Mathematics Mock Test XII for March 0 Exams Series PRACTICE Code No. 65/I Candidates must write the set code Roll No. on the title page of the answer book MATHEMATICS TIME:HR. M.MARKS: 00 cbsemathspapers.com CBSE Maths Sample Papers, Mock Tests, Interactive online Tests, Syllabus etc. cbseresults0.com Previous Years CBSE Results X, XII & AIEEE thecareerhunt.biz Placements, Web Advertisements
Mathematics Mock Test XII for March 0 Exams Section A Questions to 0 carry mark each.. If R and S are reflexive relations, defined on set A, prove that R S is also a reflexive relation.. Find the principal value of cos.. If A 0 and B 0 5 0 4. If be the cube root of unity, show that 4 5. If A 0, find adj A. 4 5 6. Evaluate dx x, verify T T T AB B A 0 cbse.biz CBSE Mathematics Sample Papers, Mock Tests, Interactive Tests, Syllabus etc. cbseresults00.com Previous Years CBSE Results X, XII & AIEEE thecareerhunt.biz Placements, Web Advertisements
Mathematics Mock Test XII for March 0 Exams 0 05 7. Find 8. If a b c 0 sin x x dx, show that a b b c c a. 9. If a is a unit vector and x a x a 8, then find x. 0. Find the point of intersection of the line x y z and the plane x y z 5 5. Show that the function f : R R find the inverse of f. Section B Questions to carry 4 mark each., defined by x y x y. Prove that tan sin cos, xy x y. xy 5 Prove that tan sec tan. 5 7 8 4. Using properties of determinants, prove that x f x, x R is one one onto. Also x x y y z z = x yy zz x cbsemathspapers.com CBSE Maths Sample Papers, Mock Tests, Interactive online Tests, Syllabus etc. cbseresults0.com Previous Years CBSE Results X, XII & AIEEE thecareerhunt.biz Placements, Web Advertisements
Mathematics Mock Test XII for March 0 Exams 4. Differentiate tan x with respect to x, ab initio. If x a cos sin ; y a sin cos, find d y dx 5. Discuss the continuity of the function : f x x e, x x e, x at x = 6. For the function f x x 6x, find the intervals in which f x ii decreases. i increases and From a cylindrical drum containing oil and kept vertical, the oil is leaking at the rate of 0cm / sec.if the radius of the drum is 0 cm and height 50 cm. find the rate at which level of oil is changing when oil level is 0 cm. x 7. Evaluate 4 dx x 4
Mathematics Mock Test XII for March 0 Exams Evaluate tan x cot x dx 8. Find the point at which the function f(x) = x + x is continuous. 9. Solve the differential equation x y dx xydy 0, given that y = when x =. Solve the differential equation dy y cos x dx. 0. The position vectors of the points A, B, C and D arei j k, i j 4k, i j k, 4i 5j k respectively. If the points A, B, C and D are coplanar, find the value of.. A variable plane which remains at a constant distance p from the origin, cut co-ordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is x y z p. The probabilities of A,B,C solving a problem are, and respectively. If all the three 7 8 try to solve the problem simultaneously, find the probability that (i) the problem is solved. (ii) exactly one of them solves the problem. Section C Questions to 9 carry 6 mark each.. Solve the equations by finding A -, x y z 6, x y z, x y z. 4. Show that the cone of greatest volume which can be inscribed in a given sphere is such that three times, its altitude is twice the diameter of the sphere. Find the volume of the largest cone inscribed in a sphere of radius R. 5
Mathematics Mock Test XII for March 0 Exams 4 log 5. Evaluate tan x dx 0 Evaluate x dx as a limit of sum. 6. Find the area of the smaller part of the circle x y a cut off by the line x a 7. Find the distance of the point,, from the plane x y z 5, measured parallel to x y z 6 8. A and B throw alternately a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. Find their respective chance of winning, if A begins. 9. If a young man rides his motorcycle at 5 kmph, he has to spend ` per km on petrol, if he rides at a faster speed of 40 kmph, the petrol cost increases to `5 per km. He has `00 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour, Express as L.P.P and solve it. Paper Sent by Pawan Kumar, St. Joseph s Convent School, Bathinda 6