· pdf fileerk hss erumiyampatti page 1 prepared by mr.p.kabilan, pg maths

ERK HSS ERUMIYAMPATTI Prepared By Mr.P.Kabilan, PG Maths

E R K Higher Secondary School - Erumiyampatti PART III- MATHEMATICS

Collection of Come Book Public One Mark Questions Mar/Jun/Sep (2006-2016)

------------------------------------------------------------------------------------------------------------------------------ UNIT: I- MATRICES AND DETERMINANTS

------------------------------------------------------------------------------------------------------------------------------

1. (AT)-1 is equal to

(a)A-1 (b) AT (c) A (d) (A-1)T

2. If (A) = r , then which of the following is correct?

(a)all the minors of order r which do not vanish.

(b) A has atleast one minor of r which does not vanish and all higher order minors vanish.

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

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

3. Which of the following is not elementary transformation?

(a)Ri Rj (b) Ri 2Ri+Rj (c) Ci Cj+Ci (d) Ri Ri+Cj

4. Equivalent matrices are obtained by

(a)taking inverses (b) taking transposes

(c) taking adjoints (d) taking finite number of elementary transformations

5. In echelon form, which of the following is incorrect?

(a) Every row of A which has all its entries 0 occurs below every row which has a non-zero

entry.

(b) The first non-zero entry in each non-zero row is 1.

(c) The number of zeros before the first non-zero element in a row is less than the number of

such zeros in the next row.

(d) Two rows can have same number of zeros before the first non-zero entry

6. In the system of 3 linear equations with three unknowns, if 0 and one of zyx

or ,, is

non-zero then the system is

(a)consistent

(b) inconsistent

(c) consistent and the system reduces to two equations

(d) consistent and the system reduces to a single equation.

7. In the system of 3 linear equations with three unknowns, if 0 and all 2x2 minors of 0

and atleast one 2x2 minor of zyx

oror is non-zero then the system is

(a)consistent

(b) inconsistent

(c) consistent and the system reduces to two equations

(d) consistent and the system reduces to a single equation.

8. Every homogeneous system(linear)

(a)is always consistent (b) has only trivial solution

(c) has infinitely many solution (d) need not be consistent

9. If BAA ,)( then the system is

(a)consistent and has infinitely many solution (b) consistent and has a unique solution

(c) consistent (d) inconsistent

10. If BAA ,)( = the number of unknowns then the system is



11. BAA ,)( then the system is



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12. In the system of 3 linear equations with three unknowns, BAA ,)( = 1, then the system

(a) has unique solution

(b) reduces to 2 equations and has infinitely many solutions

(c) reduces to a single equations and has infinitely many solutions

(d) is inconsistent

13. In the homogeneous system with three unknowns, )( A = number of unknowns then the

system has

(a)only trivial solution

(b) reduces to 2 equations and has infinitely many solutions


(d) is inconsistent

14. In the system of three linear equations with three unknowns, in the non-homogeneous system BAA ,)( = 2, then the system

(a)has unique solution

(b) reduces to two equations and has infinitely many solutions


(d) is inconsistent

15. In the homogeneous system )( A < the number of unknowns then the system has

(a)only trivial solution

(b) trivial solution and infinitely many non-trivial solutions

(c) only non-trivial solutions

(d) no solution

16. Cramer’s rule is applicable only (with three unknowns) when

(a) 0 (b) 0 (c) 0,0 x

(d) 0zyx

17. Which of the following statement is correct regarding homogeneous system?

(a)always inconsistent

(b) has only trivial solution

(c) has only non-trivial solutions

(d) has only trivial solution only if rank of the coefficient matrix is equal to the number of unknowns

------------------------------------------------------------------------------------------------------------------------------ UNIT: II- VECTOR ALGEBRA

------------------------------------------------------------------------------------------------------------------------------

1. The value of ba

when kjia

2 and kjib

744 is

(a)19 (b) 3 (c) -19 (d) 14

2. The angle between the vectors ji

and kj

is

(a) 3

(b)

