Question 1 |
Which one of the following is correct?
\lim_{x\rightarrow 0}\left ( \frac{sin4x}{sin 2x} \right )=2 and \lim_{x\rightarrow 0}\left ( \frac{tanx}{x} \right )=1
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\lim_{x\rightarrow 0}\left ( \frac{sin4x}{sin 2x} \right )=1 and \lim_{x\rightarrow 0}\left ( \frac{tanx}{x} \right )=1
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\lim_{x\rightarrow 0}\left ( \frac{sin4x}{sin 2x} \right )= \infty and \lim_{x\rightarrow 0}\left ( \frac{tanx}{x} \right )=1
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\lim_{x\rightarrow 0}\left ( \frac{sin4x}{sin 2x} \right )=2 and \lim_{x\rightarrow 0}\left ( \frac{tanx}{x} \right )= \infty
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Question 1 Explanation:
\lim_{x \to 0}\left ( \frac{\sin 4x}{\sin 2x} \right )=\lim_{x \to 0}\left ( \frac{\frac{\sin 4x}{x}}{\frac{\sin 2x}{x}} \right )=\frac{4}{2}=2 and \lim_{x \to 0}\left ( \frac{\tan x}{x} \right )=1
Question 2 |
Consider a two-dimensional flow through isotropic soil along x direction and z direction. If h is the hydraulic head, the Laplace's equation of continuity is expressed as
\frac{\partial h}{\partial x}+\frac{\partial h}{\partial z}=0 | |
\frac{\partial h}{\partial x}+\frac{\partial h}{\partial x}\frac{\partial h}{\partial z}+\frac{\partial h}{\partial z}=0 | |
\frac{\partial^2 h}{\partial x^2}+\frac{\partial^2 h}{\partial z^2}=0 | |
\frac{\partial^2 h}{\partial x^2}+\frac{\partial^2 h}{\partial x \partial z}+\frac{\partial^2 h}{\partial z^2}=0 |
Question 2 Explanation:
The Laplace's equation of continuity for two dimensional flow in a soil is expressed as:
k_x\frac{\partial^2 h}{\partial x^2}+k_z\frac{\partial^2 h}{\partial z^2}=0... for anisotropic soil [k_x\neq k_z]
:
\frac{\partial^2 h}{\partial x^2}+\frac{\partial^2 h}{\partial z^2}=0... for isotropic soil [k_x = k_z]
k_x\frac{\partial^2 h}{\partial x^2}+k_z\frac{\partial^2 h}{\partial z^2}=0... for anisotropic soil [k_x\neq k_z]
:
\frac{\partial^2 h}{\partial x^2}+\frac{\partial^2 h}{\partial z^2}=0... for isotropic soil [k_x = k_z]
Question 3 |
A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacementof the system at any time t, the equation of motion for the free vibration of the system is m\ddot{z}+kz=0. The natural frequency of the system is
\frac{k}{m} | |
\sqrt{\frac{k}{m}} | |
\frac{m}{k} | |
\sqrt{\frac{m}{k}} |
Question 3 Explanation:
\begin{aligned} m\ddot{z}+kz&=0 \\ \ddot{z}+\frac{k}{m}z&=0 \\ \text{Comparing with} \\ \ddot{z}+\omega _n^2 z&=0 \\ \text{We get}\;\; \omega _n&=\sqrt{\frac{k}{m}} \end{aligned}
Question 4 |
For a small value of h, the Taylor series expansion for f(x+h) is
f(x)+hf'(x)+\frac{h^2}{2!}f''(x)+\frac{h^3}{3!}f'''(x)+...\infty | |
f(x)-hf'(x)+\frac{h^2}{2!}f''(x)-\frac{h^3}{3!}f'''(x)+...\infty | |
f(x)+hf'(x)+\frac{h^2}{2}f''(x)+\frac{h^3}{3}f'''(x)+...\infty | |
f(x)-hf'(x)+\frac{h^2}{2}f''(x)-\frac{h^3}{3}f'''(x)+...\infty |
Question 4 Explanation:
We know that Taylor series for small h of f(x + h) is,
f(x+h)=f(x)+hf'(x)+\frac{h^2}{2!}f''(x)+\frac{h^3}{3!}f'''(x)+...
f(x+h)=f(x)+hf'(x)+\frac{h^2}{2!}f''(x)+\frac{h^3}{3!}f'''(x)+...
Question 5 |
A plane truss is shown in the figure
Which one of the options contains ONLY zero force members in the truss?
Which one of the options contains ONLY zero force members in the truss?
FG, FI, HI, RS | |
FG, FH, HI, RS | |
FI, HI, PR, RS | |
FI, FG, RS, PR |
Question 5 Explanation:
So zero force members are FI, FG, RS, PR
There are 5 questions to complete.