Question 1 |

The function f(x, y) satisfies the Laplace equation

\triangledown ^2f(x,y)=0

on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3.

The numerical value of f(0, 0) is:

\triangledown ^2f(x,y)=0

on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3.

The numerical value of f(0, 0) is:

0 | |

2 | |

3 | |

1 |

Question 1 Explanation:

According to given condition given function f(x,y) is nothing but constant function i.e. f(x,y)=3 because this is the only function whose value is 3 at any point on the boundary of unit circle and it is also satisfying Laplace equation, so

f(0,0)=3

f(0,0)=3

Question 2 |

\int \left ( x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+... \right )dx is equil to

\frac{1}{1+x}+constant | |

\frac{1}{1+x^2}+constant | |

-\frac{1}{1-x}+constant | |

-\frac{1}{1-x^2}+constant |

Question 2 Explanation:

MTA- Marks to All

I=\int \left ( x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...\infty \right )dx

I=\frac{x^2}{2}-\frac{x^3}{6}+\frac{x^4}{12}-\frac{x^5}{20}+...

Option (A)

\frac{1}{1+x}=(1+x)^{-1}=1-x+x^2-x^3...\infty

So, its incorrect.

Option (B)

\frac{1}{1+x^2}=(1+x^2)^{-1}=1-x^2+x^4-x^6...\infty

So, its incorrect.

Similarly option (C) and (D) both are incorrect.

No-correct choice given.

I=\int \left ( x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...\infty \right )dx

I=\frac{x^2}{2}-\frac{x^3}{6}+\frac{x^4}{12}-\frac{x^5}{20}+...

Option (A)

\frac{1}{1+x}=(1+x)^{-1}=1-x+x^2-x^3...\infty

So, its incorrect.

Option (B)

\frac{1}{1+x^2}=(1+x^2)^{-1}=1-x^2+x^4-x^6...\infty

So, its incorrect.

Similarly option (C) and (D) both are incorrect.

No-correct choice given.

Question 3 |

For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio (v), and shear modulus (G) is

G=\frac{E}{2(1+v)} | |

G=\frac{E}{(1+2v)} | |

E=\frac{G}{2(1+v)} | |

E=\frac{G}{(1+2v)} |

Question 3 Explanation:

E=2G(1+\mu )

G= Shear modulas

\mu =Poission's ratio

E= Young's modulus

G= Shear modulas

\mu =Poission's ratio

E= Young's modulus

Question 4 |

Read the following statements relating to flexure of reinforced concrete beams:

I. In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain in steel.

II. In under-reinforced sections, steel reaches yielding at a load lower than the load at which the concrete reaches failure strain.

III. Over-reinforced beams are recommended in practice as compared to the under-reinforced beams.

IV. In balanced sections, the concrete reaches failure strain earlier than the yield strain in tensile steel.

Each of the above statements is either True or False.

Which one of the following combinations is correct?

I. In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain in steel.

II. In under-reinforced sections, steel reaches yielding at a load lower than the load at which the concrete reaches failure strain.

III. Over-reinforced beams are recommended in practice as compared to the under-reinforced beams.

IV. In balanced sections, the concrete reaches failure strain earlier than the yield strain in tensile steel.

Each of the above statements is either True or False.

Which one of the following combinations is correct?

I (True), II (True), III (False), IV (False) | |

I (True), II (True), III (False), IV (True) | |

I (False), II (False), III (True), IV (False) | |

I (False), II (True), III (True), IV (False) |

Question 4 Explanation:

The question is based on LSM design principle
as it is describing different conditions related to
strain

Depending on amount of reinforcement in a cross- section, here ca be three types of sections viz. balanced, under reinforced and over reinforced.

Balanced section is a section that is expected to result in a balanced failure. It means at the ultimate limit state in flexure, the concrete will attain a limiting compressive strain of 0.0035 and steel will attain minimum specified tensile strain of 0.002+\frac{0.87f_y}{E_s}

Under reinforced section is a section in which steel yield before collapse. Over reinforced section is a section in which crushing of concrete in compression i.e. attainment of compressive strain of 0.0035 occurs prior to yielding of steel.