3

2 (c) -

3

(d)

3

2

3. If cba

,, are three mutually perpendicular unit vectors, then cba

(a)3 (b) 9 (c) 33 (d) 3

4. Let u

, v

and w

be vector such that 0

wvu . If 3u

, 4v

and 5w

, then

uwwvvu

is

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

5. The projection of ji

on z-axis is

(a)0 (b) 1 (c) -1 (d) 2

6. The projection of kji

22 on kji

52 is

(a)30

10 (b)

30

10 (c)

3

1 (d)

30

10

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7. The projection of kji

3 on kji

24 is

(a)21

9 (b) -

21

9 (c)

21

81 (d) -

21

81

8. The work done in moving a particle from the point A with position vector kji

762 to the

point B, with position vector kji

53 by a force F

kji

3 is

(a) 25 (b) 26 (c) 27 (d) 28

9. The work done by the force F

kjia

in moving the point of application from (1, 1, 1)

to (2, 2, 2) along a straight line is given to be 5 units. The value of a is

(a) -3 (b) 3 (c) 8 (d) -8

10. The angle between the two vectors a

and if ba

= ba

is

(a) 4

(b)

3

(c)

6

(d)

2

11. The unit normal vectors to the plane 522 zyx are

(a) kji

22 (b) kji

22

3

1 (c) kji

22

3

1 (d) kji

22

3

1

12. The length of the perpendicular from the origin to the plane 261243. kjir

is

(a)26 (b) 169

26 (c) 2 (d)

2

1

13. The distance from the origin to the plane 752. kjir

is

(a)30

7 (b)

7

30 (c)

7

30 (d)

30

7

14. Chord AB is a diameter of the sphere 1862 kjir

with coordinate of A as (3,

2, -2). Then the coordinates of B is

(a)(1, 0, 10) (b) (-1, 0, -10) (c) (-1, 0, 10) (d) (1, 0, -10)

15. The centre and radius of the sphere )42( kjir

5 are

(a)(2, -1, 4) and 5 (b) (2, 1, 4) and 5 (c) (-2, 1, 4) and 6 (d) (2, 1, -4) and 5

16. The centre and radius of the sphere )43(2 kjir

4 are

(a)

2,

2

1,

2

3, 4 (b)

2,

2

1,

2

3and 2 (c)

2,

2

1,

2

3, 6 (d)

2,

2

1,

2

3and 5

17. The vector equation of a plane passing through a point whose position vector is a

and perpendicular to a vector n

is

(a) nanr

(b) nanr

(c) nanr

(d) nanr

18. The vector equation of a plane whose distance from the origin is p and perpendicular to a unit vector n̂ is

(a) pnr

. (b) qnr ˆ.

(c) pnr

(d) pnr ˆ.

19. The non-parametric vector equation of a plane passing through a point whose position vector is a

and parallel to u

and v

is

(a) 0,, vuar

(b) 0vur

(c) 0 vuar

(d) 0vua

20. The non-parametric vector equation of a plane passing through the points whose position

vectors are a

. b

and parallel to v

is

(a) 0 vabar

(b) 0 vabr

(c) 0vba

(d) 0bar

21. The non-parametric vector equation of a plane passing through three non-collinear points

whose position vectors are cba

,, is

(a) 0 acabar

(b) 0bar

(c) 0cbr

(d) 0cba

22. The vector equation of a plane passing through the line of intersection of the planes

11

. qnr

and 22

. qnr

is

(a) 0..2211

qnrqnr

(b) 2121

.. qqnrnr

(c) 2121

qqnrnr

(d) 2121

qqnrnr

b

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23. The angle between the line btar

and the plane qnr

is connected by the relation

(a)q

na

cos (b)

nb

nb

cos (c) n

ba

sin (d) nb

nb

sin

24. The vector equation of a sphere whose centre is origin and radius ‘a’ is

(a) ar

(b) acr

(c) ar

(d) ar

------------------------------------------------------------------------------------------------------------------------------ UNIT: III - COMPLEX NUMBERS

