MM. CLASS XII TEST-1. Test class 12 : area under curve

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1 MM. CLASS XII TEST-1 Test class 1 : area under curve

2 MM. CLASS XII TEST- TEST CLASS 1 :MET AND DET

3 MM. CLASS XII TEST-3 DO THE FOLLOWING EACH OF 4 MARKS

4 MM. CLASS XII TEST-4 1 LPP (each of 6 marks)

5 MM. CLASS XII TEST-5 LPP ( 6 marks each)

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13 MM. CLASS XII TEST-13 Do differentiation of following. Each q is of 5 marks 1,

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15 MM. CLASS XII TEST-15 Q1. Solve following Class 1 mixed 0 log x x dx [( sin3x) (3x cos 3x)] dx 1/3 log I 3x-cos3xI +c [ (x a)(x b)] dx logi{x-{a+b/)}+ (x-a+b/) (a-b/) I π 4 tanx cotx) dx 0 π 3 5 ( x 3x 5) dx 118/3 6. x y = e x-y show that ( ) 7.solve 8. solve x dy y dx = dx Y= ½(sinx cox)+ ce x, y + x y = cx 9. show that cuve x =y and xy =k cut at right angle if k= F(x) = (x+1)3 (x-3)3 find interval in which function is increasing and decreasing ( in(1, ), de(-,1) 11find thg equation of tangent and the normal to thecureve x=1-cosө, y=ө sinө at Ө= π/4 ( ) ( ) ( ) 1.find the point on the on cuve y=x which is at a minimum distance from the point (1,4) (,) 13 find the area of smaller region bounded by the ellipse x/16 + y /9 =1 and x/4 + y/3 =1 [3(π-)] Q14.a right circuler cylinder is inscribed is inscribed in a right circler cone. show that the curve surface area of the cylinder is maximum when the diameter of cylinder is equal to the radius of the base of the cone

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18 MM. CLASS XII TEST-18 CLASS 1 MIXED 4 MARKS

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21 MM. CLASS XII TEST-1 emit,derivative and AOD

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24 MM. CLASS XII TEST-4 CBSE TEST PAPER-01 CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) Topic: - Application of Derivatives 1. The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y is increasing at the rate of cm/min. when x = 10cmand y = 6cm, find the ratio of change of (a) the perimeter (b) the area of the rectangle. [4]. Find the interval in which the function of given by f(x) = 4x3 6x 7x + 30 is (a) strictly increasing () strictly decreasing.[4] 3. Find point on the curve 14 5x y+ = at which the tangents are (i) parallel to x axis (ii) parallel to y axis[4] 4. Use differentiate to approximate ( )135[4] 5. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 87 of the volume of the sphere.[6] 6. The volume of a cube is increasing at a rate of 9cm3/s. How fast is the surface area increasing when the length of on edge is 10cm?[4] 7. Find the interval in which the function is strictly increasing and decreasing. (x+1)3(x-3)3[4] 8. Find the equations of the tangent and normal to curve 3 3 x y + = at (1, 1) [4] 9. IF the radius of a sphere is measured as 9cm with an error of 0.03cm, then find the approximate error in calculating its volume.[4] 10. A wire of length 8m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces to that the combined areas of the square and the circle is minimum

25 MM. CLASS XII TEST Evaluate : Cos ( Sin 1 ( )) 3 3. If A, then find k if A ka I 4 3. If sin y x sin (a y), dy sin (a y) show that. dx sin a 1 4. If y sin (msin x), d y dy show that (1 x ) x m y 0. dx dx sin x 3 3 sin x cos 3 tan x dx.. x 7. Show that function y = be x + ce x is a solution of the differential equation d y dy 3 y 0. dx dx 8. Using differentials, find the approximate value of A wire of length 8 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum If tan x tan y tan z, show that x y z xyz. 11. Find the inverse of the following matrix using elementary transformation 1 3 A and hence solve the following system of linear equations: x y 3z 4 x 3y z 3x 3y 4z Two tailors A and B earn Rs. 15 and Rs. 0 per day respectively. A can stitch 6 shirts and 4 pants while B can stitch 10 shirts and 4 pants per day. How many days shall each work if it is desired to produce at least 60 shirts and 3 pants at a minimum labour cost? Solve it by graphical method.

26 MM. CLASS XII TEST-6 TIME: HOURS MARKS 4 0=80 Evaluate the following Integrals :- 5sin x 7cos x 1. dx 3sin xcos x 1. x x n dx cos x sin x 3. dx sin x sin x 5. dx sin 4 x 4 x x 1 4. dx ( x 1) 1 x tan x x 6. 5 dx 1 x 3 x x 7. 4 x 9 dx 8. e sin x x dx 1 cos x sin( x a) 9. dx sin( x a) 4 10 x x 1 dx 11. ( 6x 5) 6 x x dx x x dx log log tan x 13. dx sin x.cos x sin x 14. dx sin x sin x 6 6 x dx 4 x x Sin x. cos x dx 3 ( x 1)( x ) 17. dx x x cos( x a) 19. dx cos x dx sin( x a)sin( x b) 1 0. dx 4cos x 3sin x

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