Math Class 12 New Book Chapter 10 MCQs Federal Board
Math Class 12 New Book Chapter 10 MCQs Federal Board
(i)
Which of the following is a root finding method?
a) Trapezoidal rule
b) Simpson’s rule
c) Bisection method
d) Both (a) and (b)
Correct option is (c)
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(ii)
Which of the following method requires the calculation of derivative of the function?
a) Trapezoidal rule
b) Bisection method
c) Regula Falsi method
d) Newton’s method
Correct option is (d)
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(iii)
Using bisection method, one root of
$$x^4-x-1=0$$ lies between 1 and 2. After 2nd iteration the root may lie in the interval:
a) (1.25, 1.5)
b) (1, 1.25)
c) (1, 1.5)
d) None of these
Correct option is (d)
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(iv)
Which of the method requires the two initial guesses?
a) Bisection method
b) Newton’s method
c) Regula Falsi method
d) Bothe (a) and (b)
Correct option is (d)
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(v)
What does the bisection method do?
a) Find the maximum of a function
b) Estimates the area under the curve
c) Find the root of the function
d) Differentiates a function
Correct option is (c)
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(vi)
The iterative formula to find the root for the equation
$$f(x)\;=x^3-5x+7=0$$ by Newton’s Raphson method is:
$$a)\;x_{k+1}=\frac{x_k^3-5x}{3x_k^2+7}\\b)\;x_{k+1}=\frac{x_k^3+5x}{3x_k^2+7}\\c)\;x_{k+1}=\frac{2x_k^3-7}{3x_k^2-5}\\d)\;x_{k+1}=\frac{x_k^3+5x-7}{3x_k^2+5}$$
Correct option is (c)
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(vii)
The trapezoidal method is used to:
a) Find roots of equations
b) Integrate functions
c) Differentiate functions
d) Solve system of equations
Correct option is (b)
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(viii)
Which method splits the half to find the root?
a) Newton’s method
b) Regula Falsi method
c) Bisection method
d) Trapezoidal rule
Correct option is (c)
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(ix)
Numerical techniques more commonly involve:
a) Elimination
b) Reduction
c) Iterative
d) Direct methods
Correct option is (c)
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