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TH86
1.
2.
3.
4.
Gauss elimination method depends on
(a) Forward substitution
(b) Back substitution
(c) Iteration
(d) Partial pivoting of elements
Any matrix A is called symmetric if A =
(a) A 1
(b) A T
(c) A 2
(d) 2A
Crout’s method is also known as
(a) Cholesky’s method
(b) Chebyshaves method
(c) Hermite method
(d) Bashforth method
2 99 
Let A  
then the trace of A 999 is

0  1
(a) 2
999
 99   1
99
9
(b) 2999   1  99
9
(c) 99999
(d) 2999   1
999
5.
6.
7.
By bisection method the second
approximation to the root of equation
x 3  x  1  0 in (1, 2) is
3
(a)
2
7
(b)
8
5
(c)
4
7
(d)
4
Eigen vector is also called as
(a) Characteristic root
(b) Latent root
(c) Latent vector
(d) Diagonal vector
If A is an non singular square matrix
and λ be it’s eigen value then
(a) λ1 is on eigen value of A 1
(b)  is an eigen value of A 1
(c) λ1 is on eigen value of A
(d) None of the above
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8.
E is equal to
(a) 1  Δ
(b) Δ  1
(c) 1  Δ
(d) 1  
9.
X
10 15 20
F(x) 14 18 28
Using Newton’s F. D. interpolation formula,
the estimated value of f(12) is
(a) 14.88
(b) 15.88
(c) 16.88
(d) 17.88
10. Given that
X 0 1
2
3
4
x
1
2.72
7.39
20.09
54.60
e
Using trapezoidal rule, the approximate
4
value of  e x dx is equal to
0
(a)
(b)
(c)
(d)
11. By
57
58
59.5
54.6
Simpson’s
1
 
 3
approximate value of
rd
5
rule,

the

 3x  2 x dx ,
2
1
take n = 4 is
(a) 138
(b) 148
(c) 158
(d) 168
12. The order and degree of the differential
4
equation d 4 y  y   dy  are respectively
dx 4
 dx 
2, 4
4, 1
4, 2
2, 2
13. Arithmetic average is also called as
(a) Mean
(b) Median
(c) Mode
(d) Harmonic mean
(a)
(b)
(c)
(d)
(1)
TH86
14. If A c is the complement of an event A,
19. To obtain the curve which passes
then P A c is equal to
(a) 1 + P(A)
(b) 1 – P(A)
(c) P(A)
(d) None of the above
15. Two cards are drawn at random from an
ordinary pack of 52 cards. If both are
spades then the probability P is given by
1
(a)
11
1
(b)
13
1
(c)
15
through the maximum number of
points, the method(a) of curve fitting is used
(b) of least value is used
(c) of least square is used
(d) None of the above
20. The normal distribution can be obtained
from
(a) Poison distribution
(b) Continuous distribution
(c) Binomial distribution
(d) None of the above
21. The normal density curve with mean
μ and standard deviation σ is given by
the equation
 
