Gate Mock Test Civil Engineering (CE) - GATE MCQ

 =∛0.5x0.5x0.5 = 0.5

There are total 1000 numbers. Each time 2 numbers are erased and replaced with their product, one number is getting reduced. After 999 such operations, 999 numbers would have got erased leaving behind exactly 1 number which means option ‘a’ or ‘b’ or ‘c’.

In 20^th century i.e. 1901 to 2000, there are 25 leap years.
The total number of people born on 29^th February = 25p and the total number of people born in entire 20th century = 36500p + 25p = 36525p; giving the required percentage of people born on 29th February = (25p/36525p) x 100 = 0.0684
Caution: A common error likely to be committed is to divide 25p by 365p which will give the required percentage as 0.0685 which is also one of the choices OR forget to multiply 25p/36525p by 100 getting a value = 0.000684 which also happens to be one of the options.

Based on the table which lists the possible options, we can clearly eliminate options ‘A’, ‘B’ and ‘C’. Rs. 7000 earns maximum interest which violates the given condition.
This leaves option ‘D’ and in this case, Rs. 7000 is not earning highest interest which leads us to the required answer i.e. option ‘d’.

In order to get the least value, we must choose the most negative value with ODD index AND most positive value for P. This rules out option ‘d’. Now if simply put the most positive and most negative values for P and Q, we end up getting

Option d will be a positive number.
So option a will be the smallest number

As shown in Figure above, at 6:00 a.m. initial angle between minute and hour hand is 180o.As we know that hour hand completes 30° in every hour (60 minutes), so angle moved by hour hand in 1 minute is 30/60. Similarly, minute hand complete 360° in every hour, so angle moved by minute hand in 1 minute is 360/60. Let us assume that after x minutes the angle is 60°. Let us assume that after x minutes the angle is 60°.

Let R and J be the length of each step of Raja and Joseph respectively.
We can write the following equations based on the given information:
3R = 4J

Now, the difference in the length of a step of Raja and Joseph = 35 cm with Joseph's step being longer. In order to catch up with Raja who is ahead of him by 300 m, the number of steps required 
= 300/0.35 = 857.14 ≌ 857

Applying L’ Hospital’s rule

The preposition ‘to’ indicates concern or likely to concern something or approaching or reaching (a particular condition). In this case, it is the expected attention.
by identifies the agent performing an action.
for as a preposition has multiple contextual
sages, none of which fits here. 
too means to a higher degree than is desirable, permissible, or possible; excessively.  
Hence, the correct answer is option b.

Most materials have poissons ratio values ranging between 0 and 0.5. a perfectly incompressible material deformed elastically at small strains would have poissons ration of exactly 0.5 at this value material is incompressible.

Given,
η = 0.4
γ_R = 0.25
γ_S = 0.4 – 0.25 = 0.15
γ_S = Amount of water drained/Amount of medium
Amount of water drained = 0.15 × 150 × 10 = 225 Ha-m

The main objective of Vee-Bee test is to determine the workability of the freshly mixed concrete.
Vee-bee test carries out the relative effort measurement to change the mass of the concrete from a definite shape to the other. That is, as per the test, from the conical shape to the cylindrical shape by undergoing vibration process. The time required for the complete remolding is a measure of the workability and is expressed in the Vee-Bee seconds.

Total depth of rainfall = 1 cm = 0.01 m
Total runoff volume = Area of hydrograph = 1/2 x time base x peak ordinate
0.01 x 150 x 10⁶ = 0.5 x ( 20 x 3600) x peak ordinate
Peak ordinate = 41.66

• In project management, a task is an activity that needs to be accomplished within a defined period of time or by a deadline to work towards work-related goals.
• A dummy activity is a simulated activity of sorts, one that is of a zero duration and is created for the sole purpose of demonstrating a specific relationship and path of action on the arrow diagramming method.
• Float, sometimes called slack, is the amount of time an activity, network path, or project can be delayed from the early start without changing the completion date of the project.
• An event is an occurrence or an outcome which is of significance and based on which typically, a business rule can be triggered. For an example, an event could be the start of an activity, end of an activity, non-completion of an activity within a certain timeframe, etc.
So, correct matching are as follows
• Activity - Element Utilizing Resource
• Dummy - Resourceless element
• Float - Spare Time
• Event - Instantaneous point of time
d option is correct!

The axis of the beam is the neutral axis.
The amount by which a layer increases or decreases in length, depends upon the position of the layer w.r.t. N-N.
In the above fig. as we move from top layer to N-N, the length of the layer increases. While moving from bottom layer to N-N, the length of the layer decreases. 

Probable maximum flood is the extreme flood that is practically possible in a region as a result of severe most combination.
The standard Project flood results from severe combinations of meteorological and hydrological factors that are reasonably applicable in that region.
According to Gumbel’s distribution, the value of flood with return period of 2.33 years is the mean annual flood.

Calculation of K force due to application of unit force in the direction of 1-4.

This is a case of combined direct and bending stress

The variation of rigidity factor for a tyre pressure is stated as:
<1 for tyre pressure greater than 7 kg/cm²
>1 for tyre pressure less than 7 kg/cm²
=1 for tyre pressure equal to 7 kg/cm²

A surge in an open channel is a sudden change of flow depth (i.e. abrupt increase or decrease in depth). An abrupt increase in flow depth is called a positive surge while a sudden decrease in depth is termed a negative surge.
So, Statement II is not the correct explanation of the statement I

Given: First Mass, mi = 10 kg
Balancing Mass, m₂ = 20 kg
We know the mass moment of inertia, I = mk2
Where, k = Radius of gyration
Case (I): When mass of 10 kg is rotates with uniform angular velocity 'ω' 
The moment of inertia I₁= m₁k₁²
I₁ = 10 x (0.2)² k₁= 200 mm = 0.2 meter
= 10 x 0.04 = 0.4 kg m²
Case (II): When balancing mass of 20 kg is attached then moment of inertia
I₂ = 10 x (0.2)² + 20 x (0.1)² Here ;Q. = 0.2m
= 0.4 + 0.2 = 0.6 and k₂= 0.1m
Percent increase in mass moment of inertia, 

Here,
f_ck = 25 ; σ = 4 MPa
and
f_m =f_ck + 1.65σ = 31.6 MPa
Using interpolation

= 46.7