← MES Jr. Grade
Past Questions
The force polygon for coplanar concurrent forces
A)
must close
B)
must not close
C)
may or may not close
D)
any of these
For coplanar concurrent forces, the force polygon is a graphical representation of the vector sum of the forces. If the forces are in equilibrium, their resultant is zero, so the polygon closes. If the forces are not in equilibrium, the resultant is not zero, so the polygon does not close. Therefore, the force polygon may or may not close depending on whether the system is in equilibrium.
If b = width and d = depth of section, Moment of inertia of a rectangle about its XX — axis is given by
A)
db²/12
B)
bd³/12
C)
bd³/6
D)
bd³/6
For a rectangular section, the moment of inertia about the centroidal XX-axis (axis parallel to the width) is I = bd^3/12, where b is the width and d is the depth. The depth is cubed because the resistance to bending depends on the dimension perpendicular to the axis. Option (a) is incorrect because it gives b² instead of d³, and options (c) and (d) are incorrect because the denominator should be 12, not 6.
Which of the following is the reason of unsymmetrical bending?
A)
The section is symmetrical but the load line is inclined to both principal axes.
B)
The section is unsymmetrical and the load line is along centroidal axis.
C)
neither (a) nor (b)
D)
both (a) and (b)
Unsymmetrical bending occurs when the bending load does not act in a principal plane or when the section itself is unsymmetrical so that bending is not about a single principal axis. In option (a), even though the section is symmetrical, the load line is inclined to both principal axes, causing bending about more than one axis. In option (b), an unsymmetrical section under a load along the centroidal axis can also produce bending about non-principal axes. Therefore, both situations can lead to unsymmetrical bending.
The ratio of linear compressive stress and compressive strain is termed as
A)
Modulus of rigidity
B)
Modulus of elasticity
C)
Poisson’s ratio
D)
Bulk Modulus of elasticity
Stress is force per unit area, and strain is the corresponding deformation per unit original dimension. The ratio of linear compressive stress to compressive strain gives Young’s modulus, also called the modulus of elasticity. Modulus of rigidity relates shear stress to shear strain, Poisson’s ratio is the ratio of lateral strain to longitudinal strain, and bulk modulus relates hydrostatic stress to volumetric strain.
Generally influence lines are drawn for a/an X load moving on the span. Find the correct replacement for X.
A)
zero
B)
unit
C)
eccentric
D)
uniformly distributed
Influence lines are generally drawn for a **unit load** moving over the span. The purpose is to determine how a response quantity such as reaction, shear force, or bending moment at a point varies as the load moves. Using a unit load makes the influence ordinate directly equal to the effect at that point. Hence, the correct replacement for X is **unit**. The other options are incorrect because influence lines are not typically drawn for zero load, eccentric load, or uniformly distributed load in the general definition.
“If three coplanar forces acting at a point on a body keep it in equilibrium then each force is proportional to the sine of the angle between the other two forces”. The above statement is known as
A)
Triangle law of forces
B)
Lami’s theorem
C)
Varignon’s theorem
D)
Polygon law of forces
The statement says that when three coplanar concurrent forces are in equilibrium, each force is proportional to the sine of the angle between the other two forces. This is exactly **Lami’s theorem**:
F1/sin(α) = F2/sin(β) = F3/sin(γ)
where each angle is the angle between the other two forces.
Why others are incorrect:
- **Triangle law of forces**: gives the resultant of two forces by the third side of a triangle, not this sine relationship.
- **Varignon’s theorem**: deals with moments of forces, not equilibrium of three concurrent forces.
- **Polygon law of forces**: states that if several forces acting at a point are in equilibrium, they can be represented by the sides of a closed polygon.
So the correct answer is **Lami’s theorem**.
The slenderness ratio of a steel member carrying compressive loads resulting from dead and imposed loads shall not exceed
A)
160
B)
180
C)
200
D)
220
For steel members carrying compressive loads due to dead and imposed loads, the permissible slenderness ratio is limited to 160 as per standard steel design provisions. This limit is used to prevent excessive buckling and ensure adequate stability under compression. Higher values like 180, 200, and 220 are not the prescribed limit for such compression members.
The energy developed by a force acting through a distance against resistance is known as
A)
power
B)
work
C)
moment
D)
torque
Work is defined as the energy transferred or developed when a force acts through a distance against resistance. Power is the rate of doing work, moment is the turning effect of a force, and torque is a moment that produces rotation.
