TEST ON ENGINEERING MATHEMATICS.docx

7/27/2019 TEST ON ENGINEERING MATHEMATICS.docx

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JH ACADEMY Page 1

1. is equal toa) 0

b) c) 1d) -1

2. For the matrix

* +the eizen values are

a) 3 and -3b) -3 and -5c) 3 and 5d) 5 and 0

3. Consider the system of simultaneousequations . The system hasa) Unique solution

b) Infinite number of solutionsc) No solutiond) Exactly two solutions

4. The area enclosed between the parabola and the straight line y=x isa)

b) c) d)

5. The solution of the differential equation isa)

b) c) d) Unsolvable as equation is non linear.

6. The vector field (where are unit vectors) isa) Divergence free, but not irrotational

b) Irrotational but not divergence freec) Divergence free and irrotationald) Neither divergence free nor

irrotational

7. Laplace transform of the function sin wt is

a)

b)

c)

d)

8. A box contains 5 black and 5 red balls.Two bars are randomly picked one after

another from the box, without

replacement. The probability for both ballsbeing red is

a) b) c) d)

9. If x=a(+) and y=a(1- , then will be equal to

a) b) c) d)

10. The angle between two unit-magnitudecoplanar vectors P(0.86, 0.5, 0) andQ(0.239, 0.956,0) will be

a) b) c) d)

11. The sum of eigen values of the matrix

given below is

a) 5 b) 7 c) 9 d) 18

12. From a pack of regular playing cardsdrawn at random . what is the probability

that both cards will be kings, if the first

card is not replaced?

a) b) c) d)

13. A delayed unit step function is defined as

u (t-a) = 0 for t < a 1 for t aIts laplace transform is

a) b)

c)


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d)

14. The volume of an object expressed inspherical co-ordinates is given by

V=

The value of the integral isa) b) c) d)

15. For which value of x will be matrix belowsingular?

a) 4

b) 6c) 8d) 12

16. Strokes theorem connectsa) A line integral and a surface integral

b) A surface integral and a volumeintegral

c) A line integral and a volume integrald) Gradient of a function and its surface

integral

17. A lot has 10% defective items. Ten items

are chosen randomly from the lot. Theprobability that exactly z of the chosen

item are defective is

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

18. is equal toa)

b) 2 c) 2 d) 0

19. A is a 34 real matrix and

is an

inconsistest system of equations. Thehigest possible rank of A is

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

20. Changing the order of the integration inthe double integral 1= leads to 1= what is q ?a) 4y

b) c) X

d) 8

21. The time variation of the position of aparticle in rectilinear motion is given by x- . if v is the velocity and a theacceleration of the particle in consistent

units, the motion started witha) b) c) d)

22. Consider a single server queuing with

Poisson arrivals andexponential service (= 4/hour). Then

number in the system is restricted to a

maximum of 10. The probability that a

person who comes in leaves without

joining the queue is

a) b) c) d)

23. A single die is thrown twice. What is theprobability that the sum is either 8 or 9?

a) b) c)

d) 24. The complete solution for the ordinarydifferential equation

is y= (i) Then P and Q area) P=3, q=3

b) P=3, q=4c) P=4, q=3d) P=4, q=4(ii) Which of the following is a

solution of the differential

equation a)

b) c) d)

25. The solution of the differential equation with y (o)=1 isa)

b) c)

d)


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26. A box contains 20 defective items and 80non defective items. If two items are

selected at random without replacement,

what will be the probability that both

items are defective?

a)

b) c) d)

27. Eign values of a matrix 3= * + are 5and 1. What are the Eigen values of the

matrix ?a) 1 and 25

b) 6 and 4c) 5 and 1d) 2 and 10

28. Equation of the line normal to function at P (0, 5) isa)

b) c) d)

29. Assuming and t is a real number. isa)

b) c) d)

30. If f(x)=

, then willbe

a) b) c) 0 d) 31. Match the following

Column I

P) Singular matrixQ) Non-square matrix

R) Real symmetric matrix

S) Orthogonal matrix

Column II1) Determinant is not defined2) Determinant is always 13) Determinant is zero4) Eigen values are always real5) Eigen values are not defined.

Codes:

A) P-3 Q-1 R-4 S-2B) P-2 Q-3 R-4 S-1

C) P-3 Q-2 R-5 S-4D) P-3 Q-4 R-2 S-1

32. For , the particular

integral is

a) b) c) d)

33. Multiplication matrices E and F is G.matrices E and G are

E= andG=

what is F.

a) b) c) d)

34. Consider a continuous random variable

with probability density function

f(t)= 1+t for -1t0= 1-t for 0t1

The standard deviation of the random variable

is

a) b) c) d)

35. The maximum value of function inthe interval isa) 0 b) 1 c) 25 d) undefined

36. If a square matrix A is real and symmetricthen the eizen values.

a) Are always realb) Are always real and positivec) Are always real and non-negatived) Occur in conjugate pairs.

