Recent questions tagged gatecivil-2026-set1

The figure below is supposed to show three non-overlapping shapes - one oval and two triangles. Which one of the following figures $\text{P, Q, R,}$ or $\text{S}$ fits th...

At how many points will the curves $y=x^{2}$ and $y=-x^{2}-2 x-1$ intersect in the real $(x, y)$ plane?$0$$1$$2$$3$

'If Anish had scored hundred runs in today's match, he would have been made the captain of his team. He would have then become the youngest captain in his team's history....

Which one of the following figures $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, or S , correctly shows the $45^{\circ}$ clockwise-rotated version of figure $\text{(I)}?$$\text{P...

Match the words in Column $\text{I}$ with their synonyms in Column $\text{II}$.\[\begin{array}{|l|c|l|}\hline\textbf{Column I} & \textbf{Column II} \\\hline(i)\ \text{Lo...

In the given figure, $\overline{P Q}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle R O S=80^{\circ}$. Wh...

Based on the relationship between each polygon and the number inside it, the value of ' $X$ ' is $\_\_\_\_$$720$$596$$24$$240$

Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, ...

$P$ and $Q$ are two positive integers such that $P^{2}=Q^{2}+13$.The product of the numbers $P$ and $Q$ is $\_\_\_\_$$13$$26$$39$$42$

Matrix $P$ is given as\[P=\left[\begin{array}{lll}1 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 1\end{array}\right]\]The TRUE option isTrace of $P$ is equal to the sum of the Eigen val...

Given:\[\left[\begin{array}{lll}1 & 1 & 1 \\1 & 0 & 2\end{array}\right]\left\{\begin{array}{l}x_{1} \\x_{2} \\x_{3}\end{array}\right\}=\left\{\begin{array}{l}0 \\0\end{ar...

A thin-walled spherical gas balloon of radius $R$ and wall thickness $t(t \ll R)$ is subjected to an internal (gauge) pressure $p$. The maximum tensile and shear stresses...

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

Which one of the following is utilized to determine the long-term deformation of concrete under sustained loading?CreepShrinkageModulus of ruptureSplit tensile strength

Two reservoirs having different water levels are connected by two long parallel pipelines of same length and same material but having diameters of $600$ mm and $400$ mm. ...

An irrigation canal is to be designed to deliver $10$ cumec to meet the peak demand of $7500$ hectare of cropped area. The estimated canal losses are $50 \%$ of the head ...

​​​​​​The name of a person in Column $1$ is to be matched with the test mentioned in Column $2$.\[\begin{array}{|l|l|}\hline\text{Column 1} & \text{Column 2} \\\hline(I)\...

Corrections are applied to the basic length of the runway strip considering:The elevation $\text{H}$ (in m) of the airport above Mean Sea Level (MSL)Corrected air tempera...

The Whole Circle Bearing (WCB) of line AB is $150^{\circ}$. The length of $\text{AB}$ is $100$ m. The latitude and departure values, respectively, for this line are:$+86....

A rapid sand filter bed of depth $0.8$ m has $40 \%$ porosity during service cycle. It is recommended that during backwash operation, the expanded filter bed should have ...

The settling velocity of inorganic particles in the sedimentation tank of a water treatment plant is governed byDarcy's lawStokes' lawDupuit's lawBernoulli's law

Gradually Varied Flow (GVF) profiles in open channels given in Column $1$ are to be matched with the water surface slopes in Column $2$ in the table below.\[\begin{array}...

Cant $C$ on a Broad Gauge railway track is calculated for an equilibrium speed $V$ (in $\mathrm{km} / \mathrm{h}$), dynamic gauge $G$ (in mm ) and radius of curve $R$ (in...

Which of the following components is/are NOT removed in the secondary treatment of sewage?Suspended settleable organic solidsColloids including dissolved organic matterPa...

Bag $\text{I}$ contains $4$ white and $6$ black balls.Bag $\text{II}$ contains $4$ white and $3$ black balls.One ball is drawn at random from any one of the two bags and ...

A matrix is given as:\[\left[\begin{array}{cc}9 & 15 \\15 & 50\end{array}\right]\]By performing Cholesky decomposition, $\left|l_{22}\right|$ of the lower triangular matr...

It is given that $x$ and $y$ are integers in the following equation:\[(x+y-7)^{2}+(y+3 x-13)^{2}=0\]The value of $\left(x^{3}+y^{3}\right)$ is $\_\_\_\_$ (in integer).

The required centre-to-centre spacing of $10$ mm diameter bars is $150$ mm to resist the design moment in a concrete slab. Instead of $10$ mm diameter bars, if $12$ mm di...

Two steel plates are to be connected together by a $5$ mm fillet weld of length $150$ mm to transfer a design load. If the size of the fillet weld used to connect the sam...

For a liquid, the permeability of a sandy soil having a void ratio of $0.60$ was determined as $0.14 \mathrm{~cm} / \mathrm{s}$. Considering the same liquid and by using ...

To obtain undisturbed clay soil sample, an Area Ratio of $10 \%$ needs to be achieved for a thin walled sampling tube. If the outer diameter of the tube is $50.8$ mm , th...

The travel times of three vehicles on a $2$ km stretch of road are $4,5,$ and $8$ minutes. Assuming the speed of each vehicle to be constant in this stretch, the Space Me...

A $30$ m long tape is standardized at $25^{\circ} \mathrm{C}$. It was used to measure the length of a line which came out to be $200$ m. The temperature during the measur...

The height of the plane of collimation of a levelling instrument is $100.000$ m from a datum. The levelling instrument measures a Back Sight of $1.500$ m on a vertically ...

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x-f(x)] d x=\dfrac{2}{3}.$The value of $f(1)$...

An ordinary differential equation is given below.\[x^{2} \frac{d^{2} y}{d x^{2}}=6 y\]Considering $a$ and $b$ as arbitrary constants, the general solution of the equation...

A plane truss consists of two linearly elastic, homogeneous, identical members, namely PQ and QR. Both members have length ( $L$ ), cross-sectional area ( $A$ ), and modu...

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height.What is the absolute value of the maximum bendin...

For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is $2$. The Froude number of supercritical stream is$\sqrt{3}$$\sqrt{5}$$\sqrt{6}...