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

Question 6 |

The state of stress represented by Mohr's circle shown in the figure is

uniaxial tension | |

biaxial tension of equal magnitude | |

hydrostatic stress | |

pure shear |

Question 6 Explanation:

In pure shear condition, Mohr's circle has its center at origin.

Question 7 |

A weightless cantilever beam of span L is loaded as shown in the figure. For the entire
span of the beam, the material properties are identical and the cross-section is rectangular
with constant width.

From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is

From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is

A | |

B | |

C | |

D |

Question 7 Explanation:

(-PL) + (PL) + (-M_A) = 0

M_A = 0

For most economical,

Maximum cross-section is given where maximum bending moment occurs.

Question 8 |

As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than

4.5 | |

5 | |

5.5 | |

6 |

Question 8 Explanation:

1. Minimum pH value of water for concrete = 6.0

As per IS code provision no. 5.4.2, the pH value of water shall not less than 6.0.

As per IS code provision no. 5.4.2, the pH value of water shall not less than 6.0.

Question 9 |

The traffic starts discharging from an approach at an intersection with the signal turning
green. The constant headway considered from the fourth or fifth headway position is
referred to as

discharge headway | |

effective headway | |

intersection headway | |

saturation headway |

Question 10 |

Soil deposit formed due to transportation by wind is termed as

aeolian deposit | |

alluvial deposit | |

estuarine deposit | |

lacustrine deposit |

Question 10 Explanation:

Soil deposited by wind is Aeolian soil.

There are 10 questions to complete.