CBSE MATHS 2010 YEAR PAPER

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1 CBSE MATHS YEAR PAPER Important Instructions: (i) The question papers consists of three sections A B and C. (ii) All questions are compulsory. (iii) Internal choices have been provided in some questions. You have to attempt only one of the choices in such questions. (iv) Use of calculators is not permitted. However you may ask for logarithmic and statistical tables if required. (v) Questions with * are now OUT Of COURSE. SECTION A Question numbers to carry mark each. What is the range of the function () = (? ). What is the principal value of. If? A then for what of is A an identity matri?. What is the value of the determinant? log. Evaluate: d 6. What is the degree of the following differential equation? 6 dy d y d d 6y log. Write a vector of magnitude units in the direction of vector î ĵ kˆ. 8. Write the vector equation of the following line: 9. If k y then write the value of k. 6 z. What is the coe of the angle which the vector î ĵ kˆ makes with y-ais? Download more free practice papers at: Page of

2 SECTION B Question numbers to carry marks each. On a multiple choice eamination with three possible answers (out of which only one is correct) for each of the five questions what is the probability that a candidate would get four or more correct answers just by guesg?. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (a b) and (a b) respectively eternally in the ratio :. Also show that P is the mid-point of the line segment RQ.. Find the Cartesian equation of the plane pasg through the points A ( ) and B ( ) and y z parallel to the line.. Ug elementary row operations find the inverse of the following matri: Download more free practice papers at: Page of. Let Z be the set of all integers and R be the relation on Z defined as R = {(a b); a b Z and (a b) is divisible by.} Prove that R is an equivalence relation. 6. Prove that following: Prove the following: tan 6 6. Show that the function defined as follows is continuous = but not differentiable thereat: f () Find dy if y d 8. Evaluate: e d Evaluate: d ( ) / 9. Evaluate: d. / 6. Find the points on the curve y = at which the slope of the tangent is equal to the y-coordinate of the point. ()

3 . Find the general solution of the differential equation log dy d y log Find the particular solution of the differential equation satisfying the given conditions: dy y tan given that y = when =. d. Find the particular solution of the differential equation satisfying the given conditions: dy + (y + y ) d = SECTION C Question numbers to 9 carry 6 marks each. A small firm manufactures gold rings and chains. The total number of rings and chains manufactured per day is atmost. It takes hour to make a ring and minutes to make a chain. The maimum number of hours available per day is 6. If the profit on a ring is Rs and that on a chain is Rs 9 find the number of rings and chains that should be manufactured per day so as to earn the maimum profit. Make it as L.P.P. and solve it graphically.. A card from a pack of cards is lost. From the remaining cards of the pack two cards are drawn at random and are found to both clubs. Find the probability of the lost card being of clubs. From a lot of bulbs which includes defectives a sample of bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.. The points A( ) B ( ) and C( ) are three vertices of a parallelogram ABCD. Find the vector equations of the sides AB and BC and also find the coordinates of point D. 6. Ug integration find the area of the region bounded by the curve = y and the line = y.. Show that the right circular cylinder open at the top and of given surface area and maimum volume is such that its height is equal to the radius of the base. 8. Find the values of for which () = [( )] is an increag function. Also find the points on the curve where the tangent is parallel to -ais. 9. Ug properties of determinants show the following: (b ab ac c) (a ab bc c) (a ca bc b) Download more free practice papers at: Page of

4 ANSWERS. Range = { }.. = o. 8 (log ). c 6. Degree =. î ĵ kˆ 8. î ĵ 6kˆ î ĵ kˆ 9. k. The coe of angle which the given vector makes with y-ais is. a b hence point P is the mid point of the line segment RQ.. 9y z =. A 6. tan 6 6. () is continuous at = not differentiable at = 8. I = e cot + C 9. log log. Required points ( ) ( ) log. y log C y log = log + C y = sec C Download more free practice papers at: Page of

5 . y + =. P(). = y = z = Hence coordinates of D are ( ) 6. 9 sq units 8 8. required points are ( ) ( ) and ( ) Download more free practice papers at: Page of

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 MATHEMATICS Time allowed : hours Maimum Marks : General Instructions:. All questions are compulsory.. The question paper consists of 9 questions divided into three sections, A, B and C. Section A comprises