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PADASALAI.NET- CENTUM COACHING TEAM 2017-18
XII MATHEMATICS
Marks: 200 Time: 3 hours
Part I Choose The Best Answer 40 x 1 = 40
1. If A is a matrix of order 3, then det(kA) is,
a) )Adet(k3 b) )Adet(k2 c) )Adet(k d) det (A)
2. Inverse of
25
13
is , a)
35
12
b)
31
52
c)
35
13 d)
21
53
3. If the equations –2x+y+z=l ; x-2y+z=m ; x+y-2z=n such that l+m+n = 0, then the system has a)
non-zero unique solution b) trivial solution
c) infinitely many solutions d) no solution
4. The area of the parallelogram having a diagonal kji3
and a side k4j3i
is,
a) 310 b) 306 c) 302
3 d) 303
5. If
PR = kji2
,
QS = k2j3i
then the area of the quadrilateral PQRS is
a) 35 b) 310 c) 2
35 d)
2
3
6. If ac,cb,ba
= 8 then c,b,a
is
a) 4 b) 16 c) 32 d) -4
7. If the magnitude of moment about the point kj
of a force kjai
acting through the point ji
is
8 then the value of a is
a) 1 b) 2 c) 3 d) 4
8. The following two lines 1
z
1
1y
2
1x
and
2
1z
5
1y
3
2x
are,
a) parallel b) intersecting c) skew d) perpendicular
9. If ia 3 and iz 32 then the points on the Argand diagram representing azaz 3, and az are
a) vertices of a right angled triangle b) vertices of an equilateral triangle
c) vertices of an isosceles triangle d) collinear
10. If 122 yx then the value of iyx
iyx
1
1 is a)
iyx b) x2 c)
iy2 d)
iyx
11. If z lies in the third quadrant then z lies in the quadrant
a) first quadrant b) second quadrant c) third quadrant d) fourth quadrant
12. The angle between the two tangents drawn from the point (-4, 4) to x16y2 is.
a) 45 b)
30 c) 60 d)
90
13. The asymptotes to the rectangular hyperbola 2cxy are.
a) cy,cx b) cy,0x c) 0y,cx d) 0y,0x
14. .The area of the triangle formed by the tangent at any point on the rectangular hyperbola xy = 72
and its asymptotes is.
a) 36 b) 18 c) 72 d) 144
15. The slope of the tangent to the curve xxy sin33 2 at 0x a) 3 b) 2 c) 1 d) -1
16. If the normal to the curve 323232 ayx makes an angle with the x axis then the slope of the
normal is. a) cot
b) tan c)tan
d) cot
17. If a normal makes at an angle with positive x axis then the slope of the curve at the point where
the normal is drawn is.
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a) cot
b) tan c)tan
d) cot
18. In which region the curve y² (a+x) = x² (3a-x) does not lie ?
a) x > 0 b) 0 < x < 3a. c) x < -a and x > 3a d) –a < x < 3a
19. The area of the region bounded by the graph of y = sin x and y = cos x between x = 0
and x = 4 is. a) 12 b)
12 c)
122 d)
222
20. The length of the arc of the curve x2/3 + y2/3 = 4 is.
a) 48 b) 24 c) 12 d) 96
21. The value of
2/
0 xcosxsin1
xcosxsin
dx is. a) 2
b) 0 c) 4
d)
22. The integrating factor of dx + xdy = e-y sec² y dy is…
a) ex. b) e-x. c) ey. d) e-y.
23. The differential equation of all circles with centre at the origin is.
a) x dy + y d x = 0 b) x dy – y d x = 0 c) x d x + y dy = 0 d) x d x – y d y =0
24. The P.I of (3D²+D-14) y = 13e2x is.. a) 26 x e2x. b) 13 x e2x. c) x e2x. d) x22
e2
x
25. The order of [7] in (Z9, +9) is…
a) 9 b) 6 c) 3 d) 1.
26. In the multiplicative group of nth roots of unity, the inverse of k is (k<n)
a) k1 b)
1 c) kn d)
kn
27. The number of rows in the truth table of ~ [ p ^ (~q) ] is.
a) 2 b) 4 c) 6 d) 8.
28. In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is
a) 5/3 b) 3/5 c) 5/9 d) 9/5
29. If f(x) is a p.d.f. of a normal distribution with mean then
dx)x(f is.
a) 1 b) 0.5 c) 0 d) 0.25
30. In 16 throws of a die getting an even number is considered a success. Then the variance of the
successes is. a) 4 b) 6 c) 2 d) 256
31. 115 12 is a) 55 b) 12 c) 7 d) 11
32. If X is a discrete random variable then which of the following is correct?
a) 10 xF
b) 0F
and 1F
c) 1 nnn xFxFxXP
d) xF
is a constant function
33. The solution of the linear differential equation QPydx
dy where P and Q are functions of x is a)
cdxQFIFIy .. b)
cdyQFIFIx ..
c) cdyQFIFIy ..
d) cdxQFIFIx ..
