Question 1 |
The ordinary differential equation \frac{d^2u}{dx^2}-2x^2u+\sin x=0 is
linear and homogeneous | |
linear and nonhomogeneous | |
nonlinear and homogeneous | |
nonlinear and nonhomogeneous |
Question 1 Explanation:
Its solution is of the type u=f(x), i.e., dependent variable is u.
Hence, given equation is Linear and Non-Homogeneous.
Hence, given equation is Linear and Non-Homogeneous.
Question 2 |
The value of \lim_{x \to \infty } \frac{\sqrt{9x^2+2020}}{x+7} is
\frac{7}{9} | |
1 | |
3 | |
Indeterminable |
Question 2 Explanation:
\lim_{x \to \infty }\frac{3x \sqrt{1+\frac{2020}{x^2}}}{x\left ( 1+\frac{7}{x} \right )}=3
Question 3 |
The integral
\int_{0}^{1}(5x^3+4x^2+3x+2)dx
is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statement is TRUE?
\int_{0}^{1}(5x^3+4x^2+3x+2)dx
is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statement is TRUE?
Simpsons rule as well as rectangular rule of estimation will give NON-zero error. | |
Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give
NON-zero error. | |
Only the rectangular rule of estimation will given zero error. | |
Only Simpson's rule of estimation will give zero error. |
Question 3 Explanation:
Because integral is a polynomial of 3rd degree so Simpson's rule will give error free answer.
Question 4 |
The following partial differential equation is defined for u:u(x,y)
\frac{\partial u}{\partial y}=\frac{\partial^2 u}{\partial x^2}; \; \; y\geq 0;\;x_1\leq x\leq x_2
The set of auxiliary conditions necessary to solve the equation uniquely, is
\frac{\partial u}{\partial y}=\frac{\partial^2 u}{\partial x^2}; \; \; y\geq 0;\;x_1\leq x\leq x_2
The set of auxiliary conditions necessary to solve the equation uniquely, is
three initial conditions | |
three boundary conditions | |
two initial conditions and one boundary condition | |
one initial condition and two boundary conditions |
Question 4 Explanation:
Given: DE is \frac{\partial u}{\partial y}=\frac{\partial^2 u}{\partial x^2}; \; y\geq 0;\; x_1 \leq x\leq x_2
\because y is given as \geq 0 so we take it as time. Hence, above equation is nothing but one-D heat equation which requires one initial condition and two boundary condition.
\because y is given as \geq 0 so we take it as time. Hence, above equation is nothing but one-D heat equation which requires one initial condition and two boundary condition.
Question 5 |
The ratio of the plastic moment capacity of a beam section to its yield moment capacity
is termed as
aspect ratio | |
load factor | |
shape factor | |
slenderness ratio |
Question 5 Explanation:
Ratio of \frac{M_p}{M_y}= Shape factor
There are 5 questions to complete.