· 12.11.2018 · INSTRUCTIONS : 1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the hall supervisor immaditely. 2 ) Use Blue or black

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Padasalai.Nets Special Centum Coaching Team Question Paper

PART - III

MATHEMATICS

XII std ( ENGLISH VERSION)

TIME ALLOWED: 2.30 HRS (2018-2019) MAXIMUM MARKS: 90

INSTRUCTIONS : 1) Check the question paper for fairness of printing. If there is

any lack of fairness, inform the hall supervisor immaditely.

2 ) Use Blue or black link to write and pencil to draw diagrams

Part-A

NOTE : 1) Answer all the 20 questions

2) Choose the most suitable answer from the given four alternatives

and write the option code and the correspoinding answer.

20 x1=20

1) The rank of the matrix

12

17 is

a) 9 b) 2 c) 1 d) 5

2) If rA then which of the following is correct ?

a) all the minors of order r which does not vanish

b) A has atleast one minor of order r which does not vanish

c) A has atleast one (r+1) order minor which vanishes

d) all (r+1) and higher order minors should not vanish

3) Let vu , and w be vector such that 0 wvu

If 4,3 vu

and 5w

then uwwvvu is

a) 25 b) -25 c) 5 d) 5

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4) The non-parametric vector equation of a plane passing through three points whose P. Vs are cba ,, is a)

0 acabar b) 0bar c) 0cbr d) 0cba

5) If 1ZZ = 2ZZ then the locus of Z is

a) a circle with centre at the origin

b) a circle with centre at 1Z

c) a straight line passing through the origin

d) is a perpendicular bisector of the line joining 1Z and 2Z

6) The condition that the line 0 nmylx may be a tangent to the ellipse 1

2

2

2

2

b

y

a

xis

a) 22222 nmbla b) nlam 2 c) 22222 nmbla d)

224 nlmc

7) The distance time relationship of a moving body is given by y = F ( t ) then the acceleration of the body is the

a) gradient of the velocity / time graph b) gradient of the distance / time graph

c) gradient of the acceleration / distance graph d) gradient of the velocity / distance graph

8) In the following figure the curve y = f ( x ) is

a) concave upwards b) convex upward

c) changes from concavity to convexity d) changes from convexity and concavity

9) Identify the false statement:

a) all the stationary numbers are critical numbers b) at the stationary point the first derivative is zero

c) at critical numbers the first derivative need not exist d) all the critical numbers are stationary numbers

10) In the law of mean, the value of satisfies the condition

a) 0 b) 0 c) 1 d) 10

11) The differential of y if 124 xxy is

a) dxxx 21

324

2

1 b) dxxxxx 241

2

1 321

24

c) 21

324

2

1 xx d) xxxx 241

2

1 321

24

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12) The curve 22 bxaxy is symmetrical about

a) origin only b) y-axis only c) x-axis only d) both x and y-axis

13)

a

dxxf0

is

a) a

dxaxf0

b) a

dxxaf0

c) a

dxxaf0

2 d) a

dxaxf0

2

14)

b

a

dxxf

a) b

a

dxxf b) a

b

dxxf c) a

o

dxxf d) b

o

dxxf2

15)

The arc length of the curve y = f (x ) from x = a to x = b is

a) dxdx

dyb

a

2

1 b) dxdy

dxd

c

2

1 c) dxdx

dyy

b

a

2

12 d) dxdy

dxy

b

a

2

12

16) dxxIn

n cos then nI

a) 21 1

sincos1

n

nI

n

nxx

n b) 2

1 1sincos

n

nI

n

nxx

c) 21 1

sincos1

n

nI

n

nxx

n d) 2

1 1sincos

1

n

nI

n

nxx

n

17) The order and degree of the differential equations are

2

2

xdy

dxx

dx

dy

a) 2,2 b) 2,1 c) 1,2 d) 1,3

18) is a binary operation on

a) N b) R c) Z d) 0C

19) In 55 ,0 Z the order of 10 is

a) 1 b) 2 c) 3 d) 4

20) If X is a continuous random variable then which of the following is incorrect?

a) xfxF ' b) 0;1 FF

c) aFbFbxaP d) aFbFbxaP

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Part -B

7 x 2 =14

NOTE:: (i) Answer 7 questions.

(ii) Q.no 30 is compulsory .select any 6 question from first 9question.

