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Discrete Mathematics
6 The interpolation error is denoted by………….
a. E n (x ¯ )=f(x ¯ )−P n (x ¯ )=∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)
b. E n (x ¯ )
=
f(x ¯ )−P n (x ¯ )
=
∑ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
c. E n (x)
=
f(x)−P n (x)
=
∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
d. E n (x ¯ )=f(x ¯ )−P n (x ¯ )=∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
7 The inverse interpolation formular is given by…………..
a. P n (y)=∏ i=0 n x i [∏ j=0,j≠i n y−y j y i −y j ]
b. P n (y)=∑ i=0 n x i [∏ j=1,j≠i n y−y j y i −y k ]
c. P n (y)=∑ i=0 n x i [∏ j=0,j=i n y−y j y i −y j ]
d. P n (y)=∑ i=0 n x i [∏ j=0,j≠i n y−y j y i −y j ]
a. E n (x ¯ )=f(x ¯ )−P n (x ¯ )=∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)
b. E n (x ¯ )
=
f(x ¯ )−P n (x ¯ )
=
∑ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
c. E n (x)
=
f(x)−P n (x)
=
∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
d. E n (x ¯ )=f(x ¯ )−P n (x ¯ )=∏ i=0 n (x ¯ −x i )f ( n+1)ℶ(x ¯ )(n+1)!
7 The inverse interpolation formular is given by…………..
a. P n (y)=∏ i=0 n x i [∏ j=0,j≠i n y−y j y i −y j ]
b. P n (y)=∑ i=0 n x i [∏ j=1,j≠i n y−y j y i −y k ]
c. P n (y)=∑ i=0 n x i [∏ j=0,j=i n y−y j y i −y j ]
d. P n (y)=∑ i=0 n x i [∏ j=0,j≠i n y−y j y i −y j ]
Discrete Mathematics
1 The technique of determining an approximate value of f(x) for a non-tabular value of x which lies outside the internal [a, b] is known as............
a. Newton’s second law
b.Newton’s first law
c. Interpolation
d. extapolation
2 The Lagrange’s interpolating polynomial P(x) is given by …………..
a. P(x)=L 0 (x)f 3 +L 1 (x)f 2 +L 2 (x)f 1 +L 3 (x)f 0
b. p(x)=L 1 (x)f 0 +L 2 (x)f 1 +L 3 (x)f 2 +L 4 (x)f 3
c. P(x)=L 0 (x)f 0 +L 1 (x)f 1 +L 2 (x)f 2 +L 3 (x)f 3
d. P(x)=L 0 (x)f 0 +L 1 (x)f 2 +L 2 (x)f 2 +L 3 (x)f 3
a. Newton’s second law
b.Newton’s first law
c. Interpolation
d. extapolation
2 The Lagrange’s interpolating polynomial P(x) is given by …………..
a. P(x)=L 0 (x)f 3 +L 1 (x)f 2 +L 2 (x)f 1 +L 3 (x)f 0
b. p(x)=L 1 (x)f 0 +L 2 (x)f 1 +L 3 (x)f 2 +L 4 (x)f 3
c. P(x)=L 0 (x)f 0 +L 1 (x)f 1 +L 2 (x)f 2 +L 3 (x)f 3
d. P(x)=L 0 (x)f 0 +L 1 (x)f 2 +L 2 (x)f 2 +L 3 (x)f 3
Discrete Mathematics
The OR gate have a Boolean mathematical equivalence of _________
Multiplication
Inversion
Negation
Addition
Multiplication
Inversion
Negation
Addition
Discrete Mathematics
Given that S = { a, b, c, d , e } and T = { a, c, e }, then one of these is untrue (a) T is a subset of S (b) T⊆S (c) S≠T (d) S⊆T
A = {x / x is an odd number between 5 and 21} is same as------------ (a) A = {5,7,9,11,13,15,17,19} (b) A = {5,7,9,11,13,15,17,19,21} (c) A = {x : x is an odd number between 5 and 21} (d) A = {7,9,11,13,15,17,19,21}
A = {x / x is an odd number between 5 and 21} is same as------------ (a) A = {5,7,9,11,13,15,17,19} (b) A = {5,7,9,11,13,15,17,19,21} (c) A = {x : x is an odd number between 5 and 21} (d) A = {7,9,11,13,15,17,19,21}
Discrete Mathematics
A salesman has below record for products sold during peak seson of October to December. The products are in three variants A, B & C. How many units of product C only is he expected to sell to earn 900 commission? Also find the unit for A & B
Discrete Mathematics
Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.
Discrete Mathematics
Please design the combinatorial circuit for: (p’ *r) + q and [(p ^ q’) V ( r V q)] ^ s
Discrete Mathematics
Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and
B. Is this data correct? Explain.
B. Is this data correct? Explain.
Discrete Mathematics
Out of 500 students investigated, 400 studies Hindi, 200 English and 50 both. Is this data correct.
Explain and justify your answer.
Explain and justify your answer.
Discrete Mathematics
Q. Show that subgroup and factor group of nilpotent group is nilpotent?