37. If are functions withcontinuous second derivatives, then can be expressed asan analytic function of

,

when

a)


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b)

c)

d)

38. The partial differential equation+ hasa) Degree 1 order 2

b) Degree 1 order 1c) Degree 2 order 1d) Degree 2 order 2

39. If y=x , then y(2) =a) 4 or 1

b) 4 onlyc) 1 onlyd) Undefined

40. The area of triangle formed by the tips of

vectors , , isa)

( ) b)

|( ) |c)

| |d)

( )41. The solution of

with initial valuey(0) =1 is bounded in the interval

a) b) 1c) d)

42. If F(s) is the Laplace transform of function

f(t), then Laplace transform of dis

a)

b)

c) SF(s)-f(o)

d)

43. =a) 0

b) c) d) 1

44. The number of linearly independent eigen

vectors of* + isa) 0 b) 1 c) 2 d) infinite

45. In the Taylor series expansion of aboutx=z, the coefficient of isa)

b) c) d) 46. Given that

and x(0)=0 , what

is x(1)?

a) -0.99b) -0.16c) 0.16d) 0.99

47. The value of isa)

b)

c)

d)

48. A coin is tossed 4 times. What is theprobability of getting heads exactly 3

times?

a) b) c) d)

49. The matrix has one eigenvalue equal to 3. The sum of the othereigen values is

a) P b) P-1 c) P-2 P-3

50. The divergence of the vector field isa) 0 b) 1 c) 2 d) 3

51. Consider the shaded triangular region P

shown in fig. what is a)

b) c) d) 1

52. The directional derivative of the scalarfunction f (x,y,z) = at thepoint P=(1,1,2) in the direction of thevector isa) -4

b) -2c) -1d) 1

53. For what value of a, if any will be thefollowing system of equations in x, y and

z have a solution.

2x+3y=4, x+y+z=4, x+2y-z=a

a) Any real numberb) 0


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c) 1d) There is no such value

54. Which of the following integral isunbounded?

a)

b) c) d)

55. The integral evaluated aroundthe unit circle on the complex plane for

f(z)= is

a) 2ib) 4ic) -2

i

d) 0

56. The length of the curve y= betweenx=0 and x=1 is

a) 0.27b) 0.67c) 1d) 1.22

57. The eigen vector of the matrix * + arewritten the form *

+ and *

+ what is a+b?

a) 0

b) c) 1d) 2

58. Let f=. what is at r=2, y=1?a) 0

b) c) 1

d)

59. It is given that

, y(o) =0,

y(1) =0 what is y(0.5)?a) 0

b) 0.37c) 0.62d) 1.13

60. For a matrix (M) = , thetranspose of the matrix is equal to the

inverse of the matrix the valueof x is given by

a)

b)

c) d)

61. The divergence of the vector field

3xzi+2xyj-y

K at a point (1, 1, 1) is

equal toa) 7b) 4c) 3d) 0

62. The inverse Laplace transform of is

a) 1+b) 1c) 1d) 1+

63. If three coins are tossed simultaneously,the probability of getting at least one head

a) b) c) d)

64. An analytic function of a complex variablez=x+iy is expressed as f(z) = u(x, y) +

iv(x, y) where i= if u= xy, theexpression for u should be

a)

b) c) d)

65. The solution of with the

condition y(1) = isa)

b) c)

d) 66. A path AB in the form of one quarter of a

circle of unit radius is shown in the figure.

Integration of on path ABtransvered in a counter clockwise since is

a)

b)

c)

d) 1


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67. The distance between the origin and the

point nearest to it on the surface isa) 1

b)

c) d) 268. The area enclosed between the curves and is

a) b) 8

c) d) 16

69. The standard deviation of a uniformlydistributed random variable between 0 and

1 is

a) b) c) d)

70. The parabolic arc y=, 1 x2 isrevolved around the x-axis. The volume of

the solid of revolution is

a)

b) c) d)

71. The Blasius equation is a

a) Second order non-linear ODEb) Third order non-linear ODEc) Third order linear ODEd) Mixed order non-linear ODE

72. The value of integral

is

a) b) c)

d)

73. The modulus of the complex number isa) 5

b) c)

d)

74. The function y = (2-3x)

a) Is continuous xR and differentiablexRb) Is continuous xR and differentiable

except at x=

c) Is continuous xR and differentiablexR except at x= d) Is continuous xR except at x =3and differentiable xR.

75. One of the Eigen vectors of the matrix A=* + isa) * + b) *+ c) *+ d) * +

76. Velocity vector of a flow is given as j =

2xyi-xzj the velocity vector at (1,1,1) is

a) 4 jb) 4 kc) d)

77. The Laplace transform of a function f(t)

= the f(t) is

a) b) c)

d) 78. A box contains 2washers, 3nuts and

4bolts. Hence are drawn from the box at

random one at a time without

replacement. The probability of drawing

2washers first followed by 3nuts and

subsequenty the 4bolts is

a)

b)

c) d)

79. A series expansion for the function isa) --------

b) --------c) ---------d)

--------

80. What is equal to?a)


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b) c) 0d) 1

81. Eigen values of a real symmetric matrixare always

a) Positive

b) Negativec) Reald) Complex

82. The product of two complex numbers and isa)

b) c) d) 83. If is an even function and a is a

equals

a) 0b) a

c) 2ad)

84. The integral ,when evaluated byusing Simpson is

rule on two equalsub intervals each of length 1,equals

a) 1.0b) 1.098c) 1.111d) 1.12

85. Consider the differential equation

The general soluation

with constant c isa)

b) c) d)

86. An unbiased coin is tossed five times.The outcome of each toss is either a

head or a tail. The probability of getting

at least one head is

a) 1/32b) 13/32c) 16/32d) 31/32

87. At x=0, the function hasa) A maximum value

b) A minimum valuec) A singularityd) A point of intcection

88. For the spherical surface,,thepoint(

, ,0) is given bya)

b)

c) K

d)

89. The given enclosed between the straight

line and the parabola inthe plane is

a) 1/6b) c) 1/3

d) 90. Consider the function in theinterval A the point x=0,

f(x) is

a) Continuous and differentiableb) Non- Continuous and differentiablec) Continuous and differentiabled) Neither Continuous and differentiable

91. isa)

b) c) 1

d) 292. A box contains 4 red balls and 6blackballs. Three balls are selected randomly

from the box one after another without

replacement. The probability that the

selected set contains one red ball and

two black ball is

a) 1/20b) 1/12c) 3/10d) 1/2

93. Consider the differential equation

with the

boundary conditions of and The complete solution of thedifferent equation is

a) b) c) d)