------------------------------------------------------------------------------------------------------------------------------

1. If )72()68( iiiba then the values of ‘a’ and ‘b’ are

(a) 15,8 (b) 15,8 (c) 9,15 (d) 8,15

2. If p+iq = (2-3i)(4+2i), then q is

(a)14 (b) -14 (c) -8 (d) 8

3. The cube roots of unity are

(a)in G.P. with common ratio (b) in G.P. with common difference 2

(c) In A.P. with common difference (d) in A.P. with common difference 2

4. The arguments of nth roots of a complex number differ by

(a) n

2 (b)

n

(c)

n

3 (d)

n

4

5. Which of the following statements is correct?

(a)negative complex numbers exist

(b) order relation does not exist in real numbers

(c) order relation exist in complex numbers

(d) )1( i > )23( i is meaningless

6. Which of the following are correct?

1) zz )(Re 2) zzmI )( 3) zz 4) nnzz

(a) (1), (2) (b) (2), (3) (c) (2), (3) and (4) (d) (1), (3) and (4)

7. The value of zz is

(a) || z (b) 2|| z (c) ||2 z (d) 2

||2 z

8. If |||| 21zzzz then the locus of z is

(a)a circle with centre at the origin

(b) a circle with centre at 1

z

(c) a straight line passing through the origin

(d) is a perpendicular bisector of the line joining 1

z and 2

z

9. The principal value of zarg lies in the interval

(a)

2,0

(b) ],( (c) ,0 (d) ]0,(

10. The number of values of q

p

i sincos where p and q are non-zero integers prime to

each other, is

(a)p (b) q (c) p+q (d)( p-q)

11. The value of iiee

is

(a) sin (b) sin2 (c) sini (d) sin2 i

12. If ibazibaz 21

, then 21

zz lies on

(a)real axis (b) imaginary axis (c) the line y= x (d) the line y = -x

13. Polynomial equation P(x)=0 admits conjugate pairs of imaginary roots only if the coefficients are

(a)imaginary (b) complex (c) real (d) either real or complex

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14. Which of the following is not true?

(a)2121

zzzz (b) 2121

zzzz (c) 2

)(Rezz

z

(d) i

zzz

2)(Im

15. Which of the following is incorrect?

(a) ||)(Re zz (b) ||)(Im zz (c) 2|| zzz (d) ||)(Re zz


(a) ||||||2121

zzzz (b) ||||||2121

zzzz

(c) ||||||2121

zzzz (d) ||||||2121

zzzz


(a) z is the mirror image of z on the real axis

(b) The polar form of z is ,r

(c) –z is the point symmetrical to z about the origin

(d) The polar form of -z is ,r

18. Which of the following is incorrect regarding nth roots of unity?

(a)The number of distinct roots is n

(b) the roots are in G.P. with common ratio n

cis2

(c) the arguments are in A.P. with common difference n

2.

(d) product of the roots is 0 and the sum of the roots is 1 .

19. Which of the following are true?

(i)If n is a positive integer then ninin

sincossincos

(ii) If n is a negative integer then ninin

sincossincos

(iii) If n is a fraction then nin sincos is one of the values of ni )sincos( .

(iv) If n is a negative integer then ninin

sincossincos

(a)(i), (ii), (iii), (iv) (b) (i), (iii), (iv) (c) (i), (iv) (d) (i) only

20. If Z = 0, then the arg(Z) is

(a) 0 (b) (c) 2

(d) Indeterminate

------------------------------------------------------------------------------------------------------------------------------ UNIT: IV- ANALYTICAL GEOMETRY

------------------------------------------------------------------------------------------------------------------------------

1. The equation of the major and minor axes of 149

22

yx

are

(a) 2,3 yx (b) 2,3 yx (c) 0,0 yx (d) 0,0 xy

2. The equation of the major and minor axes of 123422 yx are

(a) 2,3 yx (b) 0,0 yx (c) 2,3 yx (d) 0,0 xy

3. The length of the major and minor axes of 123422 yx are

(a) 32,4 (b) 3,2 (c) 4,32 (d) 2,3

4. The equation of the directrices 1916

22

yx

are

(a)7

4y (b)

