MCQ1: The following x-y data is given The Newton’s divided difference second order polynomial for the above data is given by f2x=b0+b1x-</mo Answer: -1.0480 MCQ2: The next iterative value of the root of x2-4=0 is …... using the Newton-Raphson method with the initial guess is 3. Answer: 1.5 MCQ3: Given the table below the divided differences interpolation polynomial P(x) is ….. Answer: x3-x+4 MCQ4: Given that m=12E12+E- 12 and d=E& Answer: 1+∂22 MCQ5: The eigenvalues of the matrix 329751361719 are obtained by solving the cubic equation ….. Answer: λ3-27λ2+167λ-285 MCQ6: The polynomial that passes through the following x-y data Is given by 8.125x2-324.75x+3237, 18≤t≤24The corresponding polynomial using Newton’s divided difference polynomial is given by<msu Answer: 0.2500 MCQ7: …………………. is used to denote the process of finding the values inside the interval x0,xn Answer: Interpolation MCQ8: Lagrange’s interpolation formula is used when computing data of ……………….. intervals. Answer: Equal MCQ9: Find the Taylor polynomial of fx=ln⁡x about x0=1. Answer: x-1+x-122+x-133 MCQ10: Using Gauss-Seidel method, solve the system of equations8111-5111-4x1<m Answer: -0.1255 MCQ11: If the determinant of a square matrix A is zero, then matrix A is called..... Answer: Zero matrix MCQ12: The Newton-Raphson method of finding roots of nonlinear equations falls under the category of ……………………….. methods Answer: Bracketing MCQ13: Expression of ∇3f1 as a backward difference is …………………… Answer: ∇3f4 MCQ14: If A=23-1102 and B=11224</mt Answer: 9 MCQ15: ………………….. errors are caused by using approximate formula in computation. Answer: Inherent MCQ16: The Newton Raphson method is also called …………………… Answer: Bolzano’s Bisection method MCQ17: If fx=0 has a root between a and b then f(a) and f(b) are of ………………. signs. Answer: Opposite MCQ18: If A is a singular matrix, then ……. Answer: 1 is an eigenvalue of the matrix A MCQ19: The Lagrange polynomial that passes through the 3 data points is given byf2x=Lox24+L1x</mrow&g Answer: -0.071430 MCQ20: The following data of the velocity of a body is given as a function of time.Using quadratic interpolation to the value of the velocity at t=14.9 seconds, the three data points of time needed for interpolation are Answer: 0,15,18 MCQ21: Iteration method is a ……………………………… method Answer: Direct MCQ22: To estimate the value of 1.75 from the data given belowThe interval h=……………………… Answer: - 0.05 MCQ23: The following n data points x1,y1, x2,y2, . . . <math xmlns="http://ww Answer: Equally spaced MCQ24: A polynomial of the form y=ax2+bx+c is called ………………………………… Answer: linear equation MCQ25: The Newton-Raphson method formula for finding the square root of a real number R from the equation x2-R=0 is Answer: xi+1=xi2 MCQ26: Solving the linear system of equation  2x1+3x2-x3=5, -2x2-x3</ms Answer: 5 MCQ27: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is give Answer: 16x3-11x2+34x-24 MCQ28: If one root of the equation x2+px+12=0 is 4 and the equation x2+px+q=0 have equal roots, then the value of q is ………………………… Answer: 494 MCQ29: The eigenvalues of the matrix B=100230456 are Answer: 2, 5, 6 MCQ30: If the Newton’s interpolating polynomial P4x=x4-3x3+5x2-6. Find the approximate value of f(<mi&g Answer: 381 MCQ31: The eigenvalues of 56170-19230037 are Answer: -19, 5, 37 MCQ32: …………………… method is used for finding the dominant eigenvalue of a matrix. Answer: Gauss elimination method MCQ33: The data of the velocity of a body as a function of time is given as follows:The velocity in m/s at 16s using linear polynomial interpolation is approximately ….. Answer: 27.867 MCQ34: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given Answer: 16x3-11x2+34x-24 MCQ35: If m=12E12+E- 22, where m