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1
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
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Apr 13, 2018
in
Numerical Methods
by
Mk Utkarsh
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numbertheory
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1
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2
UGC NET NOV 2017 PAPER Q69
69. Consider the following LPP : Min Z=2x1+x2+3x3 Subject to : x1−2x2+x3 / 4 2x1+x2+x3 £ 8 x1−x3 / 0 x1 , x2 , x3 / 0 The solution of this LPP using Dual Simplex Method is : (1) x1=0, x2=0, x3=3 and Z=9 (2) x1=0, x2=6, x3=0 and Z=6 (3) x1=4, x2=0, x3=0 and Z=8 (4) x1=2, xx2=0, x3=2 andZ=10
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Jan 18, 2018
in
Numerical Methods
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kavikeve
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493
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+1
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0
answers
3
UGC NET NOV 2017 PAPER 3 Q68
68. Consider the following LPP : Max Z=15x1+10x2 Subject to the constraints 4x1+6x2 ≤ 360 3x1+0x2 ≤ 180 0x1+5x2 ≤ 200 x1 , x2> / 0 The solution of the LPP using Graphical solution technique is : (1) x1=60, x2=0 and Z=900 (2) x1=60, x2=20 and Z=1100 (3) x1=60, x2=30 and Z=1200 (4) x1=50, x2=40 and Z=1150
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Jan 18, 2018
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Numerical Methods
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kavikeve
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493
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456
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+1
vote
0
answers
4
UGCNETJune2014III60
The initial basic feasible solution of the following transportion problem: is given as 5 8 7 2 2 10 then the minimum cost is 76 78 80 82
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Nov 2, 2017
in
Numerical Methods
by
Naqvi
(
29
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201
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ugcnetjune2014iii
transportationmethod
+6
votes
4
answers
5
ISRO20173
Using NewtonRaphson method, a root correct to 3 decimal places of $x^3  3x 5 = 0$ 2.222 2.275 2.279 None of the above
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May 7, 2017
in
Numerical Methods
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sh!va
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isro2017
newtonraphson
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6
GATE19881i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
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Dec 10, 2016
in
Numerical Methods
by
jothee
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gate1988
nongate
numericalmethods
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0
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7
GATE198711b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
[closed]
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Nov 15, 2016
in
Numerical Methods
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makhdoom ghaya
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gate1987
nongate
numericalmethods
simpsonsrule
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0
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8
GATE198711a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.
[closed]
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Nov 15, 2016
in
Numerical Methods
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makhdoom ghaya
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41k
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gate1987
nongate
numericalmethods
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0
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9
GATE19871xxv
Which of the following statements is true in respect of the convergence of the NewtonRephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.
[closed]
asked
Nov 9, 2016
in
Numerical Methods
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makhdoom ghaya
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41k
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gate1987
numericalmethods
nongate
newtonraphson
0
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0
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10
GATE19871xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.
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Nov 9, 2016
in
Numerical Methods
by
makhdoom ghaya
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41k
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150
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gate1987
numericalmethods
simplexmethod
nongate
+3
votes
1
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11
UGCNETDec2014III69
Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known and is given in the following table : Find out the minimum time required to complete all the jobs. $5$ $11$ $13$ $15$
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Aug 2, 2016
in
Numerical Methods
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makhdoom ghaya
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41k
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ugcnetdec2014iii
assignmentproblem
hungarianmethod
+4
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1
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12
ISRO201152
Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear interpolation is 11 4 22 10
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Jun 23, 2016
in
Numerical Methods
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jothee
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isro2011
interpolation
nongate
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2
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13
ISRO200951
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula
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Jun 15, 2016
in
Numerical Methods
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jothee
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isro2009
numericalmethods
+4
votes
1
answer
14
ISRO200948
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 1$ $x^3 +1$ $x^3 2x^2 +1$
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Jun 15, 2016
in
Numerical Methods
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jothee
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isro2009
polynomials
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1
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15
ISRO200947
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n1} + y_n)  h/12 (\triangledown y_n  \triangle y_0)$ $ h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) 19h/720 (\triangledown ^3 y_n  \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula
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Jun 15, 2016
in
Numerical Methods
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jothee
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938
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isro2009
numericalmethods
nongate
+4
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1
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16
ISRO200946
The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i h)$ then $\triangle$ (forward difference) in terms of $E$ is $E1$ $E$ $1E^{1}$ $1E$
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Jun 15, 2016
in
Numerical Methods
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jothee
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1.3k
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isro2009
+7
votes
1
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17
ISRO200944
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$
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Jun 3, 2016
in
Numerical Methods
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Desert_Warrior
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1.6k
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isro2009
numericalmethods
+3
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2
answers
18
ISRO201348
The GuassSeidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and nonlinear algebraic equations Linear differential equations Linear and nonlinear differential equations
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Apr 29, 2016
in
Numerical Methods
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makhdoom ghaya
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41k
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isro2013
numericalmethods
guassseidaliterativemethod
+10
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3
answers
19
GATE2015350
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.
