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Previous GATE
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Previous GATE Questions in Numerical Methods
2
votes
1
answer
1
GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
go_editor
asked
in
Numerical Methods
Dec 10, 2016
by
go_editor
554
views
gate1988
numerical-methods
out-of-gate-syllabus
0
votes
0
answers
2
GATE CSE 1987 | Question: 11b
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
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
698
views
gate1987
numerical-methods
simpsons-rule
out-of-gate-syllabus
0
votes
0
answers
3
GATE CSE 1987 | Question: 11a
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
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
516
views
gate1987
numerical-methods
out-of-gate-syllabus
0
votes
0
answers
4
GATE CSE 1987 | Question: 1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson 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
makhdoom ghaya
asked
in
Numerical Methods
Nov 9, 2016
by
makhdoom ghaya
700
views
gate1987
numerical-methods
newton-raphson
out-of-gate-syllabus
1
vote
1
answer
5
GATE CSE 1987 | Question: 1-xxiv
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.
makhdoom ghaya
asked
in
Numerical Methods
Nov 9, 2016
by
makhdoom ghaya
751
views
gate1987
numerical-methods
simplex-method
out-of-gate-syllabus
12
votes
3
answers
6
GATE CSE 2015 Set 3 | Question: 50
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 ________.
go_editor
asked
in
Numerical Methods
Feb 16, 2015
by
go_editor
7.5k
views
gatecse-2015-set3
numerical-methods
simpsons-rule
normal
numerical-answers
out-of-syllabus-now
non-gate
8
votes
2
answers
7
GATE CSE 2015 Set 2 | Question: 39
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 ... $x_b - (x_b-x_a) f_b / (f_b-f(x_a)) $ $x_a - (x_b-x_a) f_a / (f_b-f(x_a)) $
go_editor
asked
in
Numerical Methods
Feb 12, 2015
by
go_editor
4.7k
views
gatecse-2015-set2
numerical-methods
secant-method
4
votes
2
answers
8
GATE CSE 1996 | Question: 2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$
Kathleen
asked
in
Numerical Methods
Oct 9, 2014
by
Kathleen
1.8k
views
gate1996
numerical-methods
newton-raphson
normal
out-of-syllabus-now
0
votes
3
answers
9
GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above
Kathleen
asked
in
Numerical Methods
Oct 8, 2014
by
Kathleen
2.5k
views
gate1995
numerical-methods
newton-raphson
normal
out-of-gate-syllabus
0
votes
3
answers
10
GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
Kathleen
asked
in
Numerical Methods
Oct 4, 2014
by
Kathleen
11.6k
views
gate1994
numerical-methods
easy
out-of-gate-syllabus
0
votes
0
answers
11
GATE CSE 1994 | Question: 1.3
Backward Euler method for solving the differential equation $\frac{dy}{dx}=f(x, y)$ is specified by, (choose one of the following). $y_{n+1}=y_n+hf(x_n, y_n)$ $y_{n+1}=y_n+hf(x_{n+1}, y_{n+1})$ $y_{n+1}=y_{n-1}+2hf(x_n, y_n)$ $y_{n+1}= (1+h)f(x_{n+1}, y_{n+1})$
Kathleen
asked
in
Numerical Methods
Oct 4, 2014
by
Kathleen
1.1k
views
gate1994
numerical-methods
backward-euler-method
out-of-gate-syllabus
0
votes
1
answer
12
GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
Kathleen
asked
in
Numerical Methods
Sep 29, 2014
by
Kathleen
1.5k
views
gate1997
numerical-methods
trapezoidal-rule
normal
0
votes
0
answers
13
GATE CSE 1997 | Question: 4.3
Using the forward Euler method to solve $y’'(t) = f(t), y’(0)=0$ with a step size of $h$, we obtain the following values of $y$ in the first four iterations: $0, hf (0), h(f(0) + f(h)) \text{ and }h(f(0) - f(h) + f(2h))$ $0, 0, h^2f(0)\text{ and } 2h^2 f(0) + f(h)$ $0, 0, h^2f(0) \text{ and } 3h^2f(0)$ $0, 0, hf(0) + h^2f(0) \text{ and }hf (0) + h^2f(0) + hf(h)$
Kathleen
asked
in
Numerical Methods
Sep 29, 2014
by
Kathleen
667
views
gate1997
numerical-methods
non-gate
out-of-gate-syllabus
3
votes
2
answers
14
GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge
Kathleen
asked
in
Numerical Methods
Sep 29, 2014
by
Kathleen
11.9k
views
gate1997
numerical-methods
newton-raphson
normal
non-gate
out-of-gate-syllabus
5
votes
1
answer
15
GATE CSE 2014 Set 3 | Question: 46
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always ... ;s rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
go_editor
asked
in
Numerical Methods
Sep 28, 2014
by
go_editor
3.5k
views
gatecse-2014-set3
numerical-methods
trapezoidal-rule
simpsons-rule
normal
7
votes
1
answer
16
GATE CSE 2014 Set 2 | Question: 46
In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $0.75x^3-2x^2-2x+4=0$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE? Only I Only II Both I and II Neither I nor II
go_editor
asked
in
Numerical Methods
Sep 28, 2014
by
go_editor
2.1k
views
gatecse-2014-set2
numerical-methods
newton-raphson
normal
non-gate
1
vote
1
answer
17
GATE CSE 1998 | Question: 1.3
Which of the following statements applies to the bisection method used for finding roots of functions: converges within a few iterations guaranteed to work for all continuous functions is faster than the Newton-Raphson method requires that there be no error in determining the sign of the function
Kathleen
asked
in
Numerical Methods
Sep 25, 2014
by
Kathleen
22.1k
views
gate1998
numerical-methods
bisection-method
easy
out-of-gate-syllabus
7
votes
1
answer
18
GATE CSE 2012 | Question: 28
The bisection method is applied to compute a zero of the function $f(x) =x ^{4} – x ^{3} – x ^{2} – 4$ in the interval [1,9]. The method converges to a solution after ––––– iterations. (A) 1 (B) 3 (C) 5 (D) 7
Arjun
asked
in
Numerical Methods
Sep 25, 2014
by
Arjun
3.9k
views
gatecse-2012
numerical-methods
bisection-method
3
votes
2
answers
19
GATE CSE 2013 | Question: 23
Function $f$ is known at the following points: $x$ 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is (A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045
Arjun
asked
in
Numerical Methods
Sep 24, 2014
by
Arjun
3.5k
views
gatecse-2013
numerical-methods
trapezoidal-rule
non-gate
6
votes
2
answers
20
GATE CSE 1999 | Question: 1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above
Kathleen
asked
in
Numerical Methods
Sep 23, 2014
by
Kathleen
2.9k
views
gate1999
numerical-methods
newton-raphson
normal
out-of-syllabus-now
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