List of top Questions asked in GATE CE, GATE CY

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 held staff at a ground point \(P\). The reduced level (in m) of the ground point \(P\) with respect to the datum is (rounded off to three decimal places).

Let \(f(x)\) be a continuous function defined in \([0,2] \to \mathbb{R}\) and satisfying the equation
\[ \int_0^2 f(x)[x - f(x)]\,dx = \frac{2}{3} \]
The value of \(f(1)\) is

A 30 m long tape is standardized at \(25^{\circ}\text{C}\). It was used to measure the length of a line which came out to be 200 m. The temperature during the measurement was \(35^{\circ}\text{C}\). The coefficient of expansion of the tape was \(11 \times 10^{-6}\) per \(^{\circ}\text{C}\). The correction in the measured length (in mm) due to change in temperature is (in integer).

To obtain an 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, the inner diameter (in mm) is (rounded off to one decimal place).

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 Mean Speed (in km/h) of the vehicles is (rounded off to two decimal places).

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 same two plates is changed to 6 mm, the weld length (in mm) needed for transferring the same design load is (in integer).

For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as 0.14 cm/s. Considering the same liquid and by using Taylor's equation, the permeability (in cm/s) of this soil corresponding to the void ratio of 0.80 is (rounded off to two decimal places).

Which of the following components is/are NOT removed in the secondary treatment of sewage?

Bag I contains 4 white and 6 black balls.
Bag II contains 4 white and 3 black balls.
One ball is drawn at random from any one of the two bags and it is found to be a black ball. The probability that the black ball was drawn from Bag I is ______ (rounded off to two decimal places).

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 diameter bars of the same grade are used, the required centre-to-centre spacing (in mm) to resist the same design moment becomes (rounded off to the nearest integer).

A matrix is given as:
\[ \begin{bmatrix} 9 & 15 \\ 15 & 50 \end{bmatrix} \]
By performing Cholesky decomposition, \(|l_{22}|\) of the lower triangular matrix is ______ (in integer).

Cant \(C\) on a Broad Gauge railway track is calculated for an equilibrium speed \(V\) (in km/h), dynamic gauge \(G\) (in mm) and radius of curve \(R\) (in m) using formula/formulae:

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

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 70 % porosity. The uniform expanded depth (in m) of the filter bed during backwash is

The settling velocity of inorganic particles in the sedimentation tank of a water treatment plant is governed by

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.

Column 1 (GVF Profile)	Column 2 (Water Surface Slope)
(P) M1	(I) Positive
(Q) M2	(II) Negative
(R) M3	(III) Zero

Which of the following options is/are NOT correct?

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

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 in the balloon wall are, respectively:

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:

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. Using Darcy-Weisbach equation, the ratio of flowrate of water in the bigger diameter pipe to that in the smaller diameter pipe is

The name of a person in Column 1 is to be matched with the test mentioned in Column 2.

Column 1	Column 2
(I) Menard	(P) Dilatometer test
(II) Marchetti	(Q) Pressuremeter test
(III) Casagrande	(R) Compaction test
(IV) Proctor	(S) Liquid limit test

Option giving the CORRECT match between Column 1 and Column 2 is:

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 discharge. The duty (in hectare/cumec) on capacity of this canal is

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

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, the states of the bulbs are changed based on the following rules:

• Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
• Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
• The state of any bulb not meeting the conditions above is left unchanged.

The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______

Based on the relationship between each polygon and the number inside it, the value of \(X\) is ______