Recent questions without answers

Consider the following statements about four numbers:$\text{(S1)}$ The average of the four numbers is $25$$\text{(S2)}$ Each number is at most $40$$\text{(S3)}$ Each numb...

Consider a string $\text{P}$ of length $l$ that is laid out as a straight-line segment. Another string $\text{K}$ is laid out as a semicircular arc with string $\text{P}$...

A fifth-degree polynomial in $x$ is defined for $x>0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at ...

Periodic function $f(x)$ is given below.\[f(x)=\left\{\begin{array}{lll}-1, & \text{when} & -\pi < x < 0 \\1, & \text{when} & 0 < x < \pi\end{array}\right\};\; f(x+2\pi)...

A rectangular singly reinforced concrete beam has a width of $300 \text{ mm}$ and an effective depth of $550 \text{ mm}.$ The grades of steel and concrete are Fe$500$ and...

As per IS:$800-2007$, design of a cantilever steel beam section for its moment capacity requires fulfilment of an upper bound, expressed as:\[M_{d} \leq 1.5 Z_{e} \frac{f...

A plane strain problem (in $\text{X - Y}$ plane) must satisfy the condition:$\sigma_{z z}=0$$\epsilon_{z z}=\epsilon_{x z}=\epsilon_{y z}=0$$\sigma_{x x} \neq \sigma_{x y...

Which one of the following stress conditions represents the state of pure shear stress?

The horizontal beam shown in the figure has fixed supports at $\text{F}$ and $\text{L}.$ Internal hinges are provided at locations $\text{G}$ and $\text{J}$. The beam sup...

The Culturable Command Area (CCA) for a canal is $10000$ hectares. The base period for a crop in the CCA is $140$ days. Watering depth for the crop is $40$ cm. The outlet...

Following statements are made with respect to the mass curve of rainfall:Slope at a point on the curve can be positive.Slope at a point on the curve can be zero.Which one...

Based on the Casagrande's plasticity chart, plasticity index (in $\%$) of inorganic clays having a liquid limit of $40 \%$, ranges between$18.0$ and $28.8$$14.6$ and $28....

Information related to foundation design is provided in table below.\[\begin{array}{|l|l|}\hline\text{Column 1} & \text{Column 2} \\\hline\text{(I) Converse-Labarre formu...

An incident occurred on one side of a median on a four-lane dual carriageway road section. This incident disrupted the traffic movement in one direction. Traffic police d...

Column $\text{I}$ presents common air pollutants, and column $\text{II}$ presents treatment technologies commonly employed to control air pollutants.\[\begin{array}{|c|l|...

One-third of the solid matter in a sludge containing $90 \%$ water is composed of fixed mineral solids with specific gravity $2.5$, and two-third is composed of volatile ...

The grown algae are useful in the operation ofoxidation pond.slow sand filter.cyclone separator.septic tank.

A partial differential equation is given below.\[\frac{\partial^{2} u}{\partial x^{2}}-\frac{\partial^{2} u}{\partial y^{2}}=0\]Possible solution(s) is/are:$(x+y)^{5}$$(x...

The probability (in $\%$) that a storm having return period of $15$ years may occur in the next $10$ years is $\_\_\_\_$ (rounded off to two decimal places).

A fully saturated sandy soil deposit has water content $20 ~\%$ and specific gravity $2.65$.The critical hydraulic gradient for seepage through the soil to create the qui...

A downgrade of $1$ in $100$ meets an upgrade of $1$ in $125$ on a road. If the rate of change of grade is $0.10 \%$ per $30$ m, the length (in m ) of the vertical curve b...

A tourist visiting a city holds a map prepared at a scale of $1: 25000$. The tourist measures the distance between place $\text{A}$ and place $\text{B}$ in the city as $1...

Let $f(x)=\left|\begin{array}{ccc}x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^{2} & p^{3}\end{array}\right|$ where $p$ is a constant.The value of $\dfrac{d^{3}}{d x^{3...

Vector field $\vec{V}$ is defined as\[\vec{V}=3 x^{2} y z \hat{\imath}-5 x y \hat{\jmath}+6 y z^{2} \hat{k}\]The curl of $\vec{V}$ at point $(2,-1,1)$ is$6 \hat{\imath}-1...

A simply supported, linearly elastic, homogeneous, prismatic beam of length $L$ and flexural rigidity $E I$ is shown in the figure.The expression for the Influence Line D...

The plane truss shown in the figure is hinge-supported at $\text{E}$ and $\text{F}$. The truss is subjected to vertical downward force at $\text{R}$ and horizontal force ...

Consider the following statements with respect to rigid pavements:Statement-$1$: Bottom-up cracking (BUC) in rigid pavements is caused at the edge of the slab due to comb...

For the traverse given below, the benchmark is at ground point $\text{L}$. The Reduced Level (RL) of $\text{L}$ is $150.000$ m. The direction of the traverse is from $\te...

The $2.4$ ml of raw sewage is diluted to $240$ ml. The Dissolved Oxygen (DO) of the diluted sample at the beginning of Biochemical Oxygen Demand (BOD) test was $8 \mathrm...

Types of flood routing and methods are given in the table below.\[\begin{array}{|l|l|}\hline\begin{array}{l}\text{Column 1}\\\text{Type of Flood Routing}\end{array}&\begi...

A shallow footing is subjected to a vertical load. Within the elastic limit of the underlying soil, the TRUE statement(s) is/are:Vertical displacement below a rigid shall...

Which of the following statements is/are TRUE with respect to the type of stresses to be considered for the design of rigid pavements?Warping stress due to temperature di...

Consider differential equation $\dfrac{d y}{d x}+x y=x$ with the condition as $y=0$ at $x=0$. The value of $y$ at $x=1.0$ is $\_\_\_\_$ (rounded off to two decimal places...

The age (in years) of a population is normally distributed with a mean of $36$ and standard deviation of $12$. The height (in cm) of the same population is also normally ...

A $250 \mathrm{~mm}$ wide $\times 600 \mathrm{~mm}$ deep rectangular concrete beam is prestressed by means of $4$ high-tensile tendons, each of $14 \mathrm{~mm}$ diameter...

A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length $L$. The frame has a fixed support at one end and a roller support at the ...

Linearly elastic, homogeneous, uniform bars $\text{BCD}$ and $\text{FG}$ shown in the figure have fixed supports at $\text{B}$ and $\text{G}$, respectively. For both the ...

A simply-supported rectangular reinforced concrete beam has a width $250$ mm and an overall depth $600$ mm . The effective span of the beam is $6.23$ m. The beam carries ...

Width (in m) of a rectangular channel required to carry a discharge of $96 \mathrm{~m}^{3} / \mathrm{s}$ at a critical depth of $9.8 \text{ m}$ is $\_\_\_\_$ (rounded off...

The cross section of a $0.5$ m wide vertical gate holding water and oil is shown in the figure. The unit weights of water and oil are $10 ~\mathrm{kN} / \mathrm{m}^{3}$ a...