(d)
1
17
16. The expectation all of the following
distribution
X
2
3
11
F(x) 1 3 1 2 1 6
is given by
(a) 2
(b) 3
(c) 4
(d) None of the above
17. If a poison distribution is given by
0.72x  e 0.72 then the value of
P x  
x!
P(0) is given by
(a) 0.4688
(b) 0.4868
(c) 0.3868
(d) None of the above
18. Numerical methods ascertained the
degree of correlation in
(a) Scatter diagram
(b) Histogram
(c) Coefficient of rank correlation
(d) Bar chart
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(a) y  1 e x μ 
2
2σ 2
2π
1 x μ 2 2σ2
e
π
2
2
(c) y  1 e x μ  2σ
2π
(d) None of the above
(b) y 
22. Square matrix A is said to be unitary if
(a) ATA = I
(b) A6A = I
(c) A2
(d) AT = I
23. If Rank A = Rank C then the system of
equation is called
(a) Consistence
(b) Inconsistence
(c) Homogeneous
(d) Non - homogeneous
24. The modulus of each characteristic root
of a unitary matrix is
(a) Zero
(b) Unity
(c) Orthogonal
(d) Symmetric
25. Using Chebyshev method find the root
of the equation f(x) = sinx –x + 0.5 = 0
(a) 1.0039
(b) 1.4973
(c) 1.2254
(d) 1.3268
(2)
26. Augmented matrix C is equal to
(a) [ B : A]
(b) [ B = A ]
(c) [ A : B]
(d) [A = B]
27. A matrix obtained by interchanging
28.
29.
30.
31.
32.
33.
rows and columns is called
(a) Transpose matrix
(b) Square matrix
(c) Triangular matrix
(d) Null matrix
Adjoint of a matrix is the transpose of
matrix of
(a) Cofactors
(b) Origin values
(c) Origin vectors
(d) Unit element
Matrix multiplication is
(a) commutative
(b) Same
(c) Non-commutative
(d) Invertible
If A is any non-singular square matrix,
then by adjoint method A-1 is
Adj.A
(a)
|A|
1
(b) | A |
2
(c) AdjA. | A |
|A|
(d)
adjA
Gauss – Scidal method is applicable for
(a) Any system
(b) Non –diagonal system
(c) Diagonal system
(d) Linear Orthogonal system
If A is null matrix then its rank is
(a) 1
(b) Less than 1/2
(c) 0
(d) Greater than ½
The system AX = B will have a unique
solution only when
(a) (A) = (C) = no. of variables
(b) (A) = (C) < no. of variables
(c) (A)  (C)
(d) (A) = (C) > no. of variables
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TH86
34. If A and B are independent events, then
P(A  B) =
P(A)
(a)
P(B)
(b) P(A) <0
(c) P(A) =0
(d) 0 ≤ P(A) ≤1
35. If
the
density
function
is
1
 x ,0  x  2
f (x)   2
0 , otherwise,
then E (3x2-2x) is
equal to
10
(a)
3
5
(b)
3
1
(c) 
3
2
(d)
3
36. Out of 800 families with 5 children
each, the no. of families having exactly
3
2
3 boys is P(x =3) = 5C3  1   1  which
2 2
is equal to
5
(a)
16
1
(b)
32
5
(c)
8
(d) None of the above
37. If the r. v. X has the density function
x 2 /9 , o  x  3
then P( 1≤ X ≤2)
f (x)  
o
,
otherwise

is equal to
5
(a)
27
7
(b)
27
7
(c)
27
3
(d)
27
(3)
TH86
dy
 2 y  3e x given y (0) = 0, then
dx
using Taylor’s series method the solution is
(a) y = x + x2+x3 + ….
38. If
(b) y  3x  9 x 2  7 x 3  15 x 4  ....
2
2
8
(c) 1 + x + x2 +x3 + ……
(d) None of the above
39. If dy  y  x y(0) = 1 & h = 0.2 then y(0.2)
dx y  x
using Range Kutta forth order method is
(a) 0.678
(b) 1.1678
(c) 0.9678
(d) None of the above
40. The relative maximum error in the
function u  5xy3
z
2
at x = y = z = 1 with
x  y  z  0.001 is
(a) 0.03
(b) 0.04
(c) 0.005
(d) 0.006
41. If a matrix has characteristic equation,
2  4  5  0 , then by using Cayley –
Hamilton theorem the value of matrix A
2
= 4A + 5I is
(a) Unit matrix
(b) Null matrix
(c) A 2
(d) None of the above
42. The expected value of random variable
X is also known as
(a) Var. of X
(b) Probability of X
(c) A measure of central tendency
(d) Std. Deviation of X
43. The limiting form of the Binomial
distribution as n   and p  o in such
a way that np =  , where  is fixed
positive number is the
(a) Normal distribution
(b) Geometric distribution
(c) Poisson distribution
(d) None of the above
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44. Using modified Euler’s method solution
dy
 log( x  y) with y(0) = 2 for x =
dx
0.8 by taking h = 0.2 is
(a) 2.3217
(b) 0.3217
(c) 3.217
(d) None of the above
45. The real root of Equation 3x-cosx –1 =
0 using Neuton – Raphson method is
(a) 0.005
(b) 0.6071
(c) 0.003
(d) None of the above
 3 2
46. If A = A  
 then cofactor of 4 is
4 5
of
(a)
(b)
(c)
(d)
2
-2
5
3
0 5
 then 2A +3I is equal to
2 3
3 10
(a) 

4 9 
47. If A = 
0 3

2 5
  3 10
(c) 

 4 9 
(d) None of the above
(b) 
cos 2   sin 
then A + AT is
2 
 cos  sin  
48. If A = 
1 0

0 1 
0 1 
(b) 

0 1
1 0 
(c) 