94. The system of algebraic equations given

below has a) A unique solutions of

b) Only the two solutions of and c) Infinite numbers of solutionsd) No, feasible solution

95. The invert Laplace transform of the

function f(s)= is given by

a) F(t)= sint

b) F(t)= c) F(t)=d) F(t)=1-

96. For the matrix A= * + ,one of thenormalized eigen vectors is given by


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a) b)

c) d)

97. Math the correct paorsNumerical integration scheme order of

fitting polynomial

Q. trapezoidal rule 2.second

R. Simpsons 1/3 rule 3.third

a) p-2,q-1,r-3

b) p-3,q-2,r-1

c) p-1,q-2,r-3d)p-3,q-1,r-2

98. The eigrn values of a symmetric matrixare all

a) Complex with non=zero positiveimaginary

b) Complex with non=zero negtiveimaginary

c) Real

d) Pure imaginary

99. The partial different equation is aa) Linear equation of order 1

b) Non-linear euation of order 1c) Linear equation of order 1d) Non-linear equation of order2

100.Chook the correct set of functions,which are linearly dependent

a) b)

c) d) 101.Let x be a normal random variable withmean 1 and variance 4.the probability

p{x


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JH ACADEMY Page 9

c) Non-zero unique solutiond) Multiple solution

109.Aqure roots ofI, where i= area) i,-i

b) cos(-/4)+sin(-/4),cos(3

c) \isin(3 d) --110.the curl of the gradient of the scalar

field defined by a) b) c) d) 0

111.A continuum Random variables x hasa probability density function { }

a) 0368b) 0.5

c) 0.632

d) 1.0

112.A function is definedover an open interval x=(1,2),atleast

one point in thus interval is exactly

a) 20b) 25

c) 30

d) 35

113. evaluated anticlockwisearound the circle ,wherei= is

a) -b) 0c) d) 2+2i

114.A matrix has eigen values -1 and-2.the corresponding eigen vectors

are

*

+and

*

+respactively . the

matrix isa) * +b) * +c) * +d) * +

115.Given if c is acounter clockwise path in the z-plane

such that|z+1|=1,the value of

a) -2b) -1

c) 1

d) 2

116.Two independent random variables x

and y are uniform distributed in the

interval (-1,1), the probability thatmax[x,y] is less then is

a) b) 9/16

c) d) 2/3

117.If x=,then the vakue of isa) b) c) X

d) 1118.The unilateral Laplace transform of

,the unilateral laplace

transform of tf(t) is

a) - b) c)

d)

119.With initial condition x(1)=0.5, the

solution of the differential equation

t is

a) X=t=1/2

b) X=

c) X= d) X=t/2120.The maximum value of in the interval[1,6] is

a) 21

b) 25

c) 41d) 46

121.Given that A=* + and I=* +,the value of is

a) 15A+12I

b) 19A+30I

c) 17A+15Id) 17A+21I

122.Consider the differential equation + Withy(t) =0.Thenumerical value at

a) -2

b) -1

c) 0d) 1

123.The direction of vector A is radially

outward from rhe origin ,with|A|=kwhere and


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K is constant. The value of n for which a. -2

b. -1

c. 0d. 1

124.A fair coin tossed till a head appearsfor the first time . the probability that

the number of required tosses is oddis

a) 1/3

b) c) 2/3

d)

125.Roots of algebraic equation area. (+1,I,-i)b. (+1,I,+1)

c. (0,0,0)

d. (-1,+I,-i)

126.Given two continuous time signals

x(t)= and y(t)= which existsfor t>0, th convolution z(t)=x(t)*y(t)

isa) b) c) d)

127.The function hasa) A maxima at x=1 and minima at

x=5b) A maxima at x=1 amd minima at

x=-5c) Only a maxima at x=1

d) Only a mimima at x=1

128.The matrix [A]=* + isdecomposed into a product of a lowertriangular matrix [l] and an upper

triangular matrix [u]. the properly

decomposed [L] and [u] matrixes

respectively

a)

* +* +

b) * +* +c) * +* +d) * +* +

129.The two vectors [1,1,1] and [1,a ]where a= are

a) Orthogonal

b) Orthonormal

c) Paralleld) Collinear

130.The value of the quantity p, where

p= is equal to

a) 0

b) 1

c) E

d)

131.Divergence of the tree-dimensional

radius vector field r , is

a) 3b) 1/r

c) I+j+k

d) 3(i+j+k)

132.A box contains 4 white balls and 3red

balls. In succession,two balls are

rondemly selected and removed from

box. Given that the first removed ballis white ,the probability that the

second ball is red is

a) 3

b) 9/7

c) d) 4/7

133.At t=0, the function f(t)= has

a) A minimum

b) A discontinuity

c) A point as inflectiond) A maximum

134.A eign vector of p= isa) b)

c)

d) 135.For the set of equations and . the following statement istrue

a) Only the trivial solution

x1=x2=x3=x4=0 existsb) There is no solution

c) A unique non-trivial solution exists

d) Multiple non-trivia; solution exists136.The trace and determinant of a 2*2

matrix are know to be -2 and -35

respectively. Its eigen values area) -30 and -5b) -37 and -1

c) -7 and 5

d) 17.5 and -2137.A cubic polynomial with real co-

efficients

a) Can possibly ave no extrema andzero cronigs

b) May have up to three extreme and

up to zero crossingsc) Cannot have more than two

extreme and up to more than three

zero crossings


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d) Will always have on equal numbers

of extreme and zero

138.F(x,y)=( )ax+( h.sline integral over the straight linefrom (x,y)a,residence of X(z) at z=a for w

a) b) c) nd) n

141.consider a funcation f(x)= where x is a real numbers then thefuncation has

a) only one minimum

b) only two minima

c) three minimad) three maxima

142.a differential equation=u(t)

has to be solved using trapezoidal

rule os integration with a step size

h=0.01s function u(t) indicates a unit

step function if x(0)=0 then value of xt=0.01s will be given by

a) 0.00099

b) 0.00495

c) 0.0099

d) 0.0198

143.Divergence of vector field isa) b) c) d) None of these

144.The value of Where c is an contour a)

b) c) d)