7

16x (c)

7

16x (d)

7

16y

5. The equation of the latus rectum of 1916

22

yx

are

(a) 7y (b) 7x (c) 7x (d) 7y

6. The foci of the ellipse 194

22

yx

are

(a) 0,5 (b) 5,0 (c) 5,0 (d) 0,5

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7. The equations of transverse and conjugate axes of the hyperbola 36002514422 yx are

(a) 0;0 xy (b) 5;12 yx (c) 0;0 yx (d) 12;5 yx

8. The equation of chord of contact of tangents from the point (-3, 1) to the parabola xy 82 is

(a) 0124 yx (b) 0124 yx (c) 0124 xy (d) 0124 xy

9. The equation of chord of contact of tangents from the point (5, 3) to the hyperbola 2464

22 yx is

(a) 012109 yx (b) 012910 yx (c) 012109 yx (d) 012910 yx

10. The point of contact of the tangent cxmy and the parabola axy 42 is

(a)

m

a

m

a 2,

2 (b)

m

a

m

a,

2

2 (c)

2

2,

m

a

m

a (d)

m

a

m

a 2,

2

11. The point of contact of the tangent cxmy and the ellipse 12

2

2

2

b

y

a

x is

(a)

c

ma

c

b22

, (b)

c

b

c

ma22

, (c)

c

b

c

ma22

, (d)

c

b

c

ma22

,

12. If ''1

t , ''2

t are the extremities of any focal chord of a parabola axy 42 then ;

21tt is

(a) 1 (b) 0 (c) 1 (d) 2

1

13. The normal at ''1

t on the parabola axy 42 meets the parabola at ''

2t then

1

1

2

tt is

(a)2

t (b) 2

t (c) 21

tt (d) 2

1

t

14. The condition that the line 0 nmylx may be a normal to the ellipse 12

2

2

2

b

y

a

x is

(a) 02223

nmalmal (b) 2

222

2

2

2

2)(

n

ba

m

b

l

a

(c) 2

222

2

2

2

2)(

n

ba

m

b

l

a (d)

2

222

2

2

2

2)(

n

ba

m

b

l

a

15. The condition that the line 0 nmylx may be a normal to the parabola axy 42 is

(a) 02223

nmalmal (b) 2

222

2

2

2

2)(

n

ba

m

b

l

a

(c) 2

222

2

2

2

2)(

n

ba

m

b

l

a (d)

2

222

2

2

2

2)(

n

ba

m

b

l

a

16. The chord of contact of tangents from any point on the directrix of the hyperbola 12

2

2

2

b

y

a

x

passes through its

(a)vertex (b) focus (c) directrix (d) latus rectum

17. The point of intersection of tangents at ''1

t and ''2

t to the parabola axy 42 is

(a) )),((2121

tattta (b) ))(,(2121

ttatta (c) )2,(2

atat (d) ))(,(2121

ttatta

18. If the normal to the R.H. 2cxy at ''

1t meets the curve again at ''

2t then

2

3

1tt

(a)1 (b) 0 (c) -1 (d) -2

19. The locus of the point of intersection of perpendicular tangents to the parabola axy 42 is

(a)latus rectum (b) Directrix (c) tangent at the vertex (d) axis of the parabola

20. The locus of the foot of perpendicular from the focus on any tangent to the hyperbola

12

2

2

2

b

y

a

x is

(a) 2222bayx (b) 222

ayx (c) 2222bayx (d) 0x

21. The locus of the foot of perpendicular from the focus on any tangent to the parabola axy 42

is

(a) 2222bayx (b) 222


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22. The locus of the point of intersection of perpendicular tangents to the ellipse 12