In case of over reinforced section the deflection, crack width remain relatively low and failure occurs without any sign of warning and hence over reinforced flexural members are not recommended by IS code.

Based on the above information:

Statement I is true.

Statement II is true.

Statement III is false.

Statement IV is false.

Depending on amount of reinforcement in a cross- section, here ca be three types of sections viz. balanced, under reinforced and over reinforced.

Balanced section is a section that is expected to result in a balanced failure. It means at the ultimate limit state in flexure, the concrete will attain a limiting compressive strain of 0.0035 and steel will attain minimum specified tensile strain of 0.002+\frac{0.87f_y}{E_s}

Under reinforced section is a section in which steel yield before collapse. Over reinforced section is a section in which crushing of concrete in compression i.e. attainment of compressive strain of 0.0035 occurs prior to yielding of steel.

In case of over reinforced section the deflection, crack width remain relatively low and failure occurs without any sign of warning and hence over reinforced flexural members are not recommended by IS code.

Based on the above information:

Statement I is true.

Statement II is true.

Statement III is false.

Statement IV is false.

Question 5 |

Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties):

\begin{array}{|c|l|}\hline \text{Column X}&\text{Column Y} \\ \hline (i) C_3S & \text{(P) Early age strength} \\ \hline (ii) C_2S & \text{(Q) Later age strength}\\ \hline (iii) C_3A& \text{(R) Flash setting}\\ \hline & \text{(S) Highest heat of hydration}\\ \hline & \text{(T) Lowest heat of hydration}\\ \hline \end{array}

Which one of the following combinations is correct?

\begin{array}{|c|l|}\hline \text{Column X}&\text{Column Y} \\ \hline (i) C_3S & \text{(P) Early age strength} \\ \hline (ii) C_2S & \text{(Q) Later age strength}\\ \hline (iii) C_3A& \text{(R) Flash setting}\\ \hline & \text{(S) Highest heat of hydration}\\ \hline & \text{(T) Lowest heat of hydration}\\ \hline \end{array}

Which one of the following combinations is correct?

(i) - (P), (ii) - (Q) and (T), (iii) - (R) and (S) | |

(i) - (Q) and (T), (ii) - (P) and (S), (iii) - (R) | |

(i) - (P), (ii) - (Q) and (R), (iii) - (T) | |

(i) - (T), (ii) - (S), (iii) - (P) and (Q) |

Question 5 Explanation:

C_3S- Responsible for early age strength

C_2S - Responsible for later age strength and lowest heat of hydration

C_3A- Flash setting and highest heat of hydration

C_2S - Responsible for later age strength and lowest heat of hydration

C_3A- Flash setting and highest heat of hydration

Question 6 |

Consider a beam PQ fixed at P, hinged at Q, and subjected to a load F as shown in figure (not drawn to scale). The static and kinematic degrees of
indeterminacy, respectively, are

2 and 1 | |

2 and 0 | |

1 and 2 | |

2 and 2 |

Question 6 Explanation:

Static indeterminacy, SI=r-3=(3+2)-3=2

Kinematic indeterminacy=0+1=1

Question 7 |

Read the following statements:

(P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity.

(Q) For slope stability of an earthen dam, sudden drawdown is never a critical condition.

(R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient.

(S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill.

Which one of the following combinations is correct?

(P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity.

(Q) For slope stability of an earthen dam, sudden drawdown is never a critical condition.

(R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient.

(S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill.

Which one of the following combinations is correct?

(P)-True, (Q)-False, (R)-False, (S)-False | |

(P)-False, (Q)-True, (R)-True, (S)-True | |

(P)-True, (Q)-False, (R)-True, (S)-True | |

(P)-False, (Q)-True, (R)-False, (S)-False |

Question 7 Explanation:

In monsoon season sand will be fully
saturated hence this will be critical condition
in designing of shallow foundation.

In case of sudden drawdown flow direction reverses hence for slope stability, it will be critical condition.

In sandy sea beach, quicksand condition can arise only if existing hydraulic gradient exceeds the critical hydraulic gradient.

