Cbse 12 Class Maths Sample Papers Model 4

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Cbse 12 Class Maths Sample Papers Model 4

  1. 1. MATHEMATICS SAMPLE TEST PAPER CLASS XII Class:12 Max Mks:100 Time 3hrs No of pages: 4 General Instructions: Ò All questions are compulsory. Ò The question paper consists of 29 questions divided into three sections - A, B and C. rit e. co m Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four marks each, Section C comprises of 7 questions of six marks each. Ò Internal choice has been provided in four marks question and six marks question. You have to attempt any one of the alternatives in all such questions Ò use of calculator not permitted.. du SECTION A Question number 1 to 10 carry 1 mark each .e 1. If f: R→R is defined by f(x) =x2-3x+2, find (f(x)) w w −1 −1 2. Find the value of cos-1 2 +sin-1 2 i a ij = j w 3. construct a 2X2 matrix A =a ij whose element are given by dy 4. Find dx for x3+x2y+xy2+y3 = 81 a i 6. Find a vector in the direction of vector ⃗ = ⃗ -2 ⃗j that has a magnitude of 9 units. 5. Find the approximate value o the number (54)1/2 7. Cartesian equation of a line is x− 5 y+ 4 z− 6 3 = 7 = 2 write its vector form. 9. compute P( ∣A∣ B), if P(B) = 0.5 and P(AnB) = 0.32 8. Find the distance of the plane 3x-4y+12z = 3 from the origin 10. Find the scalar components of the vector AB with initial point A(4,2) and terminal point B(-6,5)
  2. 2. SECTION B Question numbers 11 to 22 carry 4 marks each. 1− 11. Show that sin-1(2x √ x ) = 2sin-1x 2 12. compute the following : or rit e. co m compute the following .e du 13. By using the property of determinant show that = 0, if 0≤x≤1 = 4x, if x>1 w f(x) =2x, if x<0 w w 14. Find the continuity of the function f, where f is defined by or Explain the continuity of the functions f(x) = sin x + cos x 15. Differentiate with respect to x √ ( x− 3)( x 2 + 4) 3x2+ 4x+ 5 2 16. Find the equation of all lines having slope 2 and begins tangent to the curve y+ ( x − 4)2 = 0 or The radius of a circle is increasing uniformly at the rate of 5 cm/s. Find the rate at which the area of the circle is increasing when the radius is 20cm.
  3. 3. 17. Integrate ∫ ( sinx ) sin (x− a) dx or ∫ tan− 1( 1− x ) 1+ x dx 18. Find the area of region enclosed by the parabola x2=y, the line y = x+2 and the x – axis. dy 19. Find the general solution of equation (x+3y)2 dx = y (y>0) a i k b i k 20. Show that the points A,B and C with position vectors, ⃗ =3 ⃗ -4 ⃗j -4 ⃗ , ⃗ =3 ⃗ -4 ⃗j -4 ⃗ and c i ⃗ = ⃗ -3 ⃗j +5 ⃗ respectively from the vertices of a right angled triangle. k 21. Find the angle between the following pair of lines rit e. co m x− 2 y− 1 x+ 2 z+ 3 y− 4 z− 5 = 5 = − 3 and − 1 = 8 = 4 2 22. Find the coordinates of the point where the line through the points A (3,4,1) and B(5,1,6) crosses the XY-plane. SECTION C cosx −π du Question numbers 23 to 29 carry 6 marks each. π w w .e 23. Express tan-1 1− sinx , 2 <x< 2 in the simplest form. Or w 3 8 84 show that sin-1 5 -sin-1 17 = cos-1 85 24. Find the value of x and y from the following equation 25. Examine the consistency of the system of equation 5x-y+4z = 5 2x+3y+5z = 2 5x-2y+6z = -1
  4. 4. 26. a)Prove that the function given by f(x) = log cosx is strictly decreasing on(0,π /2) and strictly increasing on (π/2,π) b)Find the equation of the normal to the curve x2 = 4y which passes through the point (1,2) 27. One kind of cake requires 200g of flour and 25g of fat, and another kind of cake required 100g of flour and 1kg of fat assuming that there is no shortage of the other ingredients used in making the cakes 28. A die is thrown three times .Events A and B are defined as below A: 4 on third throw B:6 on the first probability of A given that B has already occurred. Find the probability of A given that B has already occurred. w w w .e du rit e. co m 29. show that the plane 2x+y+3z-2 – 0 and x-2y+5 = 0 are perpendicular to each other.

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