21) Solve: 022;02;02 zyxzyxzyx

22) Find the angles which the vector kji 2 makes with the coordinate axes.

23) If 1,02 z find z.

24) Evaluate: x

x e

x2

lim

25) Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 1%

26) Evaluate a

dxxa0

22

27) Solve: 012 yDD

28) For the probability density function

0,0

0,22

x

xexf

x

, find F(2)

29) ) If 22

yxu , show that .uy

uy

x

ux

30) Find the equation of the parabola whose vertex is (1,2) and the equation of the latus rectum is x = 3.

Part c

Note:: (i) Answer any 7 question 7x3=21

(ii) Q.no 40 is compulsory. select any 6 question from first 9 question.

31) Find the adjoint of the matrix

53

21A and verify the result .A A )A adj ( )A adj (A

32) Find the meeting point of the line kjitkjir 232 and the plane 0732 zyx

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33) Solve : 010332256

234 xxxx given that one of the root is i2

34) The headlight of a motor vehicle is a parabolic reflector of diameter 12cm and depth 4cm. Find the position of

bulb on the axis of the reflector for effective functioning of the headlight.

35) If 22 zyxw and .;sin;cos tztytx Find

dt

dw.

36) Evaluate dxx

2

0

tanlog

37) Solve: 0

1

1 21

2

2

x

y

dx

dy

38) Use the truth table to determine whether the statement qpqP ~~ is a tautology.

39) The overall percentage of passes in a certain examination is 80. If 6 candidates appear in the examination what

is the probability that at least 5 pass the examination.

40) Determine for which values of x, the function 1,

1

2

x

x

xy is strictly increasing or strictly decreasing.

Part D 7 x 5 = 35

NOTE :: Anawer both the question choosing either of the alternatives.

41) Solve the equation 01

459 xxx

(or)

A cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed

horizontally. The distance between two towers if 1500ft, the points of support of the cable on the towers are 200ft

above the road way and the lowest point on the circle is 70ft above the roadway. Find the vertical distance to the

cable from a pole whose height is 122 ft.

42) Gravel is being dumped from a conveyor belt at a rate of 30 ft3 / min and its coarsened such that it forms a

pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the

pile increasing when the pile is 10 ft high? (or)

Find the surface area of the solid generated by revolving the arc of the parabola ,42

axy bounded by its latus

rectum about x - axis.

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43) A drug is excreted in a patients urine. The urine is monitored continuously using a catheter. A patient is

administered 10 mg of drug at time t = 0 , which is excreted at a Rate of 21

3t mg/h.

(i) What is the general equation for the amount of drug in the patient at time t > 0 ?

(ii) When will the patient be drug free? (or)

Obtain k , and 2

of the normal distribution whose probability distribution function is given by

.422

Xkexfxx

44) If and are the roots of 0422 xx Prove that Nn

ni

nnn

;

3sin2

1 and

deduct 99

(or)

Find the vector and Cartesian equation of the plane through the points (1,2,3) and (2,3,1) perpendicular to the plane

.05423 zyx

45) Investigate for what values of , the simultaneous equations

zyxzyxzyx 2,1032,6 have (i) no solution (ii) a unique solution and (iii) an

infinite number of solutions. (or) Find the area of the loop of the curve 223 axxay

46) Show that nnZ , forms group. (or) Using Eulers theorem prove the following :

If

yx

yxu

331

tan Prove that .2sin uy

uy

x

ux

47)Find the length of the curve 1

3232

a

y

a

x(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 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.

PREPARED BY

S. BALAKRISHNAN , M.SC, B.ED , (PG ASST IN MATHS)

SHRI MARUTHI HIGHER SECONDARY SCHOOL

V. MADEPALLI X-ROAD , VEPPANAPALLI

KRISHNAGIRI (DT) -635121

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ANSWER SCRIPTS SEND :

S. BALAKRISHNAN , M.SC, B.ED , (PG ASST IN MATHS)

S/0 B. SAMPANGIRAMAN (PWD)

V. MADEPALLI X-ROAD , VEPPANAPALLI

KRISHNAGIRI (DT) -635121

CONTACT : MOBILE :: 9159652220 .

E.MAIL ID:: [email protected]

All The Best.

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· 12.11.2018 · INSTRUCTIONS : 1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the hall supervisor immaditely. 2 ) Use Blue or black