GATE CE 2018 SET-2

 Question 1
The solution of the equation $x\frac{\mathrm{d} y}{\mathrm{d} x}+y=0$ passing through the point (1,1) is
 A $x$ B $x^{2}$ C $x^{-1}$ D $x^{-2}$
Engineering Mathematics   Calculus
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
 A 0.33 B 0.66 C 1 D 3
Engineering Mathematics   Probability and Statistics
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
 A Mean is equal to mode B Mean is greater than median but less than mode C Mean is greater than median and mode D Mode is greater than median
Engineering Mathematics   Probability and Statistics
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:
 A There are 3 members in tension, and 2 members in compression B There are 2 members in tension, 2 members in compression, and 1 zero-force member C There are 2 members in tension, 1 member in compression, and 2 zero-force members D There are 2 members in tension, and 3 zero-force members
Structural Analysis   Trusses
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
 A Le Chatelier apparatus B Briquette testing apparatus C Vicat apparatus D Casagrande's apparatus
Construction Materials and Management
Question 5 Explanation:
Vicat apparatus is used to determine the normal consistancy, IST, FST of cement.

There are 5 questions to complete.