(vi) Which element of N is invertible for operation * ?<\/p>\nQuestion 25. \nUsing the method of integration find the area of the circle x2<\/sup> + y2<\/sup> = 16 exterior to the parabola y2<\/sup> = 6x. \nOR<\/strong> \n <\/p>\nQuestion 26. \nShow that the general solution of the differential equation \\(\\frac { dy }{ dx } +\\frac { { y }^{ 2 }+y+1 }{ { x }^{ 2 }+x+1 } =0\\) is given by (x + y + 1) = A (1 – x – y – 2xy) where A is a parameter.<\/p>\n
Question 27. \nFind the length and the foot of the perpendicular from the point P(7, 14, 5) to the plane 2x + 4y – z = 2. Also find the image of point P in the plane. \nOR<\/strong> \nA line makes an angle \u03b1, \u03b2, \u03b3, \u03b4 with four diagonals of a cube prove that \\({ cos }^{ 2 }\\alpha +{ cos }^{ 2 }\\beta +{ cos }^{ 2 }\\gamma +{ cos }^{ 2 }\\delta =\\frac { 4 }{ 3 }\\)<\/p>\nQuestion 28. \nThe cost of 4 kg onion, 3 kg wheat and 2 kg rice is \u20b9 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is \u20b9 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is \u20b9 70. Find the cost of each item per kg by matrix method.<\/p>\n
Question 29. \nA helicopter is flying along the curve y = x2<\/sup> + 2. A soldier is placed at the point (3, 2). Find the nearest distance between the \nsoldier and the helicopter.<\/p>\nSolutions<\/strong><\/p>\nSolution 1. \n \nDirection ratio of a line parallel to PQ are 1, -6, 7<\/p>\n
Solution 2. \n\\(\\frac { 1 }{ 3a }\\) (ax + b)3<\/sup><\/p>\nSolution 3. \n \nHere L.H.L \u2260 R.H.L, so f(x) is not continuous at x = 0<\/p>\n
Solution 4. \n <\/p>\n
Solution 5. \n <\/p>\n
Solution 6. \n <\/p>\n
Solution 7. \n <\/p>\n
Solution 8. \n \nf(x) is differentiable at x = 2, so it is also continuous at x = 2 \nL.H.L = 4 \nR.H.L = 2a + b \n2a + b = 4 …….(2) \nFrom (1) and (2), \na = 4, b = -4<\/p>\n
Solution 9. \n <\/p>\n
Solution 10. \nP(A \u2229B) = P(A) P(B|A) = 0.32 \nP(A \u222a B) = P(A) + P(B) – P(A \u2229 B) = 0.98<\/p>\n
Solution 11. \nLet x number of cakes of one kind and number of cakes of other kind. \nObjective function is maximise Z = x + y \nSubject to constraints are \n200x + 100y \u2264 5000 \n25x + 50y \u2264 1000 \nx, y \u2265 0<\/p>\n
Solution 12. \n <\/p>\n
Solution 13. \n \n <\/p>\n
Solution 14. \nC1<\/sub> \u2192 C1<\/sub> + C2<\/sub> + C3<\/sub> \nTaking (a + x + y + z) common \nAfter this R1<\/sub> \u2192 R1<\/sub> – R2<\/sub>, R2<\/sub> \u2192 R2<\/sub> – R3<\/sub> and expand \nOR<\/strong> \nC1<\/sub> \u2192 C1<\/sub> + C2<\/sub> + C3<\/sub> \nTaking (5x + \u03bb) common \nAfter this R1<\/sub> \u2192 R1<\/sub> – R2<\/sub>, R2<\/sub> \u2192 R2<\/sub> – R3<\/sub> and expand<\/p>\nSolution 15. \n <\/p>\n
Solution 16. \n \n <\/p>\n
Solution 17. \n <\/p>\n
Solution 18. \n <\/p>\n
Solution 19. \n <\/p>\n
Solution 20. \n \n <\/p>\n
Solution 21. \nLet E : person A gets three \nF : person B gets three \n <\/p>\n
Solution 22. \nE : Number on the card drawn is even \nF : Number on the card drawn is more than 3. \nE = {2, 4, 6, 8, 10, 12}, F = {4, 5, 6, 7, 8, 9, 10, 11, 12} \nE \u2229 F = {4, 6, 8, 10, 12} \n \nValues in report card: Good performance through marks and punctuality through attendance.<\/p>\n
Solution 23. \n <\/p>\n
Solution 24. \nProve it is reflexive, Prove it is symmetric, Prove it is transitive. \nBecause it is reflexive, symmetric and transitive, so it is an equivalence relation. \nSet of lines related to the line y = 2x + 4 is y = 2x + k where k is any real number. \nOR<\/strong> \n(i) 5 * 7 = 35 \n(ii) 20 * 16 = 80 \n(iii) Prove * is commutative \n(iv) Prove * is associative \n(v) Identity of * in N = 1 \n(vi) Only the element 1 in N is invertible for the operation * because 1 * 1 = 1<\/p>\nSolution 25. \n \n <\/p>\n
Solution 26. \n \n <\/p>\n
Solution 27. \n \n <\/p>\n
Solution 28. \nLet price of 1 kg onion = \u20b9 x \nPrice of 1 kg wheat = \u20b9 y \nPrice of 1 kg rice = \u20b9 z \n4x + 3y + 2z = 60 \n2x + 4y + 6z = 90 \n6x + 2y + 3z = 70 \n <\/p>\n
Solution 29. \nLet P(x, y) be the position of helicopter and Q (3, 2) is of soldier \n <\/p>\n
We hope the CBSE Sample Papers for Class 12 Maths Paper 5 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 5, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"
CBSE Sample Papers for Class 12 Maths Paper 5 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 5. CBSE Sample Papers for Class 12 Maths Paper 5 Board CBSE Class XII Subject Maths Sample Paper Set Paper 5 Category CBSE Sample … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"\nCBSE Sample Papers for Class 12 Maths Paper 5 - CBSE Library<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n