145.the integral equals

a) sintcost

b) 0

c) (1/2)costd) (1/2)sint

146.A) A satisfies the relationa) b) c) d) Exp(A)=0

147.Two fair dice are rolled and the sum r

of the numbers turned up isconsidered

a) b)

c) d)

148.If s= then s has the valuea) -1/3

b)

c)

d) 1

149.The solution of the first order

differential equation (t)=-3x (t ) , x (0)= x0 is:

a) b) c) d)

150.For the matrix , oneof the eigen values is equal to 2.

Which of the following is an eigen

vector?

a)

b) c) d)

151.If R= the top row of isa)

b) c)


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d) * +152.A fair coin is tossed three times in

succession. If the first toss produces a

head, then the probability of getting

exactly two heads in three tosses is:

a) 1/8b) 1/2

c) 3/8

d)

153.For the function , themaximum occurs when x is equal to:

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

154.For the scalar field ,themagnitude of the gradient at the point

(1,3) is

a) b) c) d) 9/2

155.For the equation ,thesolution x (t ) approaches thefollowing values at

a) 0

b) 5/2

c) 5d) 10

156.The Laplace transform of a function f(t)

is as ,f(t)approaches

a) 3

b) 5

c) 17/2

d) 157.Consider the function

where f(s) is Laplace

transform of the function f(t). the initialvalue of f(t) is equal to

a) 5

b) 5/2

c) 5/3

d) 0

158.A control system is defined by the

following mathematical relationship Theresponse of the system as

is

a) x=6

b) x=2

c) x=2.4

d) x=-2

159.The phase margin of a system with the

open-loop transfer function isa) 0

b) 63.4c) 90

d) 160.For a bit-rate of 8 Kbps, the best

possible values of the transmitted

frequencies in a coherent binary FSK

system are

a) 16 KHz and 20 KHz

b) 20 KHz and 32 KHz

c) 20 KHz and 40 KHz

d) 32 KHz and 40 KHz

161.The eigen values of the system

represented by X= are

a) 0, 0, 0, 0

b) 1, 1, 1, 1

c) 0, 0, 0, -1

d) 1, 0, 0, 0

162.The vector is an eigen vector ofA=

One of the given

values of

A is

a) 1

b) 2

c) 5

d) -1

163.A=

The sum of the eigenvalues of the matrix A is:a) 10

b) -10

c) 24

d) 22

164.The Laplace transform of isa)

b)

c)

d) None if the above

165.A= The inverse of A is:


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JH ACADEMY Page 13

a) b)

c)

d)

[ ]

166.The value of computed usingSimpsons rule with a step size of h =

0.25is

a) 0.69430

b) 0.69385

c) 0.69325

d) 0.69415

167.The inverse of the matrix

S= isa)

b) c) d)

168.Given the matrix A= Its eigen values are:------------------

169.The rank of the matrix isa) 0b) 1

c) 2

d) 3

170. where P is a vector, isequal to

a) -b) c) d) - -171.

(

P ds ) where P is a vector, is

equal toa)

b) c) d)

172.A probability density function is of the

form

The

value of K is

a) 0.5

b) 1

c) 0.5d)

173.A solution for the differential equation with initialcondition x (0 0 =) is:

a) b) c) d)

174.The eigen values and the corresponding

eigenvectors of a 2 2 matrix are givenby Eigenvalue Eigenvector

=8 v=*+=4 v=* +

a) * +b) * +c) * +d)

* +

175.The value of the contour integral

in posiive sense isa)

b)

c)

d)

176.For the function of a complex variable

W Z = ln (where, W u j Z x jy = + = +

and ),the u = constant lines get mapped

in Z-plane as

a) set of radial straight lines

b) set of concentric circles

c) set of confocal hyperbolas

d) set of confocal ellipses

177.The integral is given bya)

b) 2/3

c) 4/3

d) 8/3

178.Consider the function f t( ) having

Laplace transform

The final value of f t( )

would be:


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JH ACADEMY Page 14

a) 0

b) 1

c) d)

179.If E denotes expectation, the variance

of a random variable X is given by

a) b) c) d)

180. isa) 0.5

b) 1

c) 2

d) Not defined

181.For the function

, the linear

approximation around x = 2 is:a) (3-x)b) 1-xc) ( )d)

182.Which one of the following functions is

strictly bounded?

a)

b) c) d)

183.Consider the function

The maximum value of f x( ) in theclosed interval [ 4, 4] is:a) 18b) 10

c) -2.25

d) indeterminate

184.An examination consists of two papers,

Paper 1 and Paper 2. The probability of

failing in Paper 1 is 0.3 and that in

Paper 2 is 0.2. Given that a student has

failed in Paper 2, the probability of

failing in Paper 1 is 0.6. The probability

of a student failing in both the papersis:

a) 0.5

b) 0.18

c) 0.12

d) 0.06

185.The solution of the differential

equation =y-y under the boundaryconditions

(1)y=y at x=0 and(2)y=y at x=

,where k,y and y are constants, is

a) p

b) p c) d) p

186.The equation

is

to be solved using the Newton-Raphsonmethod. If x = 2 is taken as the initial

approximation of the solution, then the

next approximation using this method

will be:

a) 2/3

b) 4/3

c) 1

d) 3/2

187.All the four entries of the 22 matrix

p=*p pp p+are nonzero, and one ofits eigenvalues is zero. Which of the

following statements is true?a) b) c) d)

