SLIP TEST - 1 MATHEMATICS CHAPTER 7 & 8 XII STD MAX MARKS 50 TIME 1 HR 15 MINTS PART A

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1 SLIP TEST - MATHEMATICS CHAPTER 7 & 8 XII STD MAX MARKS 50 TIME HR 5 MINTS PART A [0] Answer all the questions Each question carries one mark. The area of the region bounded by the graph of y = sin x and y = cos x between x = 0 and x = π/4 is () + () (3) (4) +. Volume of solid obtained by revolving the area of the ellipse x = about major axes are in the ratio () b : a () a : b (3) a : b (4) b : a y a + b and minor 3. The volume of the solid obtained by revolving x + y = about the minor axis is 9 6 () 48π () 64π (3) 3π (4) 8π 4. The area of the ellipse x + y = is 9 6 ( ) 9π () 6π (3) π (4) 4π 5. xdx = () () 0 (3) 4 (4) 3 6. The differential equation satisfied by all the straight lines in xy plane is () dy =a constant () dx d y dx = 0 dy (3)y + = 0 dx (4) d y dx + y = 0 7. Integrating factor of dy dx + y = xlogx x is () e x () log x (3) x 8. (4)e x

2 . 0. A particular integral of (D 4D + 4) y = e x is () x ex () xe x (3) xe x (4) x e x PART B Answer any 5 questions x 5 =0 x 3 x. Evaluate : log dx 3 x x. Find the area of the region bounded by the line y+3=x, x= and x=5 3. Find the volume of the solid that results when the region enclosed by the given curve y=x 3,x=0, y= is revolved about the y axis x 4. Solve yx dx e dy 0 5. Solve 9 D 6D y 0 dy 6.Solve y x dx 7.Find the differential equation that will represent the family of all the circles having centers on the x axis and the radius is unity PART C Answer any 5 questions 3 x 5 =5. Derive the formula for the volume of a right circular cone with radius r and height h.find the area bounded by the curve y = sin x between the coordinates x= 0, x = and x axis 0. Evaluate. Evaluate sin x Cos 0 sin 4 x Cos xdx xdx. The normal lines to a given curve at each point, x y on the cure pass through the point, 0. The curve passes through the point,3 Formulate the differential equation representing the problem and hence find the equation of the curve.

3 3.Solve xdy ydx x y dx 4.Solve D 3D y e x PART D Answer any 3 questions 3 x 5 =5 5.Find the Total Length of the curve 3 3 x y a a OR Find the surface area of the solid generated by revolving the arc of the parabola y =4ax, bounded by its latus rectum about x - axis Solve dy x 3xy dx y 3x y dy 0 Solve sin x y dx 7. Show that the equation of the curve whose slope at any point is equal to y+x and which passes through the origin is y = OR OR Solve d y dy 3 3 y e x dx When x= log, y= 0 and when x= 0, y= 0 dx Prepared by G NARASIMHAN M.Sc., M.Ed., PGDCA. Retired H.M. J.G. National Higher Secondary School., East Tambaram, Chennai-59 Residential address : No. 40/8 Buddhar Street., East Tambaram, Chennai -59 Phone No

4 SLIP TEST 3 CHAPTER, 9 & 0 STD XII Max.Marks 5 TIME hr 5 min Part A Answer all the questions Each question carries mark x =. Find the rank of the diagonal matrix 0 4 [ 0 ] () 0 () (3) 3 (4) 5. μ = 0, μ = 76 for a discrete random variable X, then the mean of the random variable X is () 6 () 5 (3) (4) 3. is not a binary operation on Z 3 C 4 Q- { 4. In echelon form which of the following is incorrect? a) Every row of A which has all its entries O occurs below every row which has a non zero entry b) The first non - zero entry in each non zero row is c) The number of zeros before the first non -zero element in a row is less than the number of such zeros in the next row d) Two rows can have same number of zeros before the first non-zero entry 5. The distribution function F(X) of a random variable X is () a decreasing function () an increasing function (3) a constant function (4) increasing first and then decreasing 6. Which of the following is not a binary operation on R () a * b = ab () a * b = a b (3) a * b = ab (4) a * b = a + b 7. A monoid becomes a group if it also satisfies the () closure axiom () associative axiom (3) identity axiom (4) inverse axiom 8. A continuous random variable takes () only a finite number of values () all possible values between certain given limits (3) infinite number of values (4) a finite or countable number of values. In the multiplicative group of n th k roots of unity, the inverse, where k<n, is k.. 3. n k 4.. In the system of 3 linear equations with three unknowns, ( A) A, B n k = then the system

