The number of iterations in Secant Method are less as compared to Newton Raphson.

Secant Method is slower than Newton Raphson Method.

A

True

B

False

In the Newton-Raphson method, an initial guess of x₀ = 2 is made and the sequence x₀, x₁, x₂ ... is obtained for the function 0.75x³ - 2x² - 2x + 4 = 0
Consider the statements
I. x₃ = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Which of the following can act as possible termination conditions in K-Means?
1. For a fixed number of iterations.
2. Assignment of observations to clusters does not change between iterations. Except for cases with a bad local minimum.
3. Centroids do not change between successive iterations.
4. Terminate when RSS falls below a threshold.

A

1, 3 and 4

B

1, 2 and 3

C

1, 2 and 4

D

1,2,3,4

K iterations by Newton-Raphson method of finding square root of a number increases accuracy in number of digits :

A

k

B

2k

C

3k

D

4k

At which point the iterations in the Newton Raphson method are stopped?

A

When the consecutive iterative values of x are not equal

B

When the consecutive iterative values of x differ by 2 decimal places

C

When the consecutive iterative values of x differ by 3 decimal places

D

When the consecutive iterative values of x are equal

The extremum (minimum or maximum) point of a function f(x) is to be determined by solving $$\frac{{{\text{df}}\left( {\text{x}} \right)}}{{{\text{dx}}}} = 0$$ using the Newton-Raphson method. Let f(x) = x³ - 6x and x₀ = 1 be the initial guess of x. The value of x after two iterations (x₂) is

A

0.0141

B

1.4142

C

1.4167

D

1.5000

The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x² - N = 0. If i denotes the iteration index, the correct iterative scheme will be

A

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

B

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{\text{x}}_{\text{i}}^2 + \frac{{\text{N}}}{{{\text{x}}_{\text{i}}^2}}} \right)$$

C

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{{{\text{N}}^2}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

D

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} - \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?

A

30

B

16

C

28

D

20

During a class experiment, a teacher took two objects and immersed them in water. She recorded the readings using a spring balance as shown below: Object Wt. of Stone in Air (Newton) Wt. of Stone in Water (Newton) Weight of Liquid Displaced (Newton) Buoyant Force acting on body (Newton) A 92 X 16 Y B Q 70 Z 10 Which of the following is correct?

A

X - 108, Y - 108, Z - 10, Q - 80

B

X - 108, Y - 16, Z - 80, Q - 80

C

X - 76, Y - 16, Z - 10, Q - 80

D

X - 76, Y - 16, Z - 80, Q - 10

From the given table, what is the percentage of students scoring 40 or more, but less than 70. Scores Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 No. of Students 12 19 22 31 38 46 50

A

8%

B

56%

C

48%

D

96%

The number of iterations in Secant Method are less as compared to Newton Raphson.

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