is the mean operator then m&l Answer: E12+E-22 MCQ36: Every polynomial equation of the nth degree has ……………………………. roots Answer: N MCQ37: If 1 is an eigenvalue of A, then ……………………… Answer: A is a singular matrix MCQ38: The following data of the velocity of a body is given as a function of timeThe quadratic interpolation Vt=8.667t2-349.67t+3523, 18≤t≤24 approximates the velocity of the body. Find the time in seconds at which the velocity of the body is 35m/s. Answer: 18.667 MCQ39: The modification of Gauss elimination method is ………………… Answer: Gauss Jordan method MCQ40: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given Answer: 16x3-11x2+34x-24 MCQ41: Consider the function fx=(x-1)(x-2)(x-3) in 0,4. Find a point X0 Answer: 3±34 MCQ42: Expression of ∆3f1 as a backward difference is …………………… Answer: ∇3f4 MCQ43: Let A=126541732, then det⁡A&l Answer: -13 MCQ44: One of the roots of the equation x3-3x2+x-3=0 is …… Answer: -1 MCQ45: The eigenvalues of the matrix A=2213 are Answer: 1, 4 MCQ46: If A=23-1102 and B=11224< Answer: 9 MCQ47: The eigenvalues of a 4x4 matrix A are given as 2, -3, 13, and 7. The detA then is ……. Answer: 546 MCQ48: If a polynomial of degree n has more than n zeros, then the polynomial is ­­­­­­_________________________ Answer: Oscillatory MCQ49: The Newton-Raphson method of finding roots of nonlinear equations falls under the category of ……………………….. methods Answer: bracketing MCQ50: Solving the linear system of equation  2x1+3x2-x3=5, -2x2-x3</ms Answer: -1 Fill in the Blank (FBQs): FBQ1: What is the coefficient of x-13 from the first three terms of the Taylor polynomial of fx=ln⁡x about x0=1</math> Answer: *1/3* FBQ2: Iteration method is a self- …… method Answer: *Correcting* FBQ3: Solving the linear system of equation  2x1+3x2-x3=5, -2x2-x3</ms Answer: *1* FBQ4: If one root of the equation x2+px+12=0 is 4 and the equation x2+px+q=0 have equal roots, then the value of q is ……… Answer: *12* FBQ5: The real root of the equation x3-3x2+x-3=0 is ……….. Answer: *3* FBQ6: …………………… method is used for finding the dominant eigenvalue of a matrix. Answer: *Power* FBQ7: The following n data points x1,y1, x2,y2, . . . <math xmlns="http://ww Answer: *quadratic spline* FBQ8: If a polynomial of degree n has more than n zeros, then the polynomial is ………………..  Answer: *zero everywhere* FBQ9: The following x-y data is given The Newton’s divided difference second order polynomial for the above data is given by f2x=b0+b1x-</mo Answer: 4.33 FBQ10: Velocity versus time data for a body is approximated by a second order Newton’s divided difference polynomial as Vt=b0+39.622t-20+0.5540(t-20)(t-15), 10</mn Answer: *36.85* FBQ11: The following data of the velocity of a body is given as a function of time.Using the quadratic interpolation to find the value of the velocity at t=14.9 seconds, the three data points of time needed for interpolation are ……………  Answer: *0,15,18* FBQ12: The Newton-Raphson method of finding roots of nonlinear equations falls under the category of ……………………….. methods Answer: *Open* FBQ13: ……………………… errors are due to computational procedure. Answer: *Round off* FBQ14: The next iterative value of the root of x2-4=0 using the Newton-Raphson method is ........ to three decimal places if the initial guess is 3. Answer: *2.167* FBQ15: The root of the equation fx=0 is found by using the Newton-Raphson method. The initial estimate of the root is x0=3, f3=5. The angle the line tangent to the function f Answer: *-0.247* FBQ16: The highest eigenvalues of 56170-19230037 is ………………. Answer: *37* FBQ17: The Lagrange polynomial that passes through the 3 data points is given byf2x=Lox24+L1x</mrow&g Answer: *0.50* FBQ18: If -4.5-41 is an eigenvector of 8-424020- Answer: *4* FBQ19: The coefficient of λ2 in cubic equation of the eigenvalues of the matrix 329751361719 is ……….. Answer: *-27* FBQ20: The eigenvalues of a 4x4 matrix A are given as 2, -3, 13, and 7. The detA then is …………… Answer: *546* FBQ21: If one of the eigenvalues of Anx2 is zero, it implies the determinant of A is ………………. Answer: *Zero* FBQ22: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given Answer: *1/30* FBQ23: The following data of the velocity of a body is given as a function of timeUsing quadratic interpolation, Vt=8.667t2-349.67t+3523, 18≤t≤24 approximates the velocity of the body. Find the time in seconds at which the velocity of the body is 35m/s to three decimal places. Answer: *22.294* FBQ24: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given Answer: *-4* FBQ25: The following data of the velocity of a body is given as a function of time One of the interpolant approximations for the velocity from the above data is given asVt=8.6667t2-349.67t+3523,18≤t≤24 using the above interpolant, the distance in meters covered by the body between <math xmlns= Answer: *10.337* FBQ26: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given as <math xmlns=" Answer: *-3* FBQ27: If the Newton’s interpolating polynomial P4x=x4-3x3+5x2-6. The approximate value of f(x& Answer: *6* FBQ28: The polynomial that passes through the following x-y data Is given by 8.125x2-324.75x+3237,18≤t≤24The corresponding polynomial using Newton’s divided difference polynomial is given by<mi Answer: *8.125* FBQ29: If the Newton’s interpolating polynomial P4x=x4-3x3+5x2-6. The approximate value of f(x& Answer: *369* FBQ30: If f1=-3, f3=9,f4=30, f6=132 and the Lagrange’s interpolating polynomial is given Answer: *1/30* FBQ31: The ....... difference interpolation polynomial and the Lagrange’s interpolating polynomial of f(x) are the same. Answer: *Divided* FBQ32: Given the table below the divided differences interpolation polynomial P(x) is x3+cx-4. What is c?&nbsp; Answer: *1* FBQ33: ……………errors are caused by using approximate formula in computation. Answer: *Truncation* FBQ34: Expression of ∆3f1 as a backward difference is ∇3fk. What is k? Answer: *4* FBQ35: Expression of ∂2f2 as a backward difference is ∆2fn. Find n. Answer: *1* FBQ36: Given that m=12E12+E-&nbsp;12 and d=E</m Answer: *Md* FBQ65: In Newton’s forward interpolation formula the first two terms will give the …………….. Interpolation. Answer: *Linear* FBQ38: In estimating the value of (1.45) from the data given belowthe interval h=…………………………… Answer: 0.1 FBQ39: If A=23-1102 and B=11224</mt Answer: *12* FBQ40: Let A=126541732, then det⁡A&l Answer: *-71* FBQ41: If the determinant of a square matrix A is zero, then matrix A is called ..... Answer: *Singular matrix* FBQ42: Solving the linear system of equation  2x1+3x2-x3=5, -2x2-x3</ms Answer: *-5* FBQ43: Using the Gauss-seidel method for solving the system of equations8111-5111-4x1</mtr& Answer: *-3.225* FBQ44: Using Gauss-Seidel method for solving the system of equations8111-5111-4x1 Answer: *-2.875* FBQ45: If A is a…………………., then det⁡A=det⁡A=0 Answer: *singular matrix* FBQ46: If 1 is an eigenvalue of A, then the eigenvalue AT is ………………. Answer: *1* FBQ47: The eigenvalues of the matrix A=2213 are …………………… Answer: *1, 4* FBQ48: The eigenvalues of the matrix B=100230456 are ……………… Answer: *1, 3, 6* FBQ49: The data of the velocity of a body as a function of time is given as follows:The velocity in m/s at 16s using linear polynomial interpolation to three decimal places is …… Answer: *28.333* FBQ50: The true value of π is 3.14159265 . . . In some mensuration problems the value 227 is commonly used as an approximation to π. The error in this approximation to 6 significant figures is ……… Answer: *– 0.00126449*