List of top Questions asked in GATE CE

The second-order differential equation in an unknown function \( u: u(x,y) \) is defined as \[ \frac{\partial^2 u}{\partial x^2} = 2 \] Assuming \( g: g(x) \), \( f: f(y) \), and \( h: h(y) \), the general solution of the above differential equation is

The three-dimensional state of stress at a point is given by \[ \sigma = \begin{pmatrix} 10 & 0 & 0
0 & 40 & 0
0 & 0 & 0 \end{pmatrix} \text{ MPa.} \] The maximum shear stress at the point is

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Text:
From the ancient Athenian arena to the modern Olympic stadiums, athletics \_\_\_\_ (i) \_\_\_\_ the potential for a spectacle. The crowd \_\_\_\_ (ii) \_\_\_\_ with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps \_\_\_\_ (iii) \_\_\_\_ in an abrupt stop on his left foot. As his body \_\_\_\_ (iv) \_\_\_\_ like a door turning on a hinge, the javelin is launched skyward at a precise angle.

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?

If \( \to \) denotes increasing order of intensity, then the meaning of the words [simmer \( \to \) seethe \( \to \) smolder] is analogous to [break \( \to \) raze \( \to \) \_\_\_\_\_\_\_].
Which one of the given options is appropriate to fill the blank?

In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road. If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is

For positive integers \( p \) and \( q \), with \( \frac{p}{q} \neq 1 \), \( \left(\frac{p}{q}\right)^q = p^{(q-1)} \). Then,

A partial differential equation
\(\frac{∂^2T}{∂x^2}+\frac{∂^2T}{∂y^2}=0\)
is defined for the two-dimensional field T: T(x, y), inside a planar square domain of size 2 m x 2 m. Three boundary edges of the square domain are maintained at value T = 50, whereas the fourth boundary edge is maintained T = 100.
The value of T at the center of the domain is

A map is prepared with a scale of 1:1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjacent contours is

A high tower appeared on an aerial photograph taken at 1000 m above mean sea level with a camera lens of 15 cm focal length. The radial distances of the top and bottom images of the tower from principal point of photograph are 92.6 mm and 78.3 mm, respectively. If the average elevation of terrain is 300 m above mean sea level, then the height of the tower above ground is _________ m (rounded off to the nearest integer).

The three-dimensional state of stress at a point is given by
\(\sigma =\begin{pmatrix} 10 & 0 & 0\\  0 & 40 & 0\\  0 & 0 & 0  \end{pmatrix} \)
The maximum shear stress at the point is

A four-band multispectral image with pixel size of 50 m x 50 m covers a ground area of 20 km × 20 km. If the radiometric resolution of the satellite data is 8 bits, then the uncompressed satellite image contains _______ kilobytes (kB) of data (in integer).

An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m³ and 10 kN/m³, respectively.
The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is _____ (rounded off to the nearest integer).

The in-situ percentage of voids of a sand deposit is 50%. The maximum and minimum densities of sand determined from the laboratory tests are 1.8 g/cm³ and 1.3 g/cm³, respectively. Assume the specific gravity of sand as 2.7.
The relative density index of the in-situ sand is ______ (rounded off to 2 decimal places).

The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle.

The mean speed (in km/hr) of the vehicles in the entire time-space domain is ______ (rounded off to the nearest integer).

Consider two matrices \(A=\begin{bmatrix} 2 & 1 & 4 \\ 1 & 0 & 3 \end{bmatrix}\) and \(B=\begin{bmatrix} -1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}\)
The determinant of the matrix AB is _____ (in integer).

The magnetic bearing of a line in the year 1990 was found to be N 40°30' W and magnetic declination was 3°30′ E. If the present magnetic declination is 2°10′ W, the magnetic bearing now (in reduced bearing system) would be

The table shows the activities and their durations and dependencies in a project.

Activity	Duration (Days)	Depends on
A	8	-
B	4	A
C	4	B
D	4	C, L
F	4	A
G	4	F
H	6	G, L
K	10	A
L	6	F, K

The total duration (in days) of the project is ______ (in integer).

Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}

The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following options is true?

A surveyor observes a zenith angle of 93° 00' 00" during a theodolite survey. The corresponding vertical angle is

A 2m × 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentration 5 g/m³ at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).

An inverted T-shaped concrete beam (B₁) in the figure, with centroidal axis X - X, is subjected to an effective prestressing force of 1000 kN acting at the bottom kern point of the beam cross-section. Also consider an identical concrete beam (B₂) with the same grade of concrete but without any prestressing force.

The additional cracking moment (in kN. m) that can be carried by beam B₁ in comparison to beam B₂ is _____ (rounded off to the nearest integer).