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MM. CLASS XII TEST-1
By Deepak sir 9811291604 ALL THE BEST
Test class 12 : area under curve
MM. CLASS XII TEST-2
By Deepak sir 9811291604 ALL THE BEST
TEST CLASS 12 :MET AND DET
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MM. CLASS XII TEST-3
By Deepak sir 9811291604 ALL THE BEST
DO THE FOLLOWING EACH OF 4 MARKS
MM. CLASS XII TEST-4
By Deepak sir 9811291604 ALL THE BEST
LPP (each of 6 marks)
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MM. CLASS XII TEST-5
By Deepak sir 9811291604 ALL THE BEST
LPP ( 6 marks each)
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MM. CLASS XII TEST-6
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-7
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-8
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-9
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-10
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-11
By Deepak sir 9811291604 ALL THE BEST
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MM. CLASS XII TEST-12
By Deepak sir 9811291604 ALL THE BEST
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MM. CLASS XII TEST-13
By Deepak sir 9811291604 ALL THE BEST
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Do differentiation of following. Each q is of 5 marks
MM. CLASS XII TEST-14
By Deepak sir 9811291604 ALL THE BEST
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MM. CLASS XII TEST-15
By Deepak sir 9811291604 ALL THE BEST
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
MM. CLASS XII TEST-16
By Deepak sir 9811291604 ALL THE BEST
Class 12:test-VECTOR
MM. CLASS XII TEST-17
By Deepak sir 9811291604 ALL THE BEST
CLASS 12: TEST-VECTOR2
MM. CLASS XII TEST-18
By Deepak sir 9811291604 ALL THE BEST
CLASS 12 MIXED 4 MARKS
MM. CLASS XII TEST-19
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-20
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-21
By Deepak sir 9811291604 ALL THE BEST
emit ,derivative and AOD
MM. CLASS XII TEST-22
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-23
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-24
By Deepak sir 9811291604 ALL THE BEST
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
MM. CLASS XII TEST-25
By Deepak sir 9811291604 ALL THE BEST
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.
MM. CLASS XII TEST-26
By Deepak sir 9811291604 ALL THE BEST
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-27
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-28
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-29
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-30
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-31
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-32
By Deepak sir 9811291604 ALL THE BEST
MM. CLASS XII TEST-33
By Deepak sir 9811291604 ALL THE BEST
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