In case of sudden drawdown flow direction reverses hence for slope stability, it will be critical condition.

In sandy sea beach, quicksand condition can arise only if existing hydraulic gradient exceeds the critical hydraulic gradient.

Question 8 |

Stresses acting on an infinitesimal soil element are shown in the figure (with \sigma _z \gt \sigma _x). The major and minor principal stresses are \sigma _1
and \sigma _3, respectively. Considering the compressive stresses as positive, which one of the
following expressions correctly represents the angle between the major
principal stress plane and the horizontal plane?

\tan ^{-1}\left ( \frac{\tau _{zx}}{\sigma _1-\sigma _x} \right ) | |

\tan ^{-1}\left ( \frac{\tau _{zx}}{\sigma _3-\sigma _x} \right ) | |

\tan ^{-1}\left ( \frac{\tau _{zx}}{\sigma _1+\sigma _x} \right ) | |

\tan ^{-1}\left ( \frac{\tau _{zx}}{\sigma _1+\sigma _3} \right ) |

Question 8 Explanation:

\begin{aligned} \Sigma F_x &=0 \\ \sigma _x(BC)-\tau _Z \times (AB)\sigma _1 \sin \theta &= 0\\ \sigma _x\left ( \frac{AC \sin \theta }{\cos \theta } \right )+\tau _{zx}\left ( \frac{AC \cos \alpha }{\cos \theta } \right ) &=\sigma _1 \frac{AC \sin \theta }{\cos \theta }\\ \sigma _x \tan \theta +\tau _{zx} &=\sigma _1 \tan \theta \\ \tan \theta(\sigma _1-\sigma _2) &= \tau _{zx}\\ \tan \theta &= \left ( \frac{\tau _{zx}}{\sigma _1-\sigma _x} \right ) \end{aligned}

Question 9 |

Match Column X with Column Y:

\begin{array}{|l|l|}\hline \text{Column X}&\text{Column Y} \\ \hline \text{(P) Horton equation} & \text{((I) Design of alluvial channel} \\ \hline \text{(Q) Penman method} & \text{(II) Maximum flood discharge}\\ \hline \text{(R) Chezys formula}& \text{(III) Evapotranspiration}\\ \hline \text{(S) Lacey's theory}& \text{(IV) Infiltration}\\ \hline \text{(T) Dicken's formula}& \text{(V) Flow velocity}\\ \hline \end{array}

Which one of the following combinations is correct?

\begin{array}{|l|l|}\hline \text{Column X}&\text{Column Y} \\ \hline \text{(P) Horton equation} & \text{((I) Design of alluvial channel} \\ \hline \text{(Q) Penman method} & \text{(II) Maximum flood discharge}\\ \hline \text{(R) Chezys formula}& \text{(III) Evapotranspiration}\\ \hline \text{(S) Lacey's theory}& \text{(IV) Infiltration}\\ \hline \text{(T) Dicken's formula}& \text{(V) Flow velocity}\\ \hline \end{array}

Which one of the following combinations is correct?

(P)-(IV), (Q)-(III), (R)-(V), (S)-(I), (T)-(II) | |

(P)-(III), (Q)-(IV), (R)-(V), (S)-(I), (T)-(II) | |

(P)-(IV), (Q)-(III), (R)-(II), (S)-(I), (T)-(V) | |

(P)-(III), (Q)-(IV), (R)-(I), (S)-(V), (T)-(II) |

Question 10 |

In a certain month, the reference crop evapotranspiration at a location is
6 mm/day. If the crop coefficient and soil coefficient are 1.2 and 0.8, respectively,
the actual evapotranspiration in mm/day is

5.76 | |

7.2 | |

6.8 | |

8 |

Question 10 Explanation:

Actual evapotranspiration (ET_C)

=K_S \times K_C \times Reference evapotranspiration (ET_0)

=0.8 \times 1.2 \times 6=5.76mm

=K_S \times K_C \times Reference evapotranspiration (ET_0)

=0.8 \times 1.2 \times 6=5.76mm

There are 10 questions to complete.