188.The system of linear equations

4x+2y=7, 2x+y=6 has

a) a unique solution

b) no solution

c) an infinite number of solutions

d) exactly two distinct solutions

189.The equation sin (z)= 10 has

a) no real or complex solutionb) exactly two distinct complex

solutions

c) a unique solution

d) an infinite number of complex

solutions

190.For real values of x, the minimum value

of the function p p isa) 2

b) 1

c) 0.5

d) 0191.Which of the following functions would

have only odd powers of x in its Taylor

series expansion about the point x=0?

a) b) c) d)

192.The recursion relation to solve using Newton Raphson method is

a) b)

c)

d)


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JH ACADEMY Page 15

193.Which of the following is a solution to

the differential equation ?

a) b)

c) d) 194.The residue of the function at z=2 isa) -1/32

b) -1/16

c) 1/16

d) 1/32

195.In the Taylor series expansion of

exp(x)+sin(x) about the point x=, the

coefficient of

is

a)

p

b) pc) p d) p

196.The value of the integral of the function along thestraight line segment from the point (0,

0) to the point (1, 2) in the x-y plane is

a) 33

b) 35

c) 40

d) 56

197.The eigen values of a skew-symmetricmatrix are

a) always zero

b) always pure imaginary

c) either zero or pure imaginary

d) always real

198.A function n(x) satisfied the differential

equation where L is a

constant. The boundary conditions are:

n(0)=K and n ( ) = 0. The solution to

this equation is

a)

b) c) d)

199.If , then y has aa) maximum at x= e

b) minimum at x= e

c) maximum at x= e-1

d) minimum at x= e-1

200.A fair coin is tossed independently four

times. The probability of the event the

number of time heads shown up is

more than the number of times tails

shown up is

a) 1/16

b) 1/8

c) 1/4

d) 5/16

201.If then overthe path shown in the figure is

a) 0

b)

c) 1

d) 202. The residues of a complex function

X(z)=at its poles are

a) ,-1/2and-1

b) ,-1/2and-1

c) ,-1and-3/2

d) 1/2 ,-1and-3/2

203.Consider differential equation with the initial condition y(0)

= 0. Using Eulers first order method

with a step size of 0.1, the value of y

(0.3) is

a) 0.01

b) 0.031

c) 0.0631

d) 0.1204.Given * +if then the value of K is

a) 1

b) 2

c) 3

d) 4

205.The solution of the differential

equation is

a) b)

c)

d)


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JH ACADEMY Page 16

206.The value of the integral where c is the circle|z|=1 is given by

a) 0

b) 1/10

c) 4/5d) 1

207.If then theinitial and final values of f(t) are

respectively

a) 0,2

b) 2,0

c) 0,2/7

d) 2/7,0

208.A numerical solution of the

equation

canbe obtained using Newton- Raphson

method. If the starting value is x = 2 forthe iteration, the value of x that is to be

used in the next step is

a) 0.306

b) 0.739

c) 1.694

d) 12.306

209.The system of equations has NO solutionfor values of and given by

a) = 6, = 20

b) = 6, 20c) 6, = 20

d) 6, 20

210.The first six points of the 8-point DFT of

a real valued sequence are5,1-j3,0,3-

j4,0 and3+j4.The last two points ofthe DFT are respectively

a) 0,1-j3

b) 0,1+j3

c) 1+j3,5

d) 1-j3,5

211.The divergence of the vector

field isa) 0b) 1/3c) 1

d) 3

212.The minimum Eigen value of the

following matrix is a) 0

b) 1

c) 2

d) 3

213.A polynomial with all coefficientspositive has

a) no real roots

b) no negative real root

c) odd number of real roots

d) at least one positive and onenegative real root

214.Let U and V be two independent zero

mean Gaussian random variables of

variances and 1/9 respectively,. The

probability P(3V2U) isa) 4/9

b)

c) 2/3

d) 5/9

215.Let A be an m x n matrix and B an n x m

matrix. It is given that determinant

determinant where I is the kk identitymatrix. Using the above property, thedeterminant of the matrix given below

is a) 2

b) 5

c) 8

d) 16

216.What is the minimum number of

multiplications involved in computing

the matrix product PQR? Matrix P has 4

rows and 2 columns, matrix Q has 2

rows and 4 columns, and matrix R has 4

rows and 1 column. __________

217.The solution for is

a) 0

b) 1/3

c) 1

d) 8/3

218.Find the value of such that thefunction f (x) is a valid probability

density function. _________ for 1x2F(x)=0 otherwise

219.Laplace equation for water flow in soils

is given below.

Head H does not vary in y and z

directions Boundary conditions are: at x

= 0, H = 5;and What is the value

of H at x = 1.2? -----------------------

220.The estimate obtained usingSimpsons rule with three-point


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JH ACADEMY Page 17

function evaluation exceeds the exact

value by

a) 0.235

b) 0.068

c) 0.024

d) 0.012

221.The infinite series corresponds toa) Sec x

b) c) Cos x

d) 222.In an experiment, positive and negative

values are equally likely to occur. The

probability of obtaining at most one

negative value in five trials is

a) 1/32

b) 2/32

c) 3/32

d) 6/32

223.The eigen values of matrix * +area) -2.42 and 6.86

b) 3.48 and 13.53

c) 4.70 and 6.86

d) 6.86 and 9.50

224.For the parallelogram OPQR shown in

the sketch,

The area of the parallelogram is

digaram

a) b) c) d)

225.The isa) 2/3

b) 1

c)

d)

226.Two coins are simultaneously tossed.

