List of top Questions asked in GATE CE

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72º anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. Moves forward by 10 cm.
2. Turns 144º clockwise.
The pattern made by the trace left behind by the ant is:

Both the numerator and the denominator of \( \frac{3}{4} \) are increased by a positive integer, \( x \), and those of \( \frac{15}{17} \) are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of \( x \)?
If \( x : y : z = \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \), what is the value of \( \frac{x + z - y}{y} \)?
The movie was funny and I _________.
The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, "two moves along one direction followed by one move in a perpendicular direction". The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is:
Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank. Which one of the following represents a possible unfolding of the cube?
Given the statements:

P is the sister of Q.
Q is the husband of R.
R is the mother of S.
T is the husband of P.
Based on the above information, T is _________ of S.
In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is
Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older.
P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, Q receives \( \frac{4}{9} \) of the total profit, what is the value of \( x \) (in ₹)?
You should ______ when to say ______.
Two straight lines pass through the origin \( (x_0, y_0) = (0, 0) \). One of them passes through the point \( (x_1, y_1) = (1, 3) \) and the other passes through the point \( (x_2, y_2) = (1, 2) \). What is the area enclosed between the straight lines in the interval \( [0, 1] \) on the x-axis?
If \[ p : q = 1 : 2, \quad q : r = 4 : 3, \quad r : s = 4 : 5 \] and \( u \) is 50% more than \( s \), what is the ratio \( p : u \)?

An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle of 50° with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface. 

Considering the trial slip circle KLM, the factor of safety against the failure of the slope under undrained condition (rounded off to two decimal places) is \(\underline{\hspace{1cm}}\).

An unlined canal under regime conditions along with a silt factor of 1 has a width of flow 71.25 m. Assuming the unlined canal as a wide channel, the corresponding average depth of flow (in m, round off to two decimal places) in the canal will be \(\underline{\hspace{1cm}}\).

A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on the other side as shown in the figure. 

The absolute ratio of the net magnitude of vertical forces to the net magnitudeof horizontal forces (round off to two decimal places) is ___________

A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m uniform thickness. A steady pumping at the rate of 40 litres/s from the well for a long time results in a steady drawdown of 4 m at the well face. The subsurface flow to the well due to pumping is steady, horizontal and Darcian and the radius of influence of the well is 245 m. The hydraulic conductivity of the aquifer (in m/day, rounded off to integer) is \(\underline{\hspace{2cm}}\).
A baghouse filter has to treat 12 m\(^3\)/s of waste gas continuously. The baghouse is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m\(^3\)/min-m\(^2\) cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the baghouse is \(\underline{\hspace{1cm}}\).
Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space-mean speed (in km/h, round off to two decimal places) of the observed vehicles is \(\underline{\hspace{1cm}}\).

The longitudinal section of a runway provides the following data: \[ \begin{array}{|c|c|} \hline \text{End-to-end runway (m)} & \text{Gradient (\%)} \\ \hline 0 \text{ to } 300 & + 1.2 \\ 300 \text{ to } 600 & - 0.7 \\ 600 \text{ to } 1100 & + 0.6 \\ 1100 \text{ to } 1400 & - 0.8 \\ 1400 \text{ to } 1700 & - 1.0 \\ \hline \end{array} \] The effective gradient of the runway (in %, rounded off to two decimal places) is \(\underline{\hspace{2cm}}\). 
 

A combined trapezoidal footing of length \( L \) supports two identical square columns \( P_1 \) and \( P_2 \) of size \( 0.5 \, \text{m} \times 0.5 \, \text{m} \), as shown in the figure. The columns \( P_1 \) and \( P_2 \) carry loads of 2000 kN and 1500 kN, respectively. 

If the stress beneath the footing is uniform, the length of the combined footing L (in m, round off to two decimal places) is \(\underline{\hspace{1cm}}\).

A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is \( 20^\circ \). The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, \( \gamma_w = 9.81 \, \text{kN/m}^3 \). 
 

The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, \( \gamma_w = 9.81 \, \text{kN/m}^3 \). 

The overconsolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is \(\underline{\hspace{1cm}}\).

A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the table. 
 

The total float of the activity “V” (in weeks, in integer) is _______________