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.