2

2

2

b

y

a

xis

(a) 2222bayx (b) 222


23. The condition that the line 0 nmylx may be a tangent to the ellipse 12

2

2

2

b

y

a

xis

(a) 22222nmbla (b) ln

2am (c) 22222

nmbla (d) 224 nlmc

24. The condition that the line 0 nmylx may be a tangent to the rectangular hyperbola 2

cxy is

(a) 22222nmbla (b) nlam

2 (c) 22222nmbla (d) 22

4 nlmc

------------------------------------------------------------------------------------------------------------------------------ UNIT: V- DIFFERENTIAL CALCULUS-APPLICATIONS - I

------------------------------------------------------------------------------------------------------------------------------

1. Food pockets were dropped from an helicopter during the flood and distance fallen in ‘t’

seconds is given by 2

2

1gty (g = 9.8 m/ 2

s ).Then the speed of the food pocket after it has

fallen for ‘2’ seconds is

(a)19.6 m/sec (b) 9.8 m/sec (c) -19.6 m/sec (d) -9.8 m/sec

2. A missile fired from ground level rises x metres vertically upwards in ‘t’ seconds and x =

t(100-1(b)5t). Then the maximum height reached by the missile is

(a) 100m (b) 150 m (c) 250 m (d) 200 m

3. The law of the mean can also be put in the form

(a) 10),(')()( hahfafhaf (b) 10),(')()( hahfafhaf

(c) 10),(')()( hahfafhaf (d) 10),(')()( hahfafhaf

4. spitaloHl 'ˆ' rule cannot be applied to 3

1

x

x as 0x because f(x) = x+1 and g(x) = x+3are

(a)not continuous (b) not differentiable

(c) not in the indeterminate form as 0x (d) in the indeterminate form as 0x

5. x

x

x tanlim

0

is

(a)1 (b) -1 (c) 0 (d)

6. f is differentiable function defined on an interval I with positive derivative. Then f is

(a)increasing on I (b) decreasing on I

(c) strictly increasing on I (d) strictly decreasing on I

7. If the gradient of a curve changes from positive just before P to negative just after then “P”is a

(a)minimum point (b) maximum point (c) inflection point (d) discontinuous point

8. The function f (x) = x2 has

(a)a maximum value at x=0 (b) minimum value at x=0

(c) finite no. of maximum values (d) infinite no. of maximum values

9. If f has a local extremum at a and if )(' af exists then

(a) )(' af <0 (b) )(' af >0 (c) )(' af =0 (d) )(" af =0

10. The point that separates the convex part of a continuous curve from the concave part is

(a)the maximum point (b) the minimum point

(c) the inflection point (d) critical point

11. 0

xx is a root of even order for the equation )(' xf = 0, then 0

xx is a

(a)maximum point (b) minimum point (c) inflection point (d) critical point

12. The statement “If f is continuous on a closed interval [a, b], then f attains an absolute

maximum value )(cf and an absolute minimum value )(df at some number c and d in [a, b] ”is

(a)The extreme value theorem (b) Fermat’s theorem

(c) Law of mean (d) Rolle’s theorem

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13. The statement: “ If f has a local extremum (minimum or maximum) at c and if )(' cf exists

then 0)(' cf ” is

(a)the extreme value theorem (b) Fermat’s theorem

(c) Law of mean (d) Rolle’s theorem

14. 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

15. Identify the correct statement:

(i) a continuous function has local maximum then it has absolute maximum

(ii) a continuous function has local minimum then it has absolute minimum

(iii) a continuous function has absolute maximum then it has local maximum

(iv) a continuous function has absolute minimum then it has local minimum

(a) i and ii (b) i and iii (c) iii and iv (d) i, iii and iv

16. Identify the correct statements:

(i) Every constant function is an increasing function

(ii) Every constant function is a decreasing function

(iii) Every identity function is an increasing function

(iv) Every identity function is a decreasing function

(a) i, ii and iii (b) i and iii (c) iii and iv (d) i, iii and iv

17. Which of the following statement is incorrect?

(a)Initial velocity means velocity at t = 0

(b) Initial acceleration means acceleration at t = 0

(c) If the motion is upward, at the maximum height, the velocity is not zero

(d) If the motion is horizontal, v = 0 when the particle comes to rest

18. Which of the following statements are correct (1

m and 2

m are slopes of two lines)