5 has unique solution reduces to equations and has infinitely many solutions 3reduces to single equation and has infinitely many solution 4 is inconsistent Part B Answer any five questions Each question carries marks x 5 =. State and Prove reversal law for inverses of matrices. Solve by rank method x- y + z =3; x+y-z=7 ; 3x+y = 3. Prove that the inverse of each element of a Group is unique 4. Show that the fourth roots of unity form an abelian group 5. The difference between mean and variance of a Binomial; distribution is and the difference between their squares is find n 6. In a Poisson Distribution Prove that the total probability is one 7.Use the truth table to determine whether the statement { (~p) v q ) v (p^(~q)) is a tautology Part C Answer any five questions Each question carries 3 marks 3 x 5 =5.Verify that T T A A for the matrix A= For what values of the equation x+y+3z =0,4x+3y+z=0, x+y+z=0 have a (i) trivial solution (ii) non trivial solution ( use rank method).show that the set of all matrices of the form a 0, ar-{0} forms an abelian group under matrix 0 0 multiplication..show that the set { [], [3], [4], [5], [9] } forms an abelian group under multiplication modulo. Find the order of all the elements of the Group [ Z 6, Marks in an aptitude test given to students of a school was found to be normally distributed % of the students scored below 4 marks and % of the students scored above marks Find the number of students scored betweenm 4 and 4. Obtain K, and of the normal distribution whose probability distribution function is given by

6 f(x) = k x 4x e, - <x< Part D Answer any 3 questions Each question carries 5 marks 3 x 5 =5 5. A small seminar hall can hold 00 chairs. Three different colour ( red, blue, and green) of chairs are available. The cost of a red chair is Rs. 40, cost of a blue chair is Rs.60 and the cost of a green chair is Rs. 300 The total cost of chair is Rs. 5,000 Find at least different solution of the number of chairs in each co lour to be purchased OR The mean weight of 500 male students in a certain college is 5 pounds and the standard deviation is 5 pounds Assuming the weights are normally distributed Find how many students (i) between 0 and 55 pounds (ii) more than 85 pounds Given that Z=.067 Z=.667 Z =.667 Area Area 0..6 Area An urn contains 4 white and 3 red balls. Find the probability distribution of number of red balls in three draws one by one from the urn with replacement without replacement OR Let G be the set of all rational numbers except and be defined on G by ab = a +b-ab for all a, b G Show that G, is an infinite abelian group 7. The number of accidents in a year involving taxi drivers in a city follows a Poisson Distribution with mean equal to 3. Out of taxi drivers find approximately the number of drivers with no accident in a year more than 3 accident in a year [ e -3 =.4 OR Using rank method, for what values of k has the system of equation k x + y + z=, x + k y +z=, x + y + k z= (i) unique solution? (ii) more than one solution (iii) no solution

Downloaded from MATHEMATICS ISC Question Paper XII (Commerce & Science Group) 2009 SECTION A

Downloaded from MATHEMATICS ISC Question Paper XII (Commerce & Science Group) 2009 SECTION A MATHEMATICS ISC Question Paper XII (Commerce & Science Group) 2009 General Instruction: (i). Candidates are allowed additional 15 minutes for only reading the paper. (ii). They must NOT start writing during