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2nd Year Mathematics Chapter 8 Test

2nd Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 22Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

In the field of cryptography, nonlinear equations play an important role in designing:
1. Linear database management grids
2. Mechanical safety locks
3. Secure communication systems and encryption algorithms
4. Sorting algorithms for big data sets
Geometrically, the straight line drawn through the points (a, f(a)) and (b, f(b)) in the Regula-Falsi method is called a:
1. Tangent line
2. Normal line
3. Secant line
4. Asymptote
For the equation what is the functional value f(1) using radian mode?
1. -0.1585
2. 0.8415
3. -1.0000
4. 0.1585
Geometrically, the Newton-Raphson method finds the next root approximation by extending what line from the current curve point to the x-axis?
1. Secant line
2. Chord line
3. Tangent line
4. Normal line
The equilibrium charge \[q\] in an LC circuit satisfies q³-4q+2=0. What are the functional values at the interval boundaries [0,1] used to start the Regula-Falsi method?
1. f(0)=2 and f(1)=1
2. f(0)= -2 and f(1)=-1
3. f(0)= 2 and f(1)=-1
4. f(0)=0 and f(1)= -2
For the Newton-Raphson between which two consecutive integers does the real root lie?
1. [0,1]
2. [1,2]
3. [2,3]
4. [-1,0]
Which method offers a visual foundation for approximating roots by plotting functions and identifying axis intersections?
1. Newton-Raphson Method
2. Bisection Method
3. Graphical Method
4. Regula-Falsi Method
What is the real root of the polynomial function correct to two decimal places?
1. 1.68
2. 1.74
3. 1.86
4. 1.92
In biology and medicine, nonlinear mathematical models are explicitly mentioned to be involved in the regulation of:
1. Cell division rates and bone density
2. Heartbeats and nerve signals
3. Blood glucose levels and respiration
4. Muscle mass and physical velocity
with n=8 what are the evenly spaced grid points at which the function must be evaluated?
1. 0,0.5,1.0,1.5,2.0
2. 0,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.0
3. 1,2,1,5,1,5,6
4. 0,1,2,3,4,5,6,7,8

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

The electrical activity of the heart is represented by a variable x, which measures the signal strength of the heartbeat. At steady-state, the signal satisfies the nonlinear equation:
Find the real roots of the following functions correct to two decimal places using the graphical method, by finding some interval of sign change.
Find the real roots of nonlinear equations using the Newton-Raphson method. accurate to 4 decimal places.
Find the real roots of the following functions correct to two decimal places using the graphical method, within the specified interval of sign change.
In a nonlinear LC circuit, the equilibrium charge q on the capacitor satisfies q³-4q+2=0. Find the equilibrium values of charge stored on the capacitor lying in the interval [0, 1] using Regula-Falsi method accurate to three decimal places.
In a certain chemical reaction, the concentration of a substance at equilibrium is governed by the relation , where x is the equilibrium concentration (in moles per liter). Use bisection method to find the positive equilibrium concentration of the substance accurate to two decimal places.
Use Trapezoidal Rule to approximate the value of the following definite integrals. taking h = 0.2
Use Trapezoidal Rule to approximate the value of the following definite integrals. taking n=7