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TANCET ME Basic Engineering mathematics Question Paper 2013

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ME Basic Engineering mathematics Entrance 2013 
question paper

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Question 1
If every minor of order r of a matrix is zero, then rank of A is    
A    less than or equal to r
B    equal to r
C    greater than r
D    less than r

Question 2
The system AX= 0 of equations is consistent if
A    det A≠ 0
B    . det A= 0
C    A is non- singular
D    A is orthogonal

Question 3
If 3x + 2y + z =0, x + 4y + z = 0, 2x + y + 4z = 0 is a system of equations, then    
A    it is inconsistent
B    it has only the trivial solution x = 0, y = 0, z = 0.
C    determinant of the matrix of coefficients is zero
D    It can be reduced to a single equation and so solution does not exist

Question 4
By eliminating constants a and b from z = a(x + y) +b, the partial differential equation formed is    
A    p + q = 1
B    p –q = 1
C    p – q = 0
D    p + q = 0

Question 5
The value of div (grad f), where f = tan-1 (y / x) is   
A    -1
B    0
C    1
D    2

Question 6
The work done by the force F = yz I + zx k, in moving a particular from the point (1, 1, 1) to the point (3, 3, 2) along a path C is   
A    4
B    10
C    17
D    14

Question 7
Bilinear transformation always transforms circles into   
A    straight lines
B    ellipses
C    parabolas
D    circles

Question 8
If F(s) Fourier transform of f(x), then the Fourier transform of f(ax) is    
A    aF(s/a)
B    1/a F(as)
C    1/a F(s/a)
D    aF(as)

Question 9
The sufficient conditions for the convergence of iteration method is   
A    the co- efficient matrix is a real symmetric matrix
B    the co- efficient matrix is a diagonally dominant
C    the augmented matrix is an orthogonal matrix
D    the co- efficient matrix is a symmetric matrix

Question 10
The n th divided difference of a n th degree polynomial is a    
A    polynomial of degree more than 1
B    polynomial of degree more than 2
C    polynomial of degree more than 0
D    constant

Question 11
What is the order of Runge – kutta method is a modified Euler’s method?    
A    3
B    4
C    2
D    1

Question 12
If the two regression co- efficients are -0.4 and -0.9, then the correlation co-efficient is
A    0.6
B    0.36
C    √0.6
D    -0.6

Question 13
If some of the eigen values of the matrix A of the quadratic form the positive and others negative, then quadratic form is     
A    positive semi definite
B    indefinite
C    negative semi definite
D    negative definite

Question 14
Singularity of zez1/2 at z = 0is of the type
A    isolated singularity
B    removable singularity
C    essential singularity
D    isolated and removable singularities

Question 15
The rate of convergence is the Gauss – Seidal method is …………………as fast as in Gauss- Jacobi’s method.     
A    thrice
B    half- times
C    twice
D    three by two times

Question 16
In application of Simpsons 1/3rd rule, the interval h for closer approximation should be     
A    small
B    odd or large
C    large
D    even and small

Question 17
Which of the following is a step by step method?    
A    Taylor’s method
B    Picard’s method
C    Adam’s Bash forth method
D    Euler’s method

Question 18
The resultant of a coplanar concurrent force system will have the same moment as the sum of moments of each force and is known as    
A    Varignon’s theorem
B    Lame’s theorem
C    Pappus and Guldinus theorem
D    Principle of transmissibility

Question 19
The maximum tension is the belt, for limiting friction conditions, occurs at     
A    starting
B    stopping
C    maximum power speed
D    specific speed

Question 20
Which one of the following pairs of phenomena illustrates the particle aspect of wave particle duality?      
A    Compton Effect and Bragg’s law
B    Photoelectric effect and Compton Effect
C    Compton Effect and pauli’s principle
D    Bragg’s law and photoelectric effect

Question 21
The operation of the laser is based on     
A    The uncertainty principle
B    The exclusion principle
C    Induced emission of radiation
D    Interference of matter waves