(i) If the two lines are perpendicular then 1

m2

m = -1

(ii) If 1

m2

m = -1, then two lines are perpendicular

(iii) If 1

m = 2

m , then the two lines are parallel

(iv) If 2

1

1

mm

then the two lines are perpendicular

(a)ii,iii and iv (b) i,ii and iv (c) iii and ii (d) i and ii

19. One of the conditions of Rolle’s theorem is

(a) f is defined and continuous on (a, b) (b) f is differentiable on [a, b]

(c) )()( bfaf (d) f is differentiable on ],( ba

20. In the law of mean, the value '' satisfies the condition

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

UNIT: VI - DIFFERENTIAL CALCULUS-APPLICATIONS-II ------------------------------------------------------------------------------------------------------------------------------

1. The curve )6()2(22

xxxy exists for

(a) 62 x (b) 62 x (c) 62 x (d) 62 x

2. The curve )1(22

xxy is defined only for

(a) 1x (b) 1x (c) 1x (d) 1x

3. The curve 22)()( bxaxy , 0, ba and ba does not exist for

(a) ax (b) bx (c) axb (d) ax

4. The curve )1()1(22

xxxy is defined for

(a) 11 x (b) 11 x (c) 11 x (d) 11 x

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5. The curve )(22222

xaxya is defined for

(a) ax and ax (b) ax and ax

(c) ax and ax (d) ax and ax

6. The curve 22)2()1( xxy is not defined for

(a) 1x (b) 2x (c) 2x (d) 1x

------------------------------------------------------------------------------------------------------------------------------ UNIT: VII- INTEGRAL CALCULUS

------------------------------------------------------------------------------------------------------------------------------

1. If xdxIn

nsin , then

nI

(a)2

1 1cossin

1

n

nI

n

nxx

n (b)

2

1 1cossin

1

n

nI

n

nxx

n

(c) 2

1 1cossin

1

n

nI

n

nxx

n (d)

n

nI

n

nxx

n

1cossin

1 1

2. dxxf

a

)(

2

0

= ,)(2

0

dxxf

a

if

(a)f(2a-x) = f(x) (b) f(a-x) = f(x) (c) f(x) = -f(x) (d) f(-x) = f(x)

3. dxxf

a

)(

2

0

= 0 , if

(a)f(2a-x) = f(x) (b) f(2a-x) = -f(x) (c) f(x) = -f(x) (d) f(-x) = f(x)

4. If f(x) is an odd function then dxxf

a

a

)(

is

(a) dxxf

a

)(2

0

(b) dxxf

a

)(

0

(c)0 (d)

a

dxxaf

0

)(

5. dxxf

a

)(

0

+ dxxaf

a

)2(

0

=

(a) dxxf

a

)(

0

(b) 2 dxxf

a

)(

0

(c) dxxf

a

)(

2

0

(d) dxxaf

a

)(

2

0

6. If f(x) is even then dxxf

a

a

)(

is

(a)0 (b) 2 dxxf

a

)(

0

(c) dxxf

a

)(

0

(d) -2 dxxf

a

)(

0

7. dxxf

b

a

)( is

(a)

a

dxxf

0

)(2 (b)

b

a

dxxaf )( (c)

b

a

dxxbf )(

(d)

b

a

dxxbaf )(

8. The area bounded by the curve x = f(y), y-axis and the lines y=c and y=d is rotated about y-axis. Then the volume of the solid is

(a) dyx

d

c

2

(b) dxx

d

c

2

(c) dxy

d

c

2

(d) dyy

d

c

2

9. The area bounded by the curve x = f(y) to the leftof y-axis and between the lines y=c and y=d is

(a) xdy

d

c

(b) - xdy

d

c

(c) ydx

d

c

(d) - ydx

d

c

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

(a)

b

a

dxdx

dy2

1 (b)

d

c

dxdy

dx2

1 (c) 2

b

a

dxdx

dyy

2

1 (d) dxdy

dxy

b

a

2

12

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11. The surface area obtained by revolving the area bounded by the curve y= f(x), the two ordinates x=a, x=b and x-axis, about x-axis is