34.
dxxe mx 7
0
is a)
m
m
7
!
b)7
!7
m c)17
!
m
m
d)8
!7
m
35. The curve 22 21 xxy
has
a) an asymptote x = 1 b) an asymptote x = 2
c) two asymptotes x = 1 and x = 2 d) no asymptote
36. If 1Z and 2Z are complex numbers then which of the following is meaningful ?
a) 21 ZZ b) 21 ZZ
c) 21 ZZ d) 21 ZZ
37. 37. If4,3 vu
and 9 ba then ba is
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a) 73 b) 63 c) 69 d) 69
38. 38. The foot of a perpendicular from a focus of the hyperbola on an asymptote lies on the -----
a) Centre b) corresponding directrix c) vertex d) L.R.
39. 39. The focus of the parabola xy 82 is a) (0,-2) b) (0,2) c) (-2,0) d) (2,0)
40. Cramer’s rule is applicable only ( with three unknowns ) when
a) 0
b) 0
c) 0,0 x d) 0 zyx
Part II Answer Any 10 Of The Following Questions 10 X 6 = 60
Q.no 55 is compulsory
41. Solve. 1664;832 yxyx
42. For
544
434
221
A
show that 1 AA .
43. Prove that the area of a quadrilateral BDAC 2
1where AC and BD are its diagonals.
44. The mid point of the hypotenuse of a right angled triangle is equidistant from its vertices
45. If
61arg
z
and
321arg
zthen prove that 1z
46. Show that for any polynomial equation 0xP with real coefficients imaginary roots occur
in conjugate pairs.
47. It took 14 sec for a thermometer to rise from -19° C to 100°C when it was taken from a
freezer and placed in boiling water. Show that somewhere along the way the mercury was
rising at exactly 8.5 ° C / sec.
48. Prove that the function 12 xxxf is neither increasing nor decreasing in 1,0
49. The time of swing T of a pendulum is given by kT where k is a constant. Determine the
percentage error in the time of swing if the length of the pendulum / changes from 32.1 cm to 32.0 cm.
50. Find the volume of the solid that results when the ellipse
012
2
2
2
bab
y
a
x is revolved about the minor axis.
51. Solve : x
y
x
y
dx
dytan
52. Show that qpq ~ is a contradiction
53. Show that .,0R is an infinite abelian group. Here denotes usual multiplication.
54. A continuous random variable X has p.d.f. 23xxf , 10 x ,Find a and b such that.
(i) aXPaXP
and (ii) 05.0 bXP
55. The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months. (Or) Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a triangle of constant area.
Part III Answer Any 10 Of The Following Questions 10 X 10 = 100 Q.no 70 is compulsory
56. A bag contains 3 types of coins namely Re.1, Rs. 2 and Rs. 5. There are 30 coins
amounting to Rs. 100 in total. Find the number of coins in each category. 57. Derive the equation of the plane in the intercept form.( both in vector and cartesion form )
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58. Show that the lines0
1
1
1
3
1
zyx and
3
1
02
4
zyx intersect and hence find the
point of intersection
59. If 2sin2cos,2sin2cos ibia and 2sin2cos ic Prove that
(i) cos2
1
abcabc
(ii)
2cos2222
abc
cba
60. A cable of a suspension bridge is in the form of a parabola whose span is 40 mts. The road
way is 5 mts below the lowest point of the cable. If an extra support is provided across
the cable 30 mts above the ground level find the length of the support if the height of
the pillars are 55 mts.
61. Prove that the line 9125 yx touches the hyperbola 99 22 yx and find its point of
contact.
62. Assume that water issuing from the end of a horizontal pipe, 7.5m above the ground,
describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position 2.5m below the line of the pipe, the flow of water has curved outward 3m beyond the vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground?
63. Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2° / min. How fast is the length of third side increasing when the angle between the sides of fixed length is 60° ?
64. If veuw 2 where
y
xu and ,log xyv find
x
w
and
y
w
65. Find the area bounded by x-axis and an arch of the cycloid tayttax 2cos1,2sin2 .
66. Find the length of the curve 1
3232
a
y
a
x
67. For a postmortem report, a doctor requires to know approximately the time of death of the
deceased. He records the first temperature at 10.00 a.m. to be 93.4 ° F. After 2 hours he
finds the temperature to be 91.4° F. If the room temperature ( which is constant) is 72° F,
estimate the time of death. (Assume normal temperature of a human body to be 98.6° F).
19.4 26.6log 0.0426 2.303 log 0.00945 2.303
21.4 21.4e eand
68. Show that the set of all matrices of the form 0,00
0
Ra
aforms an abelian group
under matrix multiplication
69. The air pressure in a randomly selected tyre put on a certain model new car is normally
distributed with mean value 31 psi and standard deviation 0.2 psi.
(i) What is the probability that the pressure for a randomly selected tyre (a)
between 30.5 and 31.5 psi
(b) between 30 and 32 psi
(ii) What is the probability that the pressure for a randomly selected tyre exceeds 30.5
psi?
70. Find the cubic polynomial in x which attains its maximum value 4 and minimum value 0
at x = -1 and 1 respectively. (Or)
A closed (cuboid) box with a square base is to have a volume of 2000 c.c. The material for
the top and bottom of the box is to cost Rs. 3 per square cm. and the material for the sides
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is to cost Rs. 1.50 per square cm. If the cost of the materials is to be the least, find the
dimensions of the box
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MARY ANN MATRIC HIGHER SECONDARY SCHOOL
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