Numerical Methods and Calculus

Question 71

Find the equation of the circle x²+y²=1 in terms of x\'y\' coordinates, assuming that the xy coordinate system results from a scaling of 3 units in the x\' direction and 4 units in the y\' direction.

• 3(x\')² + 4(y\')² = 1
• (x\'/3)² + (y\'/4)² = 1
• (3x\')² + 4(y\')² = 1
• 1/3(x\')² + 1/4(y\')² = 1

Question 72

Find the normalization transformation that maps a window whose lower left corner is at (1, 1) and upper right corner is at (3, 5) onto a viewport that is the entire normalized device screen.

• (1)
• (2)
• (3)
• (4)

Question 73

For any binary (n, h) linear code with minimum distance (2t+1) or greater

• 2t+1
• t+1
• t
• t-1

Question 74

Consider a single perceptron with sign activation function. The perceptron is represented by weight vector [0.4 −0.3 0.1]_t and a bias θ = 0. If the input vector to the perceptron is X = [0.2 0.6 0.5] then the output of the perceptron is:

• 1
• 0
• -0.25
• -1

Question 75

The Sigmoid activation function f(t) is defined as:

• 
• 
• 
• 

Question 76

Using Newton-Raphson method, a root correct to 3 decimal places of the equation x³ - 3x - 5 = 0

• 2.222
• 2.275
• 2.279
• None of the above

Question 77

The functions mapping R into R are defined as : f(x) = x³ – 4x, g(x) = 1/(x² + 1) and h(x) = x⁴. Then find the value of the following composite functions : hog(x) and hogof(x)

• (x² + 1)⁴ and [(x³ – 4x)² + 1]⁴
• (x² + 1)⁴ and [(x³ – 4x)² + 1]^-4
• (x² + 1)^-4 and [(x³ – 4x)² + 1]⁴
• (x² + 1)^-4 and [(x³ – 4x)² + 1]^-4

Question 78

The conic section that is obtained when a right circular cone is cut through a plane that is parallel to the side of the cone is called

• parabola
• hyperpola
• circle
• ellipse

Question 79

What is the least value of the function f(x) = 2x²- 8x - 3 in the interval [ 0 , 5] ?

• -15

• 7

• -11

• -3

Question 80

Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear interpolation is

• 11
• 4
• 22
• 10