The first product in the process of conversion of Iron ore into Steel is
A)
pigiron
B)
cast iron
C)
wrought iron
D)
metallic iron
Iron ore is first reduced in a blast furnace to form pig iron. Pig iron is the initial product obtained from the smelting of iron ore and is then further refined to produce cast iron, wrought iron, or steel. Cast iron and wrought iron are processed forms, while metallic iron is not the standard first product in this conversion sequence.
The ratio of lateral strain to linear strain is known as
A)
Modulus of rigidity
B)
Modulus of elasticity
C)
Poisson’s ratio
D)
Bulk Modulus of elasticity
The ratio of lateral strain to longitudinal (linear) strain is called Poisson’s ratio. It describes how much a material contracts or expands in directions perpendicular to the applied load. The other options are different elastic constants: modulus of rigidity relates shear stress to shear strain, modulus of elasticity relates normal stress to longitudinal strain, and bulk modulus relates volumetric stress to volumetric strain.
A beam of length L is fixed at one end and simply supported at the other end. If EI is the flexural rigidity, the stiffness factor of the beam is
A)
EIL
B)
2EI/L
C)
3EI/L
D)
4EI/L
For a beam fixed at one end and simply supported at the other, the end stiffness factor is the same as the fixed-end stiffness when the far end is partially restrained. The standard stiffness factor for a fixed-pinned beam is 4EI/L. By comparison, a cantilever fixed-free beam has stiffness 3EI/L, and a beam fixed at both ends has higher rotational restraint. Therefore, the correct answer is 4EI/L.
Which of the following is usually considered as a basic or fundamental quantity?
A)
Mass
B)
Length
C)
Time
D)
All of these
In engineering mechanics, mass, length, and time are all considered fundamental (basic) quantities. They are independent quantities and are not derived from other physical quantities. Hence, the correct choice is 'All of these'.
The body of a bolt is termed as
A)
shank
B)
nut
C)
head
D)
washer
In a bolt, the cylindrical body portion between the head and the threaded end is called the shank. The nut is the fastener that fits onto the threads, the head is the top enlarged portion used for tightening, and the washer is a separate disc placed under the nut or head to distribute load.
A beam of length L, fixed at both ends, carries a uniformly distributed load of w per unit length throughout the span. If EI is the flexural rigidity of the beam, the maximum deflection of the beam is
A)
wL⁴/12EI
B)
wL⁴/24EI
C)
wL⁴/192EI
D)
wL⁴/384EI
For a beam fixed at both ends and carrying a uniformly distributed load over the full span, the standard result from strength of materials is that the maximum deflection occurs at midspan and equals wL⁴/192EI. This is much smaller than the simply supported beam case because the fixed ends develop end moments that reduce deflection. Hence, option (c) is correct.
A beam of length L is simply supported at both ends. If EI is the flexural rigidity, the stiffness factor of the beam is
A)
EIL
B)
2EI/L
C)
3EI/L
D)
4EI/L
For a simply supported beam, the end-stiffness factor used in slope-deflection/moment distribution analysis is 3EI/L. This comes from the relation between end moment and end rotation for a member with the far end hinged. Hence, the correct stiffness factor is 3EI/L. The other options correspond to incorrect or different boundary conditions.
If Poisson’s ratio = 1/m, E = Modulus of Elasticity and K = Bulk Modulus of Elasticity, then their relation is given by
A)
E=K(1-2/m)
B)
E=2K(1-2/m)
C)
E=3K(1-2/m)
D)
E=4K(1-2/m)
For an isotropic elastic material, the relation between Young’s modulus E, bulk modulus K, and Poisson’s ratio ν is:
E = 3K(1 - 2ν)
Given ν = 1/m, substitute into the formula:
E = 3K\left(1 - 2/m\right)
So the correct option is (c). Options (a), (b), and (d) are incorrect because the coefficient relating E and K is 3, not 1, 2, or 4.
Plug weld is also known as
A)
lap weld
B)
fillet weld
C)
butt weld
D)
slot weld
A plug weld is a type of weld made through a round hole in one plate to fuse it to another plate below. In welding terminology, a slot weld is the closely related term used for this kind of weld when the opening is elongated; in many exam contexts, plug weld is identified with slot weld as the equivalent category among the given options. The other options are different weld types: lap weld is a joint arrangement, fillet weld is for corner/T-joints, and butt weld joins members edge-to-edge.