0 1
(a) 
(d) None of the above
(4)
3 5
 then origin values of A
 2 4
are obtained by solving | A  I| = 0
which is equal to
(a) 2 10  12  0
(b) 2  7  2  0
(c) 2  7  2  0
(d) None of the above
cos   sin 
50. If A = 
 then A is
 sin  cos  
(a) Singular
(b) Idempotent
(c) Non-singular
(d) None of the above
2 1 
2
51. If M = 
 then M –3M+I is equal to
3
4


49. If A = 
2  3

8 9 
 2 0
(b) 

 0 3
5 4
(c) 

3 8
2 3
(d) 

9 8
(a) 
52. The normalized representation of floating
– point number 44.88 × 106 is represented
as 0.4488 E8. The exponent is(a) 0.8
TH86
54. The overflow condition can occur in the
case of(a) Addition
(b) Subtraction
(c) Both (a) and (b)
(d) None of the above
55. A polynomial (function) f(x) of degree
n is equal as ___
(a) f(x) = a0 + a1 + a2 + …….. + an
(b) f(x) = x + x2 + x3 + …….. + xn
(c) f(x) = a0 + a1x + a2x + …….. + anx
(d) None of the above
56. The
linear multi-step method is
convergent if the method is consistent
and satisfies
(a) value condition
(b) root condition
(c) absolute condition
(d) error condition
57. Using trapezoidal rule and dividing the
interval [-3, 3] into 6 equal intervals, the
3
approximate value of  x 4 dx is equal to
3
(a)
(b)
(c)
(d)
112
115
117
120
(b) 8
58. Find approximately the value of
(c) 0.88
9.91
10
9.90
9.99
59. Find the mode of the following items 0,
1, 6, 7, 2, 3, 7, 6, 6, 2, 6, 0, 5, 6, 0
(a) 3
(b) 5
(c) 6
(d) 7
(d) None of the above
53. Normalisation is the shifting of _____
to the left till its most significant digit is
non-zero.
(a) Exponent
(b) Mantissa
(c) Both (a) and (b)
(d) None of the above
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3
997
(a)
(b)
(c)
(d)
(5)
TH86
60. A player tosses two fair coins, he wins
Rs. 5.00 if 2 heads occurs Rs. 2.00 if
one head occurs and Rs. 1.00 if no head
occurs his expected winning is given by
(a) Rs. 2.25
(b) Rs. 2.50
(c) Rs. 3.50
(d) None of the above
1  4P 1  P
1  2P are
61. If
the
,
, and
4
4
66.
2
probabilities of three mutuary exclusive
events then,
1
(a) P 
2
1
1
(b)  P 
3
2
1
2
P
(c)
3
3
1
1
P
(d)
6
2
62. A problems in mathematics is given to
three students A, B, C whose chances of
1 1 1
solving it are , , respectively then
2 3 4
the probability that the problem will be
solved is given by
1
(a)
2
1
(b)
3
1
(c)
4
3
(d)
4
63. The curve fitting is the representation of
relationship between the two variables
by means of
(a) polynomial expression
(b) algebraic expression
(c) rational expression
(d) None of the above
64. The degree of relationship existing between
three or more variables is called
(a) multiple correlation
(b) simple correlation
(c) linear correlation
(d) None of the above of the above
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65. Histograms and frequency polygons are
67.
68.
69.
70.
two graphic representation of
(a) normal distribution
(b) frequency distribution
(c) relative distribution
(d) binomial distribution
Three athletes, A, B and C participate in
a race. Both A & B have the same
probability of winning the race and each
is twice as likely to win as C. The
probability that B or C win the race is
given by
(a) 2/3
(b) 3/4
(c) 3/5
(d) 13/25
The rank of a matrix A is said to be ‘r’
and all the minors of order
(a) Less than r are zero
(b) Equal to r are zero
(c) c)Greater then ‘r’ are zeros
r
(d)
are zero
2
If the random variable takes non-count
ably infinite no. of values then it is
called
(a) Discrete r. v.
(b) Continuous r. v
(c) Random variable
(d) Non-zero random variable
e  x , x  0
If density function is f ( x )  
,
0
,
x

0

then E = (e2x/3) is equal to
(a) 0
(b) 2
(c) 3
(d) None of the above
The predictor formula is given by
h
(a) ¼ = y 2  (2f1-f2+2f3)
3
4h
(2f1  f 2  2f 3 )
(b) y 4  y 0 
3
h
(c) y 4  y 0  (f1  2f 2  f 3 )
3
(d) None of the above
(6)