**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 : sec^{2}(tan^{-1}2)+cosec^{2}(cot^{-1}3)

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

**Q4.** Evaluate the following Integrals:

**(i). **** (ii). **

**Q5.** Differentiate by first principle:- (i) (ii)

**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

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

**Q9.**

**Q10.** Check the monotonocity i.e. increasing & decreasing of .

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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

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

**Q14.** Solve for x : .

**Q15.** At what points on the curve,is the tangent parallel to y-axis?

**Q16.** **If , find at .**

**Q17.** If x,y,z are different and A==0, then show that 1+xyz=0.

**Q18.** Solve the differential equation : .

**Q19.** Verify mean value theorem for f(x) =x(x-1)(x-2) in the interval .

**Q20.** Evaluate the following Integrals:

(i). (ii). (iii).

**Q21.** Find the equations of the tangent and the normal to the curve 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

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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 = .

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

(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 .