A column is treated as a short column if the slenderness ratio with respect to major and minor axes are both less than
A)
10
B)
12
C)
14
D)
16
A column is considered a short column when its slenderness ratio (effective length divided by least lateral dimension/radius of gyration, as applicable) about both the major and minor axes is less than 12 in RCC design practice. If either axis exceeds this limit, the column is treated as a long/slender column. Hence, the correct answer is 12.
The distance between centre of rivets (minimum pitch) should not be less than X times the nominal diameter of rivets. Find the correct replacement for X.
A)
1.50
B)
2.00
C)
2.50
D)
3.00
In steel structures, the minimum pitch (distance between the centers of adjacent rivets) is specified as not less than 2 times the nominal diameter of the rivet. This prevents interference between rivets and allows proper riveting. Therefore, X = 2.00. The other options are too small or not the standard minimum requirement.
Development of these trees takes place by addition of one annular ring every year. Identify the type of tree.
A)
Endogenous
B)
Exogenous
C)
Cambium
D)
Medullary
Trees that grow by adding one annual ring every year are called exogenous trees. In these trees, growth occurs from the cambium layer outward, producing annual rings. Endogenous plants grow from within and do not form such rings. Cambium is the growth tissue itself, not the tree type. Medullary refers to the pith/central region, not the growth pattern.
The black bolts cannot carry loads equal to those of a rivet with the same diameter. In such cases, the remedial measures adopted is the use of
A)
unfinished bolts
B)
turned bolts
C)
rough bolts
D)
common bolts
Black bolts are ordinary bolts and their load-carrying capacity is lower than that of a rivet of the same diameter because of play between the bolt and hole. When equal or higher load capacity is needed, the usual remedial measure is to use turned bolts, which fit more closely in the holes and provide better shear resistance. The other options are not standard remedies in steel structure design.
Which of the following statements is/are true about electric current? 1. The drift speed of electrons inside a conductor is almost equal to the speed of light in vacuum. 2. The motion of electrons in the conductor is similar to flow of charges in empty space.
A)
1 only
B)
2 only
C)
Both 1 and 2
D)
Neither 1 nor 2
Statement 1 is false because the drift speed of electrons in a conductor is very small, not close to the speed of light. Statement 2 is also false because electrons in a conductor do not move like charges in empty space; they undergo frequent collisions with the lattice while drifting slowly under an electric field. Hence, both statements are incorrect.
How many members of the Lok Sabha are elected by the States?
A)
Nearly 540
B)
Nearly 535
C)
Nearly 530
D)
Nearly 528
The Lok Sabha has a total strength of 545 members: up to 530 elected from the States, up to 20 elected from the Union Territories, and 2 nominated from the Anglo-Indian community (as per the pre-2019 constitutional provision). Therefore, the number elected by the States is nearly 530, but since the question asks for the number of members of the Lok Sabha elected by the States and the closest option given is 530, the correct option is (c). Wait—carefully reading the options, the exact constitutional figure is 530, not 540. So the correct answer is option (c): Nearly 530.
According to the latest Socio-Economic and Caste Census 2011, which state has the highest number of households headed by women?
A)
Mizoram
B)
Sikkim
C)
Kerala
D)
Karnataka
According to the Socio-Economic and Caste Census (SECC) 2011, Mizoram had the highest proportion and also one of the highest counts among states of households headed by women. This is consistent with the social structure in the state, where female-headed households are comparatively more common. The other options—Sikkim, Kerala, and Karnataka—do not rank as high as Mizoram in this indicator.
The RBI has estimated the current account deficit at 1.5 per cent in FY 16. The estimation is based on
A)
sharp decrease in oil demand in the country
B)
sharp fall in oil prices
C)
sharp fall in international demand for gold imports
D)
sharp rise in IT exports
The RBI’s FY16 current account deficit estimate of about 1.5% of GDP was mainly based on lower crude oil prices, which reduced the import bill. This was the key macroeconomic factor behind the improved CAD outlook.
Why others are incorrect:
- (a) Oil demand in the country: demand conditions were not the stated basis of the estimate.
- (c) Fall in international demand for gold imports: gold imports can affect CAD, but the RBI’s FY16 estimate was specifically tied to lower oil prices.
- (d) Rise in IT exports: IT exports help the current account, but this was not the main basis of the 1.5% estimate.