Question 22
During propagation of ultrasonic wave, if there is a rigid wall between two media, the incident wave is      
A    completely transmitted
B    completely reflected
C    partly reflected and partly transmitted
D    completely absorbed

Question 23
Radiographic inspection is based on    
A    differential absorption
B    diffraction
C    interference
D    fluorescence

Question 24
Glass- ceramics are obtained by    
A    controlled heat treatment of ceramics
B    controlled heat treatment of glass
C    mixing glass powder with ceramics
D    melting and cooling the raw material

Question 25
The transition from the ferromagnetic to the paramagnetic state is named after     
A    Curie
B    Curie- Weiss
C    Neel
D    Debye
Question 26
Pure silicon at O K is an    
A    intrinsic semiconductor
B    extrinsic semiconductor
C    metal
D    insulator
Question 27
The magnetization of a superconductor is
A    0
B    –B
C    -1
D    –H
Question 28
At room temperature, fracture of ceramic materials almost always occur by     
A    slow propagation of cracks
B    plastic deformation
C    slow propagation of cracks and plastic deformation
D    fast propagation of cracks
Question 29
For stable equilibrium of floating bodies, the centre of gravity has to be always    
A    below the centre of buoyancy
B    above the centre of buoyancy
C    above the metacentre
D    below the metacentre
Question 30
An oil of kinematic viscosity 0.25 stokes flows through a pipe of 10 cm diameter. The flow is critical at a velocity of about
A    0.5 m/s
B    1.5 m/s
C    2.8 m/s
D    4.6 m/s
Question 31
Water is to be lifted by a net head of 180m. Identical pumps with specific speed of 30, rotational speed of 1450 rpm and capable of discharging 200 liters per second are available. The number of pumps required is
A    1
B    2
C    3
D    4
Question 32
The BOD5 of waste water is determined to be 150mg/L at 200C. The k value is known to be 0.23 per day. What would be ultimate BOD?
A    180 mg/L
B    205 mg/L
C    220 mg/L
D    250 mg/L
Question 33
On no- load the efficiency of a distribution transformer is governed by the
A    relative magnitudes of the core loss and the copper loss
B    magnitude of the core loss
C    magnitude of the primary voltage
D    magnitude of the secondary voltage
Question 34
The purpose of including an external resistance at the time of starting a DC motor is to    
A    increases the starting torque
B    increase the armature flux
C    reduce the starting current
D    maintain the constant flux
Question 35
Which of the following can be used to extend the range of an ammeter?    
A    A low resistance is series with the ammeter
B    A high resistance is series with the ammeter
C    A low resistance in parallel with the ammeter
D    A high resistance in parallel with the ammeter
Question 36
Error due to improper zero adjustment classified as    
A    operator error
B    environment error
C    instrument error
D    random error
Question 37
The rating of transformer is represented in
A    KW
B    KWH
C    KVA
D    Voltas
Question 38
Mutual inductance is define as the ratio of change of   
A    flux in coil 1 to the change of flux in coil 2
B    current in coil 1 to the change of current in coil 2
C    flux in coil 1 to the change of current in coil 1
D    flux coil 2 to the change of current in coil 1
Question 39
What is the work done by air which enters into an evacuated vessel from atmosphere when the valve is opened? The atmospheric pressure is 1.013 bar and 1.5 m3 of air at atmospheric condition enters into the vessel.    
A    100.2 kJ
B    120.5 kJ
C    140.65 kJ
D    151.95 kJ
Question 40
Most of the energy generated in the engine of a car is rejected to the air by the radiator thought the circulating water. Should the radiator be analyzed as    
A    a closed system
B    an open system
C    an isolated system
D    combination of (A) and (B)
Question 41
Kelvin –Planck’s law deals with     
A    conservation of energy
B    conservation of heat into work
C    conservation of work into heat
D    conservation of heat
Question 42
To increases the work capacity of energy transferred by heat transfer from high temperature to low temperature the     
A    lower temperature should be lowered keeping temperature difference same
B    higher temperature should be increased keeping temperature difference same
C    temperature difference should be increased
D    temperature difference should be decreased
Question 43
The characteristic equation of gases pV= mRT holds good for     
A    mono- atomic gases
B    diatomic gases
C    real gases
D    ideal gases
Question 44
Booths algorithm is used for     
A    floating point division
B    restoring division
C    integer multiplication
D    square root
Question 45
Which of the following addressing modes is convenient to handle pointers?     
A    immediate and direct addressing
B    indirect addressing
C    base addressing
D    relative addressing

