Cbse 12 Class Maths Sample Paper Model 5


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Cbse 12 Class Maths Sample Paper Model 5

  1. 1. MATHEMATICS SAMPLE TEST PAPER CLASS XII Class:12 Max Mks:100 Time 3hrs No of pages: 4 Ò 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 .e Question number 1 to 10 carry 1 mark each w w 1. Show that the functions f:R→R given by f(x) = x3 is injective. 2. Find the value of sin-1x = y when 0<y<π w 3. Find the value of x,y an d z in from the following equations. 4. Find the derivative with respect to x sec(tan√x) 5. The radius of an air bubble increasing at the rate of 5cm/s. At what rate is the volume of the bubble increasing when the radius is 2cm. 6. Find the area between the curve y=x and y = x2 7. Find the direction cosine of the ides of the triangle whose vertices are (3,5,-4) ,(-1,1,2) and (-5,5,-2) 8. Evaluate sin-1(sin1000)+cos-1(cos1000) 9. f(x) = e2log(sinx) then find f' (π/4)
  2. 2. 10. Find the amplitude of the number (1+cos Ө+isin Ө) SECTION B Question numbers 11 to 22 carry 4 marks each. x 11. show that the function f:R→{xέ R:-1<X<1} defined by f(x) = (1+∣ x∣) , x belongs to R is one and onto function rit e. co m 12. Simplify du 13. Write the Minors and Co factors of the determinant .e or w w w Given A , show that A2-5A+7I = 0. Hence find A-1 dy 14. Without eliminating the parameter find dx x = cos θ -cos2θ , y= sin θ -sin2θ or x = 5at3, y = 2at2+6t 15. Find the equation of the tangent and normal to the hyperbola 16. Evaluate: limit 0-π/2 or √ sinx √ dx cosx √sinx + √ x 2 a 2 - y 2 b 2 =1 at the point (x0,y0)
  3. 3. Evaluate: limit a-0 √ √x dx a− √x + √ x 17. Find the area enclosed between the parabola y2 = 4ax and the line y = mx dy x + 1 18. Find the differential solution of the differential equation dx = 2− y ,y# 2 or dy Find the general solution of: dx =(1+x)2 (1+y)2 i k i k 19. Two adjacent sides of a parallelogram are 2 ⃗ -4 ⃗j +4 ⃗ and ⃗ -2 ⃗j -3 ⃗ , find the unit vector r i 20. Find the shortest distance between the lines whose vector equation are ⃗ = (1-t) ⃗ +(t-2) ⃗j +(3- parallel to its diagonal. Also find its area. rit e. co m r i k k 2t) ⃗ and re ⃗ = (s+1) ⃗ +(2s-1) ⃗j -(2s+1) ⃗ 21. A company manufactures two types of novelly souvenirs made of plywood. Souvenirs of type A require 5 mint each for cutting and 10 mint each for assembling. Souvenirs of type B requires 8 mint each for cutting 8 mint and 8 mint for assembling. The profit is Rs 5 each for du type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the .e company manufactures in order to maximize the profit ? 22. A and b throw a die alternately till one of them gets a '6' and wins the game . Find their w SECTION C w w respective probability of winning , if A starts first. Question numbers 23 to 29 carry 6 marks each. 1+ √ x 2− 1 23. Write the function in simplest form tan-1 x or √ 1− cosx Write the function in simplest form tan-1 1+ cosx ,x<π ,x#0
  4. 4. 24. If A = , prove that A3-6A2+7A+2I = 0 25. Solve system of linear equations, using matrix method 2x+3y+3z = 5 x-2y+z = - 4 rit e. co m 3x-y-2z = 3 sinx 26. Differentiate with respect to x tan-1 1+ cosx 27. Find tanx ∫ ( √cotx+ √ dx) 28. Find the equation of the plane through the line of intersection of the planes x+y+z = 1 and 2x+3y+4z = 5 which is perpendicular to the plane x-y+z = 0. 29. A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture du contains at least 10 units of vitamins A,12 units of vitamin B and 8 units of vitamin C. The .e vitamin content of 1 kg food is below. 1 kg of food X costs Rs 16 and 1 kg of food Y costs Rs w w w 20.Find the least cost of mixture which will produce the required diet?