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Feb 16, 2015
in
Numerical Methods
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jothee
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112k
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gate20153
numericalmethods
simpsonsrule
normal
numericalanswers
+7
votes
2
answers
20
GATE2015239
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is the solution. ... $x_b  (x_bx_a) f_b / (f_bf(x_a)) $ $x_a  (x_bx_a) f_a / (f_bf(x_a)) $
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Feb 13, 2015
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Numerical Methods
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jothee
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gate20152
numericalmethods
secantmethod
normal
0
votes
1
answer
21
calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012
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Jan 30, 2015
in
Numerical Methods
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Nisha kumari
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485
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184
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numericalmethods
simpsonsrule
nongate
0
votes
0
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22
2012 numerical methed
asked
Jan 29, 2015
in
Numerical Methods
by
Nisha kumari
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485
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102
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numericalmethods
outofsyllabusnow
nongate
+1
vote
1
answer
23
GATE2005IT2
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)
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Nov 3, 2014
in
Numerical Methods
by
Ishrat Jahan
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gate2005it
numericalmethods
trapezoidalrule
normal
+2
votes
2
answers
24
GATE2004IT39
Consider the following iterative root finding methods and convergence properties: Iterative root finding methods Convergence properties Q. False Position I. Order of convergence = 1.62 R. Newton Raphson II. Order of convergence = 2 S. Secant III. Order of convergence = 1 with guarantee of convergence T. Successive ... , RII, SI, TIV QII, RI, SIV, TIII QI, RIV, SII, TIII
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Nov 2, 2014
in
Numerical Methods
by
Ishrat Jahan
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19.1k
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225
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gate2004it
numericalmethods
normal
+2
votes
1
answer
25
GATE2004IT38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9
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Nov 2, 2014
in
Numerical Methods
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Ishrat Jahan
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gate2004it
numericalmethods
lagrangesinterpolation
normal
+5
votes
2
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26
GATE2006IT28
The following definite integral evaluates to $\int_{\infty}^{0} e^ {\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
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Oct 31, 2014
in
Numerical Methods
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Ishrat Jahan
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19.1k
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805
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gate2006it
numericalmethods
normal
nongate
0
votes
2
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27
GATE2006IT27
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence 1. Bisection P. 2 or more 2. NewtonRaphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration IR, IIS, IIIP, IVQ IS, IIR, IIIQ, IVP IS, IIQ, IIIR, IVP IS, IIP, IIIQ, IVR
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Oct 31, 2014
in
Numerical Methods
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Ishrat Jahan
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gate2006it
numericalmethods
normal
+4
votes
1
answer
28
GATE2007IT77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2  2$, where $c > 0$. For which of the following values of $c$, does there exist a nonempty open interval $(a, b)$ such that the sequence $x_n$ ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
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Oct 31, 2014
in
Numerical Methods
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Ishrat Jahan
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19.1k
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534
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gate2007it
numericalmethods
normal
nongate
0
votes
1
answer
29
GATE2007IT22
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h. 102 103 104 105 For which of these values of the step size h, is the computed value guaranteed to be correct to ... Assume that there are no roundoff errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv
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Oct 30, 2014
in
Numerical Methods
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Ishrat Jahan
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19.1k
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367
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gate2007it
numericalmethods
trapezoidalrule
normal
outofsyllabusnow
0
votes
1
answer
30
Is the value obtained by trapezoidal rule greater than
Is the value obtained by trapezoidal rule greater than the exact value and also compare the value obtained in the case of simpsons rule.
asked
Oct 26, 2014
in
Numerical Methods
by
kireeti
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109
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trapezoidalrule
nongate
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