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http://www.cbseguess.com/ GUESS PAPER-2013 Class-XII Subject : - MATHEMATICS Section – A (10 x 1 = 10 marks) 1 1 1 sin 2 2 1. Find the value of tan 1 1 cos 1 2. On the set Q+ of all positive rational numbers a binary operation * is defined by a b ab 2 for all a,b Q+, Find the identity element. 1 3 2 3. Write the cofactors of the elements of the third row of the determinant 4 3 4. 5. 6. 1 2 5 2 3 2 1 0 and 2X+Y = 3 2 1 4 2 1 10 If x y , find the value of x and y. 3 1 5 Find X, if Y = Evaluate ex (tan x sec 2 x)dx tan1 x dx 3 7. Evaluate 8. In a triangle ABC, the sides AB and BC are represented by vectors 3i 2 j k ; and 3i 4 j 3k then find the vector represented by AC. 9. Find the intercepts made by the plane r (iˆ 3 jˆ kˆ ) 5 on the co-ordinate axes. (1 x2 ) 10. Find the angle between the lines x 1 y 2 z 3 x 2 y 1 z 2 = = and . 2 1 1 2 2 3 Section – B (12 x 4 = 48 marks) 11. (a)Let * be a binary operation on the set Q of rational numbers as follows: (i)a * b = a2 + b2, (ii) a * b = a+ab,. Which of these binary operation are commutative and which are associative. (OR) www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com|www.aipmtguess.com | www.aieeeguess.com | www.niosguess.com | www.iitguess.com http://www.cbseguess.com/ (b) Let * be a binary operation defined on NXN, by (a,b)*(c,d) = (ac, bd). Show that * is commutative and associative. Also find the identity element for * on NxN. a cos x b sin x (OR) b cos x a sin x 12. Simplify tan1 Solve the following equations simultaneously: sin1 x sin1 y abc c b c bc a a b a c ab 13. Show that 2 and cos 1 x cos 1 y 3 3 2(a b)(b c )(c a) 1 14. (a)Differentiate y (xcos x)x (x sin x) x w.r.t.x (b) If y x2 1 log 15. (OR) x2 1 x , Show that (x2 1) dy xy 1 0 dx 1 sin3 x ;x 2 2 3cos x Find the values of a and b if is continuous at x f(x) a ;x 4 2 b(1 sin x) ( 2x)2 ; x 2 16. Find the equation of the normals to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0 17. Evaluate 18. Solve cosx(1+cosy)dxsiny(1+sinx)dy=0. 19. x 20. Prove that [ a b b c c a ] 2[a b c ] (OR) x2 x 1 dx (x 2)(x 2 1) dy y x xy cot x 0; x 0 dx Let a ˆi ˆj, b 3ˆj kˆ and c 7iˆ kˆ find a vector d which perpendicular to a and b and also given c d 1. 21. Find the equation of the plane passing through the intersection of the planes 2x8y+4z = 3 and 3x5y+4z+10 = 0 and perpendicular to the plane 3xy2z4=0 22. If a fair coin is tossed 10 times, find the probability of (i) exactly six heads (ii) at least six heads (iii) at most six heads www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com|www.aipmtguess.com | www.aieeeguess.com | www.niosguess.com | www.iitguess.com http://www.cbseguess.com/ Section – C (7 x 6 = 42 marks) 23. 3 4 then, 1 1 Prove the following by principle of mathematical induction, If A 1 2n 4n An for every positive integer n 1 2n n 24. (a)An open tank with square base and vertical sides is to be constructed from metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half the width (OR) (b) Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cms 25. Evaluate cot x tan x dx 26. Find the area lying above the x-axis and included between the circle x2+y2=16 and the parabola y2=6x 27. Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black 28. There are two types of fertilisers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost? 29. Find the distance of the point (2,3,4) from the line x 2 2y 3 3z 4 measured parallel to 3 4 5 the plane 4x+12y3z+1 = 0. WISH YOU ALL THE BEST D. VASU RAJ, CHENNAI. www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com|www.aipmtguess.com | www.aieeeguess.com | www.niosguess.com | www.iitguess.com