Quiz about Numerical Methods (MAT302-4)_CIA III_4BSc (PM and DM)

Question 1

Kavya is studying the concept of forward differences in her mathematics class. She comes across the notation $$\Delta^4y_0$$ and wonders what it represents.

Accepted Answer

$$y_4-4y_3+6y_2-4y_1+y_0$$

Answer

$$y_4+4y_3-6y_2+4y_1-y_0$$

Answer

$$y_4-6y_3+4y_2-6y_1+y_0$$

Answer

$$y_4-4y_3+6y_2+4y_1-y_0$$

Question 2

Aisha is analyzing the temperature readings of her science project over the last four days. What is $$ abla^3y_3$$ in backward difference?

Accepted Answer

$$y_3-3y_2+3y_1-y_0$$

Answer

$$y_3+3y_2-3y_1+y_0$$

Answer

$$y_3-y_2+y_1-y_0$$

Answer

$$y_3+3y_2+3y_1+y_0$$

Question 3

Sanya is studying the behavior of a certain function and has calculated the values $$y(0.1)=0.1003,\ y(0.15)=0.1511,\ y(0.20)=0.2027,\ y(0.25)=0.2553,\ y(0.3)=0.3093$$ for different inputs. She wants to find the fourth order forward difference column for these values. What is the result?

Accepted Answer

$$0.0002$$

Answer

$$0.002$$

Answer

$$0.00002$$

Answer

$$0.000002$$

Question 4

Rohan has a function $$y(1)=4,\ y(3)=12,\ y(4)=19,$$ and $$y(x)=7$$ find $$x$$ .

Accepted Answer

$$1.86$$

Answer

$$1.83$$

Answer

$$1.89$$

Answer

$$1.81$$

Question 5

Find the area bounded by the curve and the x-axis from $$x=7.47$$ to $$x=7.52$$ by using Trapezoidal rule. Given that

$$f\left(7.47\right)=1.93,\ f\left(7.48\right)=1.95,\ f\left(7.49\right)=1.98,\ f\left(7.50\right)=2.01,\ f\left(7.51\right)=2.03,\ f\left(7.52\right)=2.06$$

Accepted Answer

$$0.0996$$

Answer

$$0.007$$

Answer

$$0.996$$

Answer

$$0.0099$$

Question 6

A solid of revolution iss formed by rotating about the x-axis. The area between the x-axis, the lines $$x=0$$ and $$x=1$$ and a curve passing through the points $$\left(0,1\right),\ \left(0.25,\ 0.9896\right),\ \left(0.5,\ 0.9589\right),\ \left(0.75,\ 0.9089\right),\ \left(1,0.8415\right)$$ . Estimate the volume of the solid formed using Simpson's 1/3rd rule if volume $$V=\pi\ \int_0^1y^2dx$$

Accepted Answer

$$2.8192$$

Answer

$$2.9419$$

Answer

$$0.98976$$

Answer

$$0.9361$$

Question 7

Evaluate $$y=\int_0^6f\left(x\right)dx\ $$ using Simpson's 1/3rd rule and 3/8th rule given that $$y\left(0\right)=1,\ y\left(1\right)=0.5,\ y\left(2\right)=0.2,\ y\left(3\right)=0.1,\ y\left(4\right)=0.0588,\ y\left(5\right)=0.0385,\ y\left(6\right)=0.027$$

Accepted Answer

$$1.3662,\ 1.3571$$

Answer

$$1.4108,\ 1.3662$$

Answer

$$1.3571,\ 1.3735$$

Answer

$$1.4108,\ 1.3735$$

Question 8

Which of the following is Unit 2?

Accepted Answer

Finite Differences, Interpolation, and Numerical differentiation and Integration

Answer

Interpolation, and Numerical differentiation and Integration

Answer

Finite Differences, Numerical differentiation and Integration

Answer

Finite Differences, Interpolation,differentiation and Integration

Question 9

Which of the following is/are the course outcomes with respect to Unit 2

Accepted Answer

derive numerical methods for various mathematical operations, including interpolation, differentiation, and integration

Answer

understand floating point numbers and the role of errors and its analysis in numerical methods.

Answer

apply numerical methods to obtain approximate solutions to mathematical problems

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