The probability of two heads

simultaneously appearing is

a) 1/8

b) 1/6

c)

d)

227.The order and degree of the differential

equation are

respectively

a) 3 and 2

b) 2 and 3

c) 3 and 3

d) 3 and 1

228.The effective length of a column of

length L fixed against rotation and

translation at one end and free at the

other end is

a) 0.5L

b) 0.7Lc) 1.414L

d) 2L

229.The solution to the ordinary differential

equation is

a) b) c) d)

230.The inverse of the matrix

* +is

a) * +b) * +c)

* +d)

* +231.The table below gives values of a

function F(x) obtained for values of x at

intervals of 0.25.

x

0

0.25 0.5 0.75 1.0

f(x) 1

0.94

12

0.8

0

0.6

40

0.5

0

The value of the integral of the function

between the limits 0 to 1 using Simpsons

rule is

a) 0.7854

b) 2.3562

c) 3.1416

d) 7.5000

232.The partial differential equation that

can be formed from

has the form a) b) c) d)

233.Given a function The optimal valueof f(x, y)

a) Is a minimum equal to 10/3

b) Is a maximum equal to 10/3

c) Is a minimum equal to 8/3

d) Is a maximum equal to 8/3234.A square matrix B is skew symmetric if


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JH ACADEMY Page 18

a) b) c) d)

235.For a scalar function

the gradient at the point P

(1,2,-1) isa) b) c) d)

236.The analytic function hassingularities at

a) 1 and -1

b) 1 and i

c) 1 andi

d) i and -i

237.For a scalar function

,the directional derivative atthe point P(1, 2, -1) in the direction of avector is

a) -18

b) -3c) 3d) 18

238.The value of the integral (where C is a closedcurve given by |z|= 1 is

a)

i

b) c)

d)

239.Solution of the differential equation represents a familyof

a) ellipses

b) circles

c) parabolas

d) Hyperbolas

240.Laplace transform for the function

isa) b)

c)

d)

241.In the solution of the following set of

linear equations by Gauss elimination

using partial pivoting 5x +y+ 2z= 34;4y -3z =12; and 10x-2y+z=-4 The pivots for

elimination of x and y are

a) 10 and 4

b) 10 and 2c) 5 and 4

d) 5 and -4

242.The standard normal probability function can

be approximated as where

standard normal deviate. If mean and

standard deviation of annual precipitation are102cm and 27cm respectively, the probability

that the annual precipitation will be between

90cm and 102cm is

a) 66.7%

b) 50%

c) 33.3%

d) 16.7%

243.The product of matrices (PQ)P is

a) b) c)

d)

244.The general solution of isa) b) c) d)

245.The equation canbe transformed to

bysubstituting

a) b)

c) d)

246.The value of isa) 13.5

b) 27.0

c) 40.5

d) 54.0

247.Three values of x and y are to be fittedin a straight line in the form

the method of least squares.Given: , the values of a and b arerespectively

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

248.Solution of at x=1 and y= isa) b) c)

d)


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JH ACADEMY Page 19

249.If probability density function of arandom variable X is

= Then, the percentage probability

is

a) 0.247b) 2.47c) 24.7d) 247

250.The Eigen values of the matrix * + area) -7 and 8b) -6 and 5c) 3 and 4d) 1 and 2

251.The following simultaneous equations will NOT have a uniquesolution for k equal to

a) 0b) 30c) 6d) 7

252.A person on a trip has a choicebetween private car and public

transport. The probability of using a

private car is 0.45. While using the

public transport, further choices

available are bus and metro, out ofwhich the probability of commuting by

a bus is 0.55. In such a situation, the

probability (rounded up to two

decimals) of using a car, bus and

metro, respectively would be

a) 0.45, 0.30 and 0.25b) 0.45, 0.25 and 0.30c) 0.45, 0.55 and 0.00d) 0.45, 0.35 and 0.20

253.The inner (dot) product of two vectors

is zero. The angle (degrees)

between the two vectors isa) 0b) 5c) 90d) 120

254.The minimum and the maximum eigenvalues of the matrix are -2and 6, respectively. What is the other

eigen value?

a) 5b) 3c) 1d) -1

255.The degree of the differential equation isa) 0b) 1c) 2d)

3

256.The solution for the differentialequation

with condition thaty = 1 at x=0 is

a) b) c) d)

257.For what values of and thefollowing simultaneous equations

have an infinite number of solutions? a) 2,7b) 3,8c) 8,3d) 7,2

258.A velocity vector is given as Thedivergence of this velocity vector at

(1,1,1) is

a) 9b) 10c) 14d) 15

259.The iterative equation for this purposeis (k indicates the iteration level)

(1,1,1) is The iterative equation for this purpose

is (k indicates the iteration level)

a) b) c)

d) 260.Evaluate

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

261.Potential function is given is . What will be the streamfunction ()with the condition

a) 2xyb) x+yc) x-y


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JH ACADEMY Page 20

d) 2xy262.The inverse of the 2 x 2 matrix* + is

a) *

+b) * +c) * +d) * +

263.Given that one root of theequation ,Given that one root of the equation

a) 2 and 3b) 2 and 4c) 3 and 4d) -2 and -3

264.If the standard deviation of the spotspeed of vehicles in a highway is 8.8

kmph and the mean speed of the

vehicles is 33kmph, the coefficient of

variation in speed is

a) 0.1517b) 0.1867c) 0.2666d) 0.3646

265.Solution for the system by the set ofequations4y + 3z = 8 ; 2x-z = 2; and 3x +

2y = 5 is

a) x = 0; y = 1; z = 4/3b) x = 0; y = 1/2; z = 2c) x = 1; y = 1/2 ; z = 2d) Nonexistent

266.For a given matrix A = ,one of the eigenvalues is 3. The other

two eigenvalues are

a) 2,-5b) 3,-5c) 2,5d) 3,5

267.The directional derivative of at thepoint P : (2, 1, 3) in the direction of the

a) -2.785b) -2.145c) 1.789d) 1.000

268.A class of first year B. Tech. students iscomposed of four bathes A,B,C and D,

each consisting of 30 students. It is

found that the sessional marks of

students in Engineering Drawing in

batch C have a mean of 6.6 and

standard deviation of 2.3. The mean

and standard deviation of the marks

for the entire class are 5.5 and 4.2,

respectively. It is decided by the

course instructor to normalize the

marks of the students of all batches tohave the same mean and standard

deviation as that of the entire class.

