mm. class xii test-1 - deepak sir...mm. class xii test-25 by deepak sir 9811291604 all the best 1....

MM. CLASS XII TEST-1

By Deepak sir 9811291604 ALL THE BEST

Test class 12 : area under curve



TEST CLASS 12 :MET AND DET

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2

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4

5

6

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8



DO THE FOLLOWING EACH OF 4 MARKS



LPP (each of 6 marks)

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2

3

4

5

6



LPP ( 6 marks each)

1

2

3

4

5



1

2

3

4

5

6



1

2

3

4

5

6

7



1,2

3

4

5

6

7

8

9

10

Do differentiation of following. Each q is of 5 marks



1

2

3

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5

6

7

8

9

10



Class 12 mixed

Q1. Solve following

6. xy = ex-y show that

( ) 7.solve

8 . solve x dy – y dx = √ dx

9. show that cuve 2x =y2 and 2xy =k cut at right angle if k2=8.

10. 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

(√ ) ( √ ) (√ )

12.find the point on the on cuve y2=2x which is at a minimum distance from the point (1,4) (2,2)

13 find the area of smaller region bounded by the ellipse x2/16 + y2 /9 =1 and x/4 + y/3 =1 [3(π-2)]

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

log 𝑥

𝑥 𝑑𝑥

0

[( 𝑠𝑖𝑛3𝑥) ÷ (3𝑥 cos 3𝑥)] 𝑑𝑥

1/3 log I 3x-cos3xI +c

[ √(𝑥 𝑎)(𝑥 𝑏)] 𝑑𝑥

logI{x-{a+b/2)}+ √(x-a+b/2)2 – (a-b/2)2 I

4 √𝑡𝑎𝑛𝑥 √𝑐𝑜𝑡𝑥)𝜋

0 dx

π√

5 ( 𝑥 3𝑥 5)3

dx

118/3

Y= ½(sinx –cox)+ c𝑒𝑥 , y +√𝑥 𝑦 = cx2



Class 12:test-VECTOR



CLASS 12: TEST-VECTOR2



CLASS 12 MIXED 4 MARKS



emit ,derivative and AOD



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 2cm/min. when x = 10cmand y = 6cm, find the ratio of change of (a) the

perimeter (b) the area of the rectangle. [4]

2. Find the interval in which the function of given by f(x) = 4x3– 6x2 – 72x + 30 is (a) strictly

increasing () strictly decreasing.[4]

3. Find point on the curve2 214 25x y+ = at which the tangents are (i) parallel to x –axis (ii)

parallel to y – axis[4]

4. Use differentiate to approximate ( )1325[4]

5. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 827

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 2 3 2 32 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 28m 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



1. Evaluate : Cos ))2

3(

3( 1 Sin

2. IkAAifkfindthenAIf 2,24

232

3. If

2dy sin (a y)sin y xsin (a y), show that .

dx sin a

4. If2

1 2 2

2

d y dyy sin (msin x), show that (1 x ) x m y 0.

dxdx

5. 32

3 3

0

sin.

sin cosx

x x

6. 4

3

0

tan . x dx

7. Show that function y = bex + ce2x is a solution of the differential equation

2

23 2 0.

d y dyy

dxdx

8. Using differentials, find the approximate value of 3 0.009 .

9. A wire of length 28 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

10. If 1 1 1tan x tan y tan z , show that x y z xyz.

11. Find the inverse of the following matrix using elementary transformation

1 2 3

A 2 3 2

3 3 4

and hence solve the following system of linear equations:

x 2y 3z 4

2 x 3y 2z 2

3x 3y 4z 11.

12. Two tailors A and B earn Rs. 15 and Rs. 20 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 32 pants at a minimum labour cost? Solve it by graphical method.



TIME:2 HOURS MARKS 420=80

Evaluate the following Integrals :-

1.

dxxx

xx22

22

cossin3

cos7sin5 2.

dx

x

xn

1

3.

dxx

xx

2sin

sincos 4.

dx

x

xx

)1(2

12

24

5. dxx

x

4sin

sin 6.

dxx

xxx

2

2tan

1

25

1

7.

dx

x

xx

94

23

8.

dx

x

xe x

2cos1

2sin2

9.

dx

ax

ax

)sin(

)sin( 10 dxxx 14

11. dxxxx 26)56( 12. dx

xx 2log

1

log

1

13. dxxx

x

cos.sin

tan 14.

dx

xx

x

6sin

6sin

2sin

15. dx

xx

x

124 16. dxxxSin 103 cos.

17.

dx

xx

xx

2

)2)(1(2

3

18. dx

bxax )sin()sin(

1

19.

dxx

ax

cos

)cos( 20.

dxxx sin3cos4

1

mm. class xii test-1 - deepak sir...mm. class xii test-25 by deepak sir 9811291604 all the best 1....

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