(a)

b

a

dxdx

dy2

1 (b)

d

c

dxdy

dx2

1 (c) 2

b

a

dxdx

dyy

2

1 (d) dxdy

dxy

b

a

2

12

12. dxexx45

0

is

(a)6

4

6 (b)

54

6 (c)

64

5 (d)

54

5

13. dxxemx 7

0

is

(a)m

m

7

(b)

7

7

m

(c)

17

m

m (d)

8

7

m

14. dxex

x

26

0

is

(a)7

2

6 (b)

62

6 (c) 62

6 (d) 62

7

------------------------------------------------------------------------------------------------------------------------------ UNIT: VIII- DIFFERENTIAL EQUATIONS

------------------------------------------------------------------------------------------------------------------------------

1. The order and degree of the differential equation dy

dxx

dx

dyy 34 are

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

2. The order and degree of the differential equation 4

32

2

2

4

dx

dy

dx

yd are

(a) 2, 1 (b) 1, 2 (c) 2, 4 (d) 4,2

3. The order and degree of the differential equation 22')'1( yy are

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


2

3

3

3

2

2

dx

yd

dx

dyy

dx

yd are

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


2

3)'(" yyy are

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

6. The order and degree of the differential equation 22)"()"(' yxyy are

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

7. The order and degree of the differential equation 22)"()"(' yxxyy are

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


2

xdy

dxx

dx

dy

are

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

9. The order and degree of the differential equation sinx(dx+dy) = cosx(dx-dy) are

(a) 1, 1 (b) 0, 0 (c) 1, 2 (d) 2, 1

10. The differential equation corresponding to xy = c2 where c is an arbitrary constant, is

(a) 0" xxy (b) 0" y (c) 0' yxy (d) 0" xxy

11. In finding the differential equation corresponding to y = emx where m is the arbitrary constant, then m is

(a) 'y

y (b)

y

y ' (c) 'y (d) y

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12. The solution of a linear differential equation QPxdy

dx where P and Q are functions of y is

(a) cQdxFIFIy .. (b) cQdyFIFIx ..

(c) cQdyFIFIy .. (d) cQdxFIFIx ..

13. Identify the incorrect statement.

(a) The order of a differential equation is the order of the highest order derivative occurring

in it.

(b) The degree of the differential equation is the degree of the highest order derivative

which occurs in it. (The derivatives are free from radicals and fractions).

(c) ),(

),(

2

1

yxf

yxf

dx

dy is the first order first degree homogeneous differential equation.

(d) xexy

dx

dy is a linear differential equation in x.

------------------------------------------------------------------------------------------------------------------------------ UNIT: IX- DISCRETE MATHEMATICS

------------------------------------------------------------------------------------------------------------------------------

1. Which of the following are not statements?

(i) Three plus four is eight. (ii) The sun is a planet.

(iii) Switch on the light. (iv) Where are you going?

(a)(i) and (ii) (b) (ii) and (iii) (c) (iii) and (iv) (d) (iv) only

2. Which of the following are statements?

(i) 7+2<10. (ii) The set of rational numbers is finite.

(iii) How beautiful you are! (iv) Wish you all success.

(a) (iii), (iv) (b) (i), (ii) (c) (i), (iii) (d) (ii), (iv)

3. Let p be “Kamala is going to school” and q be “There are twenty students in the class”.“Kamala is not going to school or there are twenty students in the class” stands for

(a) qp (b) qp (c) p (d) qp

4. If p is true and q is unknown then

(a) p is true (b) )( pp is false (c) )( pp is true (d) qp is true

5. If p is true and q is false then which of the following is not true?

(a) qp is false (b) qp is true (c) qp is false (d) qp is true

6. ‘+’ is not a binary operation on

(a)N (b) Z (c) C (d) Q-{0}

7. ‘-’ is a binary operation on

(a)N (b) Q-{0} (c) R-{0} (d) Z

8. ‘ ’ is a binary operation on

(a)N (b) R (c) Z (d) C-{0}

9. In congruence modulo5, },25/{ zkkxzx represents

(a) 0 (b) 5 (c) 7 (d) 2 .

