Question 1 |
The solution of the equation x\frac{\mathrm{d} y}{\mathrm{d} x}+y=0 passing through the point (1,1) is
x | |
x^{2} | |
x^{-1} | |
x^{-2} |
Question 1 Explanation:
\begin{aligned}x\frac{dy}{dx}+y&=0 \\ x\frac{dy}{dx}&=-y \\ \frac{dy}{y}&=-\frac{dx}{x} \\ \int \frac{1}{y}dy&=\int \frac{-1}{x}dx \\ \ln y&=-\ln x+c\\ \text{when } y&=1, x=1\\ c&=0\\ \Rightarrow \;\; y&=\frac{1}{x}=x^{-1} \end{aligned}
Question 2 |
The graph of a function f(x) is shown in the figure.
For f(x) to be a valid probability density function, the value of h is
For f(x) to be a valid probability density function, the value of h is
0.33 | |
0.66 | |
1 | |
3 |
Question 2 Explanation:
\begin{aligned} \int_{0}^{3}f\left ( x \right )dx &=1 \\ \int_{0}^{1}f\left ( x \right )dx+\int_{1}^{2}f\left ( x \right )dx+\int_{2}^{3}f\left ( x \right )dx &=1 \\ \frac{h}{2}+\frac{2h}{2+\frac{3h}{2}} &=1 \\ 6h &=2 \\ \Rightarrow\; \; h &=\frac{1}{3} \end{aligned}
Question 3 |
A probability distribution with right skew is shown in the figure.
The correct statement for the probability distribution is
The correct statement for the probability distribution is
Mean is equal to mode | |
Mean is greater than median but less than mode | |
Mean is greater than median and mode | |
Mode is greater than median |
Question 3 Explanation:
t_{L}\lt t_{mean}=Curve is skew to right.
Mode \lt mean
i.e., Mean \gt median and mode
Mean is greater than the mode and the median.This is common for a distribution that is skewed to the right [i.e., bunched up toward the left and a 'tail' stretching toward the right].
Question 4 |
All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (A) and modulus of elasticity (E).
For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:
For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:
There are 3 members in tension, and 2 members in compression | |
There are 2 members in tension, 2 members in compression, and 1 zero-force member | |
There are 2 members in tension, 1 member in compression, and 2 zero-force members | |
There are 2 members in tension, and 3 zero-force members |
Question 4 Explanation:
Since member BDneither elongate nor contract.
Hence, \quad F_{B D}=0 . So, there are 2 tension members (AB and DC) and 3 zero force members (AD, BD, BC).
Question 5 |
The setting time of cement is determined using
Le Chatelier apparatus | |
Briquette testing apparatus | |
Vicat apparatus | |
Casagrande's apparatus |
Question 5 Explanation:
Vicat apparatus is used to determine the normal consistancy, IST, FST of cement.
There are 5 questions to complete.