List of top Questions asked in GATE CE

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown. The area of the shaded region is cm$^2$.

In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm$^2$) of the shaded region? (The diagram is representative)

Eject : Insert :: Advance : \(\underline{\hspace{1cm}}\) (By word meaning)

“I have not yet decided what I will do this evening; I \(\underline{\hspace{2cm}}\) visit a friend.”

For the integral \[ I = \int_{-1}^{1} \frac{1}{x^2}\, dx \] which of the following statements is TRUE?

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three point loads in the mid-vertical plane as shown: the upper bar is $100\, \text{mm}\times100\, \text{mm}$ and the lower bar is $50\, \text{mm}\times50\, \text{mm}$. Ignore self-weight and stress concentration. What is the maximum tensile stress (in N/mm$^2$) anywhere in the hanger? 

Creep of concrete under compression is defined as the 

Which one of the following statements is TRUE for Greenhouse Gas (GHG) in the atmosphere?

Given \( G_1 \) and \( G_2 \) are the slopes of the approach and departure grades of a vertical curve, respectively.
Given \( |G_1| < |G_2| \) and \( |G_1| \neq |G_2| \neq 0 \), Statement 1: \( +G_1 \) followed by \( +G_2 \) results in a sag vertical curve.
Statement 2: \( -G_1 \) followed by \( -G_2 \) results in a sag vertical curve.
Statement 3: \( +G_1 \) followed by \( -G_2 \) results in a crest vertical curve.
Which option amongst the following is true?

The direct and reversed zenith angles observed by a theodolite are $56^\circ 00' 00''$ and $303^\circ 00' 00''$, respectively. What is the vertical collimation correction?

A student is scanning his 10 inch $\times$ 10 inch certificate at 600 dots per inch (dpi) to convert it to raster. What is the percentage reduction in number of pixels if the same certificate is scanned at 300 dpi?

If $M$ is an arbitrary real $n \times n$ matrix, then which of the following matrices will have non-negative eigenvalues?

The following function is defined over the interval \([-L, L]\): \[ f(x) = px^4 + qx^5 \] If it is expressed as a Fourier series, \[ f(x) = a_0 + \sum_{n=1}^{\infty} \left( a_n \sin \left( \frac{n \pi x}{L} \right) + b_n \cos \left( \frac{n \pi x}{L} \right) \right), \] which options amongst the following are true?

Consider the following three structures (shown):  

Which of the following statements is/are TRUE?

Identify the waterborne diseases caused by viral pathogens:

Which of the following statements is/are TRUE for the Refuse-Derived Fuel (RDF) in the context of Municipal Solid Waste (MSW) management?

When a supercritical stream enters a mild-sloped (M) channel section, the type of flow profile would become 

The probabilities of occurrences of two independent events \( A \) and \( B \) are 0.5 and 0.8, respectively. What is the probability of occurrence of at least \( A \) or \( B \) (rounded off to one decimal place)?

A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle \(\phi' = 32^\circ\). What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each sample to identify the failure mechanism? 

P: Triaxial compression test 
Q: Triaxial extension test 
R: Direct shear (shear box) test 
S: Vane shear test 

The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is 

In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE?

A singly reinforced concrete beam of balanced section is made of M20 grade concrete and Fe415 grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are

In the differential equation $\dfrac{dy}{dx} + \alpha x y = 0$, $\alpha$ is a positive constant. If $y=1.0$ at $x=0.0$, and $y=0.8$ at $x=1.0$, the value of $\alpha$ is  (rounded off to three decimal places). 

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. The weld size is 8 mm, and the permissible stress in the weld is 120 MPa. What is the safe load $P$ (in kN, rounded off to one decimal place) that can be transmitted by this welded joint?