Question 46
Which one of the following is false about Pipelining?     
A    Increases the CPU instruction throughput
B    Reduces the execution time of an individual instruction
C    Increases the program speed
D    (A) and (B)

Question 47
What is the output of the following code fragment for n= 4?Int sum(n)Int n;{if (n<1)return n;else return (n+ sum(n-1)); }
A    10
B    16
C    14
D    15

Question 48
What is the output of the following code?Main( ){ int i=3While (i--){Int i=100;i--;printf(‘’%d..”,i);}}
A    infinite loop
B    compilation error
C    99..99..99..
D    3..2..1..

Question 49
Which of the following statements regarding the adsorption of a gas on a solid is not correct?    
A    The amount of gas adsorbed increase with increase is pressure
B    The amount of gas adsorbed decreases with increases in temperature
C    The amount of gas adsorbed decreases with increase in the area of the absorbent
D    the adsorption is accompanied by decrease in entropy of the system

Question 50
The specific rate constant of a first order reaction depends on     
A    concentration to the product
B    concentration of the reactant
C    temperature
D    time

Question 51
The total number of vibrational degrees of freedom of hydrogen peroxide molecule is
A    seven
B    six
C    four
D    nine

Question 52
The increasing order of boiling range for petroleum fractions is given by    
A    naphtha < gasoline
B    gasoline < naphtha < kerosene < diesel oil
C    kerosene < naphtha < gasoline < diesel oil
D    naphtha < gasoline < diesel oil < kerosene

Question 53
Let z = ax + by + xy where a and b are arbitrary constants and x, y are independent variables. The differential equation which is related to the above is     
A    ordinary differential equations with order 2
B    ordinary differential equation with order 1
C    partial differential equation with order 2
D    partial differential equation with order 1

Question 54
The volume bounded by the cylinder x2 + y2 = 4, and the plane y + z = 3 and z = 0 is     
A    12π
B    6π
C    3π
D    π

Question 55
The value of the integral ʃ (x – 2y) dx + xdy taken over the circle x2 + y2 = 1 is     
A    4π
B    3π
C    2π
D    π

Question 56
Let f(z) = u + iv be an analytic function, which of the following statement are correct?I. Both u and v satisfy Laplace equationII. Family of curves u = c1 and v = c2 cut orthogonallyIII. ux = -vy and uy = vzIV. u – iv is also an analytic function     
A    (I) and (II) only
B    (I), (II) and (III) only
C    (I), (II) and (IV) only
D    (II), (III) and (IV) only

Question 57
Variance of the random variable X is 4. It’s mean is 2. Then E(x2) is     
A    2
B    4
C    6
D    8

Question 58
The marks secured by 600 students in a Mathematics test were normally distributed with mean 55. If 100 students get marks above 75, the number of students securing marks between 35 and 55 is   
A    150
B    200
C    300
D    500

Question 59
If A is a 4 x 4 matrix. A second order minor of A has its value as 0. Then the rank of A is    
A    < 2
B    = 2
C    > 2
D    anything

Question 60
If f(z) = u + iv an analytic function and u and v are harmonic, then u and v will satisfy    
A    One dimensional wave equation
B    One dimensional heat equation
C    Laplace equation
D    Poission equation

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