Due to this, the marks of a student in

batch C are changed from 8.5 to

a) 6.0b) 7.0c) 8.0d) 9.0

269.A degree polynomial, f(x), hasvalues of 1,4, and 15 at x = 0, and 2,

respectively. The integral isto be estimated by applying thetrapezoidal rule to this data. What is

the error (defined as true value

approximate value) in the estimate?

a) -4/3b) 2/3c) 0d) -2/3

270.What is the area common to the circlesr= and

?

a) 0.524 ab) 0.614 ac) 0.147 ad) 1.228 a

271.Using Cauchys integral theorem, thevalue of the integral (integration being

taken in counter clockwise direction) isa) b) c)

d) 1272.There are 25 calculators in a box. Twoof hem are defective. Suppose 5

calculators are randomly picked for

inspecion ((i.e., each has the same

chance of being selected), what is the

probability that only one of the

defective calculators will be included

in the inspection ?

a) b) 1/3c) d)

1/5


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JH ACADEMY Page 21

273.The solution of the differentialequation, given that at x = 1, y = 0 is

a) b)

c) d) 274.Consider the matrices X(4x 3) Y(4x3) and

P(2x 3).The order of [P(XTY)

-1P

T)

Twill

be

a) (2 x 2)b) (3 x 3)c) (4 x 3)d) (3x4)

275.Consider a non-homogeneous system oflinear equations representing

mathematically an over-determined

system. Such a system will be

a) consistent having a uniquesolution

b) consistent having a manysolutions

c) inconsistent having a uniquesolution

d) inconsistent having nosolution

276.Which one of the following is NOT

true for complex number Z1 and

Z2 ?

a)

b) |Z1 + Z2| |Z1| + |Z2|

c) |Z1 Z2| |Z1| |Z2|

d) |Z1 + Z2|2

+ |Z1 Z2|2

=

2|Z1|2

+ 2 |Z2|2

277.Transformation to linear form by

substituting v = y1-n

of the equation

+ p(t)y = q(t)yn; n > 0 will be

a) + (1 n)pv =(1 n)q

b) + (1 n)pv = (1 + n)q

c) + (n + n)pv (n n)q

d) + (1 + n) pv = (1 + n)

278.The solution of + 17y

= 0; (0) = 1, = 0 in the

range 0 < x < is given by

a)b)

c)

d)279.A rail engine accelerates from its

stationary position for 8 secondsand travels a distance of 280 m.

According to the Mean ValueTheorem, the speedometer at acertain time during accelerationmust read exactly

a) 0 km/hb) 8 kmc) 75 km/hd) 126 km/h

280.Value of the

integral , where, cis the square cut from the firstquadrant by the linex = 1 and y = 1 will be (Use Green'stheorem to change the line integralinto double integral)

a)b) 1

c)

d)281.Consider likely applicability of

Cauchy's Integral Theorem toevaluate the following integralcounter clockwise around the unitcircle c.

I = z being a complexvariable. The value of I will be

a) I = 0 : singularities set =


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JH ACADEMY Page 22

b) I = 0: singularities set

=c) I = /2 : singularities set = {n | n =

0, 1, 2, ........}

d) None of above282.Real matrices [A]31, [b]33,

[C]35, [D]53, [E]55, [F]51 aregiven. Matrices [B] and [E]symmetric. Following statements aremade with respect to these matrices

(I) Matrix product [F]T [C]T [B] [C] [F]is a scalar(II) Matrix product [D]T [F] [D] is

always symmetric

With reference to above statements,which of the following applies ?

a) Statement I is true but II is falseb) Statement I is false but II is true

c) Both the statements are true

d) Both the statements are false.283.The summation of series

S = + ...... is

a) 4.50

b) 6.0

c) 6.75

d) 10.0

284.The value of the function

f(x) = is

a) 0

b)

c)

d) 285.The function f(x) = 2x2 - 3x2 - 36x + 2

ha sits maxima at

a) x = 2 only

b) x=0 only

c) x = 3 onlyd) both x= -2 and x=3

286.The eigenvalues of the

matrixa) are 1 and 4

b) are -1 and 2

c) are 0 and 5

d) cannot be determined287.Given Matrix

[A] = , the rank of the

matrix is

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

288.A box contains 10 screws, 3 of whichare defective. Two screws are drawn at

random with replacement. The

probability that none of the two screws

is defective will bea) 100%

b) 50%

c) 49%d) None of these

289.If P, Q and R are three points havingcoordinates (3,-2,01), (1,3,4), (2,1,-2) in

XYZ space, then the distance from point

P to plane OQR (O being the origin of

the coordinate system) is given by

a) 3b) 5c) 7d) 9

290.If L defines the Laplace Transform of afunction, L [sin (at)] will be equal to

a) a/ (s2

-a2

)b) a/ (s2+a2)c) s/ (s

2+a

2)

d) s/ (s2-a2)291.Eigen values of the following matrix

are:

a) 3 and-5b) -3 and 5c) -3 and-5

d) 3 and 5

292. The value of the following definite

integral is

a) -2 in 2b) 2c) 0


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JH ACADEMY Page 23

293.The following function has a localminima at which value of x:

a)

b)

c)

d)