10. In the group (G, .), G = {1, -1, i, -i} the order of -1 is

(a)-1 (b) 1 (c) 2 (d) 0

11. In the group ),(44

Z , )]3[(O is

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

12. In ,S , Syxxyx ,, then ‘ ’ is

(a)only associative (b) only commutative

(c) associative and commutative (d) neither associative nor commutative

13. In (N, *), x*y = max{x, y}, x, y N, then (N, *) is

(a)only closed (b) only semi group (c) only monoid (d) a group

14. The set of positive even integers, with usual multiplication forms

(a)a finite group (b) only a semi group (c) only a monoid (d) an infinite group

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15. The set of positive even integers, with usual addition forms

(a)a finite group (b) only a semi group (c) only a monoid (d) an infinite group

16. In the group ),0(55

Z , ]3[O is

(a)5 (b) 3 (c) 4 (d) 2

17. In the group (G, .), G = {1, -1, i, -i} the order of i is

(a)2 (b) 0 (c) 4 (d) 3


Z , ]2[O is

(a)5 (b) 3 (c) 4 (d) 2


Z , ]4[O is

(a)5 (b) 3 (c) 4 (d) 2

------------------------------------------------------------------------------------------------------------------------------ UNIT: X- PROBABILITY DISTRIBUTIONS

------------------------------------------------------------------------------------------------------------------------------

1. A discrete random variable takes

(a) only a finite number of values (b) all possible values between certain given limits

(c) infinite number of values (d) a finite or countable number of value

2. A continuous random variable takes

(a) only a finite number of values (b) all possible values between certain given limits

(c) infinite number of values (d) a finite or countable number of values

3. If X is a discrete random variable then P(X a) =

(a)P(X<a) (b) 1 – P(X a) (c) 1 – P(X<a) (d) 0

4. If X is a continuous random variable then P(X a) =

1. P(X<a) (b) 1 – P(X>a) (c) P(X>a) (d) 1-P(X a-1)

5 If X is a continuous random variable then P(a<X<b) =

(a)P(a X b) (b) P(a<X b) (c) P(a X<b) (d) all the three above

6. A discrete random variable X has probability mass function p(x), then

(a) 1)(0 xp (b) 0)( xp (c) 1)( xp (d) 1)(0 xp

7. Which of the following is or are correct regarding normal distribution curve ?

(i) symmetrical about the line X = (mean) (ii) Mean = median = mode

(iii) unimodal (iv) Points of inflection are at X =

(a) i, ii only (b) i, iv only (c) i, ii, iii only (d) all

8. For a standard normal distribution the mean and variance are

(a) 2, (b) , (c) 0, 1 (d) 1, 1

9. If X is a discrete random variable then which of the following is correct ?

(a) 1)(0 xF (b) 1)(0)( FandF

(c) )(][1

nnn

xFxFxXP (d) F(x) is a constant function

10. If X is a continuous random variable then which of the following is incorrect ?

(a) )()(' xfxF (b) 0)(1)( FandF

(c) )()(][ aFbFbxaP (d) )()(][ aFbFbxaP

11. Which of the following are correct?

(i) E(aX+b) = aE(X)+b (ii) 2

122)'('

(iii) iancevar2 (iv) var(aX+b) = a2var(X)

(a)all (b) (i), (ii), (iii) (c) (ii), (iii) (d) (i), (iv)

12. Which of the following is not true regarding the normal distribution?

(a)skewness is zero. (b) mean = median = mode

(c) the points of inflection are at X = (d) maximum height of the curve is 2

1

******************

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· pdf fileerk hss erumiyampatti page 1 prepared by mr.p.kabilan, pg maths

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