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CBSE Board Guess Paper Mathematics Class – XII (2010) [Set-3]

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CBSE Board Guess Paper - 2010

Class – XII

Mathematics

General Instructions:

(i) Question numbers 1 to 10 in section A are of 1 mark each.

(ii) Question numbers 11 to 22 in section B are of 4 marks each.

(iii) Question numbers 23 to 29 in section C are of 6 marks each.

(iv) All questions are compulsory.

Q1. From a well shuffled pack of 52 cards, 3 cards are drawn one-by-one with replacement. Find the probability distribution of number of queens.

Q2. Evaluate : sec2(tan-12)+cosec2(cot-13)

Q3. Write the equation of plane passing through (1,2,3) and perpendicular to line clip_image002 in vector form .

 

Q4. Evaluate the following Integrals:

(i).   clip_image002[5]         (ii).   clip_image002[7]

Q5. Differentiate by first principle:- (i)clip_image002[9]         (ii) clip_image004

Q6. Find the value of cos (sec–1 x + cosec–1 x), | x | ≥ 1

Q7. Find values of x for which the matrix is Singular clip_image002[13]

Q8. If a is unit vector and (x – a). (x + a) = 8, then find |x|.

Q9. clip_image002[15]

Q10. Check the monotonocity  i.e. increasing & decreasing of clip_image002[17].

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Section – B

Q11. Show that the value relation R in set of all integers I defined as R = {(a, b) : a+ b = even integer} is an equivalence relation.

Q12. Using properties of determinants, find the solutions of following

clip_image002[19]

Q13. If the function clip_image002[21] is continuous at x = 3 and x = 5, then find the value of a & b.

Q14. Solve for x : clip_image002[23].

Q15. At what points on the curveclip_image002[25],is the tangent parallel to y-axis?

Q16. If clip_image002[27], find clip_image004[5] at clip_image006.

Q17. If x,y,z are different and A=clip_image002[29]=0, then show that 1+xyz=0.

Q18. Solve the differential equation : clip_image002[31].

Q19. Verify mean value theorem for f(x) =x(x-1)(x-2) in the interval clip_image002[33].

Q20. Evaluate the following Integrals:

(i). clip_image002[35]    (ii). clip_image002[37]    (iii). clip_image002[39]

Q21. Find the equations of the tangent and the normal to the curve clip_image002[41] at the point whose x-coordinate is 3.

Q22. Find the distance of the point (1, ‐2, 3) from the plane x – y + z = 5 measured parallel to the line

                                                 clip_image002[43]

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Section – C

Q23. If the lengths of three sides of trapezium other than base are equal to 10 cm, then find the area of the trapezium when it is maximum.

Q24. Prove that clip_image002[45] = clip_image004[7]clip_image006[5].

Q25. Show that the volume of the greatest cylinder which can be inscribed in a cone of height hand semi-vertical angle α is 4/27 πh3 tan2 α.

Q26. Let X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that

 clip_image002[47]

(a) Find the value of k.

(b) What is the probability that you will get admission in exactly two colleges?

(c) Find the mean and variance of the probability distribution.

Q27. A company produces two types of goods A and B that require gold and silver. Each unit of A requires 1 g of silver and 2 g of gold. each unit of B requires 2 g of silver and 1 g of gold. The company has only 100 grams of silver and 80 grams of gold. Each unit of type A brings a profit of Rs. 500 and each unit of type B brings a profit of Rs. 400. Find the number of units of each type the company should produce to maximize the profit.

Q28. Using matrices solve the system of equations:

              x-4 y+ 7z=4 , 2x+3y- 5z=0 , x+ 5y-3z=3 .





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