294.The value of the following improper

integral is

d) 0e) f) -1/4g) 1

295.The directional derivative of the

following function at (1,2) inthe direction of (4i+3j) is:

a) 4b) 4/5c) 2/5d) 1

296.The Laplace Transform of the following

function is

a) for all s>0

b) for all s < p

c) for all s>0

d) for all s >0

297.The limit of the following sequence as n

is a) 1

b) 0

c)

d) -

298.The number of boundaryconditions required to solve the

differential equation is is

a) 2b) 4

c) 1d) 1

299.The value of the integral is

I =

a)

b)

c)

d)

300.Determinant of the following matrix

Is

a) -76b) -28c) 28

d) +72

301.The limit of the following series as x

approaches is

a)

b)

c) d) 1


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JH ACADEMY Page 24

302.The inverse Laplace Transform

of is,

a) (b)

b)

c)

d)

303.The solution for the followingdifferential equation with boundary

conditions y(0) = 2 and y'(1) =- 3 is,

a)

b)

c)

d)

304.The product [p][Q] T of the followingtwo matrices [P] and [Q] is

a)

b)

c)

d)

305.The given values of the

matrix are,

a) (5.13,9.42) (b)b) (3.85,2.93)c) (9.00,5.00)d) (10.16,3.84)

306.If A, B, C are square matrices of thesame order, (ABC) -l is equal to

a) C -l A -1 B -1b) C -l B -1 A -1c) A -1 B -1 Cld) A -1 C -l B -1

307.The following integral lim a

a) Diverges

b) Converges to

c) Converges tod) Converges to 0

308.If f(x, y, z) = (x 2 +y 2 +z 2) -1/2

is equal to

a) Zerob) 1c) 2

d) - 3 (x 2 + y 2 + z 2) -5/2

309.The Taylor expansion of sin x about x =

p /6 is given by

a)

b)

c)

d)


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JH ACADEMY Page 25

310.Let F(s) = [f(t)] denote the Laplacetransform of the function f(t). Which of

the following statements is correct?

a)

b)

c)

d)

311.The limit of the function f(x) = [1- a 4 /x 4] as x is given by

a) 1b) exp[- a 4 ]

c) d) Zero

312.The maxima and minima of the functionf(x) = 2x 3 - 15x 2 + 36x + 10 occur,

respectively, at

a) X = 3 and X = 2b) X = 1 and X = 3c) X = 2 and X = 3d) X = 3 and X = 4

313.Limit of the function lim n

a)b) 0c) d) 1

314.The function f(x) = e x is

a) Evenb) Odd

c) Neither even nor oddd) None of the above

315.If A is any n x n matrix and k is a scalar,| kA | = a | A |, where a is

a) knb) n kc) k nd) k/n

316.The infinite series

a) Convergesb) Divergesc) is unstabled) Oscillates

317.Number of inflection points for the

curve y = x + 2 x 4 is

a) 3b) 1c) nd) (n + 1) 2

318.Number of terms in the expansion ofgeneral determinant of order n is

a) n 2b) n!

c) nd) (n + 1) 2

319.lf c is a constant, solution of the

equation = 1 +y 2 is

a) y = sin (x + c)b) y = cos (x + c)c) Y = tan (x + c)d) Y = e x + c

320.The equation represents aparabola passing through the points

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

321.The Laplace transform of the function

f(t) = k, 0 < t < C= 0, c < t < , is

a)

b)

c)

d)

322.Value of the function lim (x- a) (x-a) is


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JH ACADEMY Page 26

x a

a) 1b) 0c)

d) A

323.If the real square matrix ,then isa) Unsymmetric

b) Always symmetricc) Skew symmetricd) Sometimes symmetric

324.A matrix algebra arematrixes of appropriate order ) impliesS=T only if

a) A is symmetricb) A is singularc) A is none singular

d) A is skew symmetric325.A discontinues real function can beexpressed as

a) Taylors series and Fouriers seriesb) Taylors series and not by

Fouriers series

c) Nether Taylors series and norFouriers series

d) Not by Taylors series , but byFouriers series

326.The Laplace transform of a unit step

function , defined as {

is

a) b) c) d)

327.The continues functions f(x,y) is said tohave saddle point at (a,b) if

a) b) c)

d) 328.The Taylors series expansion of sinx is

a) b) c) d)

329.The infinite series ---------------

a) Convergesb) Divergesc) Oscillates

d) Unstable330.The real symmetric matrix C

corresponding to the quadratic from a)

* +

b) * +c) * +d) * +

331.For the differential equation to be exacta)

b)

c) d)

332.The differential equation p isa liner equation of first order only ifa) P is constant but Q is a function y

b) PandQ are function of y orconstants

c) P is a function y but Q is constantd) PandQ are functions of x or

constant

333.For real values of x,cox(x) can bewritten in one of the forms of aconvergent series given below :

a)

b) c) d)

334.If A anb B are two matrixes and if ABexists ,then BA existsa) Only if A has many rows as B has

columns

b) Only if both A and B are squarematrixes

c) Only if A and B are skewmatrixes

d) Only if A and B are symmetric335.If the determination of matrix

is 26,then determination ofmatrix is

a) -26b) 26c) 0d) 52

336.Inverse of matrix is


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a) b)

c) d)

337.Area bounded by the curve andlines x=4 and y=1 is given by

a) 64b) 64/3c) 128/3d) 128/4

338.The curve is given by equation

, is

a) Symmetrical about x-axisb) Symmetrical about y-axisc) Symmetrical about line y=xd) Langential to x=y=a/3

339. is periodic , with a period ofa) 2

b) 2ic) d) i

340. , where m is am integer , isone of the following

a)

b) c) d) 1

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