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CBSE Class 12 Pre Board 2020 : Mathematics (Kendriya Vidyalaya (KV) Agra)

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KENDRIYA VIDYALAYA SANGATHAN, AGRA REGION PRE BOARD QUESTION PAPER 2019-20 Class XII SET : H MATHEMATICS-040 Time: 3 Hrs. Maximum Marks: 80 General Instructions: (i) All the questions are compulsory. (ii) The question paper consists of 36 questions divided into 4 Sections A, B, C and D. (iii) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 6 questions of 4 marks each. Section D comprises of 4 questions of 6 marks each. (iv) There is no overall choice. However ,an internal choice has been provided In 3 questions of 1 marks each, two questions of 2 marks each , two questions of 4 marks each, two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. SECTION A 1 If f(x)=( ) The value of cot ( (a) 3 5 6 ) ( )( ) ( ) 1 ( ) 1 ) is (b) (b) If A is a 3-rowed square matrix and | | (d) 1 If A , B are symmetric matrices of same order, AB -BA is a 1 ( ) | |=? (a) 4 ( ( ) (a) 2 ( ) ( ) ( ) ( ) ( ) Symmetric matrix ( ) ( ) If A= * + and B=[ 1 ], then ( ) (b) ( ) ( ) The approximate change in the volume of a cube of side x meters caused by increasing the side by 3% is ( ) ( ) ( ) Page 1 of 4 ( ) 1 OR The points on the curve ,where the normal to the curve makes equal intercepts with the axes are (a) ( 7 ) | | (a) | | | | If | Let and ) ( ) ( ) (d) ( ( ) on is , then the projection of ( ) ) 1 ( ) (b) (2,1) (c) (2,3) is 1 (d) (-3,2) 1 is equal to (b) (c) (d) If A and B are any two events such that P(A)+P(B)-P(A and B)= P(A), then (a) P(B/A)=1 11 (c) ( The point which does not lie in the half plane 2x+3y-12 (a) 10 ( ) (a) (1,2) 9 ) | ( ) (a) 8 ( )( (b) P(A/B)=1 (c) P(B/A)=0 1 (d) P(A/B)=0 If P(A) = 0.4, P(B) = p , P(A U B)= 0.6 where A and B are independent events 1 then the value of p is .. 12 13 14 ( If x = a( ) Let A= | | then | If ( ).( ) 1 1 | = .| | )=0 and vector and are of same magnitude then 1 = 15 The degree of the differential equation ( 16 Find the distance (in units) between two planes 3x+5y+7z = 3 and ) ( ) 1 1 9x+15y+21z = 9 . 17 Evaluate 18 Write the Cartesian equation of a line parallel to x- axis and passing through 1 . 1 the origin. 19 1 Evaluate : OR Evaluate : 20 Evaluate ( )dx Page 2 of 4 SECTION B 21 For what value of k, the function f(x) = k (x+ sinx) +k is increasing? 2 OR Find the point at which the tangent of the curve y= has its slope 2/3 22 Find the value of k for which the function ( ) { is continuous at x= 23 Solve the equation: 24 If 2 ( 2 perpendicular to ) ( ) 2 such that is 2 then find the value of OR | = 40, | If | 25 |= 60 and | | , then find | |. A die is thrown 6 times. If getting an odd number is a success, then what is the 2 probability of 5 success? 26 Find the angle between the lines ( ( ) 2 ) SECTION C 27 There are three coins. One is a two headed coin ( having head on both faces), 4 another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows head. What is the probability that it was the two headed coin? 28 A dietician wishes to mix two types of food P and Q in such a way that the 4 vitamin contents of mixture contains at least 8 units of vitamin A and 11 units of vitamin B. Food P contains 3 units/kg of vitamin A and 5 units/kg of vitamin B. While food Q contains 4 units/kg of vitamin A and 2 units/kg of vitamin B. It costs Rs 60 per kg to purchase food P and Rs 80 per kg to purchase food Q. Determine the minimum cost of such a mixture. Formulate the above as a LPP and solve it graphically. 29 Show that the relation R in the Page 3 of 4 set Z of integers given by 4 R *( ) + is an equivalence relation 30 Evaluate using properties of Integration : 4 31 Solve the following differential equation 4 given that y=0 when x= OR Form the differential equation representing the family of ellipse whose foci is on x- axis and Centre at origin. 32 If ( ) 4 OR ) and y=a(sin2 If x=a(cos2 ) , find SECTION D 33 6 ]. Find If A=[ solve the system of equations. x+y+z=6 , x+2z= 7 , 3x+y+z = 12 OR Find the inverse of the following matrix using elementary transformation. A=[ 34 ] Using integration, find the area of triangle ABC, whose vertices are A (2,5), 6 B(4,7), C(6,2). OR Find the area of the region lying above X- axis and included between the circle 35 Find the equation of the plane which contains the line of intersection of the 6 plane ( ) ( perpendicular to the plane ( 36 ) and is ) Show that the altitude of a right circular cone of maximum volume that can be 6 inscribed in a sphere or radius R is Also find the maximum volume of the cone. END OF QUESTION PAPE Page 4 of 4

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