Application
A. (1/12)(3t – 1)4 + C
What is the integral of (3t – 1)3 dt?
A. (1/12)(3t – 1)4 + C
B. (1/12)(3t – 4)4 + C
C. (1/4)(3t – 1)4 + C
D. (1/4)(3t – 1)3 + C
D. ln 2
Evaluate the integral of dx / (x + 2) from -6 to -10.
A. 21/2
B. 1/2
C. ln 3
D. ln 2
B. 0.293
Evaluate the integral of cos x dx limits from π/4 to π/2.
A. 0.423
B. 0.293
C. 0.923
D. 0.329
B. 1
Evaluate the integral of ln x dx, the limit are 1 and e.
A. 0
B. 1
C. 2
D. 3
A. sin x + C
The integral of cos x with respect to x is
A. sin x + C
B. sec x + C
C. –sin x + C
D. csc x + C
c) Γ(n+1) = nΓ(n) for n>1
1. Which of the following is true?
a) Γ(n+1) = nΓ(n) for any real number
b) Γ(n) = nΓ(n+1) for any real number
c) Γ(n+1) = nΓ(n) for n>1
d) Γ(n) = nΓ(n+1) for n>1
b) n is a positive integer
2. Γ(n+1) = n! can be used when ____________
a) n is any integer
b) n is a positive integer
c) n is a negative integer
d) n is any real number
a) True
4. Gamma function is said to be as Euler’s integral of second kind.
a) True
b) False
a) True
6. Is the given statement true or false?
β(m,n)=Γ(m).Γ(n)Γ(m+n)
a) True
b) False
a) Linear
1. Rate of convergence of the Newton-Raphson method is generally __________
a) Linear
b) Quadratic
c) Super-linear
d) Cubic
b) 1.33
2. The equation f(x) is given as x3 – x2 + 4x – 4 = 0. Considering the initial approximation at x=2 then the value of next approximation correct upto 2 decimal places is given as __________
a) 0.67
b) 1.33
c) 1.00
d) 1.50
b) open
3. The Newton-Raphson method of finding roots of nonlinear equations falls under the category of which of the following methods?
a) bracketing
b) open
c) random
d) graphical
c) f’(x)=0
6. In Newton Raphson method if the curve f f(x) is constant then __________
a) f’’(x)=0
b) f(x)=0
c) f’(x)=0
d) f’(x)=c
b) 90 degrees
7. For what values of 0 the initial guess will be equal to the next iterative values?
a) 70 degrees
b) 90 degrees
c) 100 degrees
d) 55 degrees
d) When the consecutive iterative values of x are equal
9. At which point the iterations in the Newton Raphson method are stopped?
a) When the consecutive iterative values of x are not equal
b) When the consecutive iterative values of x differ by 2 decimal places
c) When the consecutive iterative values of x differ by 3 decimal places
d) When the consecutive iterative values of x are equal
a) At the (n+0.5)th point
The first two steps of the fourth-order Runge-Kutta method finds the value at which point?
a) At the (n+0.5)th point
b) At the (n+1)th point
c) At the (n-1)th point
d) At the nth point
c) Four steps
3. How many steps does the fourth-order Runge-Kutta method use?
a) Two steps
b) Five steps
c) Four steps
d) Three steps
a) Euler methods
6. The first two steps of the fourth-order Runge-Kutta method use __________
a) Euler methods
b) Forward Euler method
c) Backward Euler method
d) Explicit Euler method
c) Simpson’s rule
7. The final corrector of the fourth-order Runge-Kutta method uses ___________
a) Midpoint rule
b) Backward Euler method
c) Simpson’s rule
d) Trapezoidal rule
d) n times
8. Consider an nth order accurate Runge-Kutta method. How many times is the derivative evaluated at the fourth time-step?
a) one time
b) two times
c) four times
d) n times
a) Solenoidal field
6. A vector field which has a vanishing divergence is called as ____________
a) Solenoidal field
b) Rotational field
c) Hemispheroidal field
d) Irrotational field
b) Scalar & Vector
7. Divergence and Curl of a vector field are ___________
a) Scalar & Scalar
b) Scalar & Vector
c) Vector & Vector
d) Vector & Scalar
a) Irrotational
8. A vector field with a vanishing curl is called as __________
a) Irrotational
b) Solenoidal
c) Rotational
d) Cycloidal
a) Circular
1. Which of these is not a type of flows based on their mathematical behaviour?
a) Circular
b) Elliptic
c) Parabolic
d) Hyperbolic
b) characteristic lines
3. The lines along which the derivatives of the dependent variables are indeterminate are called ___________
a) parabolic lines
b) characteristic lines
c) hyperbolic lines
d) transition lines