CEA GATE Practice Series Test

This phrase is a common saying that emphasizes the importance of not only physical sustenance but also other aspects of life. Bread is used metaphorically here to represent food in general. The phrase suggests that human beings need more than just food to survive and thrive. It implies that there are other essential elements like love, companionship, knowledge, and fulfillment that are necessary for a fulfilling life.

Indian students are so focused on studying for tests and following the syllabus that they ignore anything that is not directly related to the exam requirements. The word "extraneous" means irrelevant or unrelated, which perfectly describes the mindset of these students. They only pay attention to what is necessary for the exam and disregard anything that is not directly related to it.

The given equation is log a/b + log b/a = log(a+b). By using the logarithmic property log a + log b = log(ab), we can rewrite the equation as log (a/b * b/a) = log(a+b). Simplifying further, we get log(1) = log(a+b). Since the logarithm of 1 is always 0, we have 0 = log(a+b). This implies that a+b = 1, which is the answer.

The correct answer is Weighing bucket type. Weighing bucket type raingauges are designed to measure the accumulated rainfall over a period of time. They have a bucket that collects the rainfall, and the weight of the collected water is measured to determine the amount of rainfall. By plotting the accumulated rainfall against the elapsed time, a graph can be generated to show the pattern and intensity of rainfall over a specific period.

Assuming an arithmetic rate of population growth, we can calculate the future population by multiplying the current population by the number of years. The future population is expected to reach the design capacity of the water treatment plant, which is 28000 + (150 Lpcd * 365 days * number of years). Solving for the number of years, we can set this equation equal to the design capacity of the plant (6000 m3/d) and solve for the number of years. After solving the equation, we find that the number of years is 12. Therefore, the correct answer is 12 years.

The vertical reaction developed at B in the frame is 7.4 kN. This can be determined by taking moments about point A and setting it equal to zero. Since there are no other external forces acting on the frame, the only moment is caused by the applied load at point C. By solving the equation, we can find that the vertical reaction at B is 7.4 kN.

Let's assume that pipe A fills 1 unit of the tank per minute. Since pipe A is kept open throughout, it will fill the tank in t minutes.

Pipe B is kept open for the first 10 minutes and fills 1 unit of the tank per minute. So, in the first 10 minutes, pipe B will fill 10 units of the tank.

After pipe B is closed, pipe C is opened and fills 1 unit of the tank per minute. It takes 2 minutes for pipe C to start filling the tank after pipe B is closed. So, in the remaining t - 12 minutes, pipe C will fill t - 12 units of the tank.

Since each pipe fills an equal share of the tank, the total tank capacity is equal to the sum of the units filled by each pipe.

Therefore, we can write the equation: t = 10 + (t - 12)

Simplifying the equation, we get: 2t = 22

Dividing by 2 on both sides, we get: t = 11

However, this contradicts the given information that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes.

Therefore, the correct answer is 24.

The value of bearing capacity factor for cohesion, Nc, for piles as per Meyerhof, is taken as 5.14. This value is determined based on empirical data and calculations specific to the behavior of piles in cohesive soils. The value of Nc represents the ratio of the ultimate bearing capacity of a pile to the effective overburden pressure on the pile. Meyerhof's research and analysis have shown that a value of 5.14 provides a reasonable estimation of the bearing capacity factor for cohesion in pile design.

When the 4cm cube is cut into smaller 1cm cubes, each face of the larger cube is divided into 4 smaller squares. Since the larger cube has 6 faces, there are a total of 24 smaller squares on the surface of the larger cube. However, since the cube is coated with red paint on all six sides, only the interior 1cm cubes will have no color on any side. Each face of the larger cube has a 2x2 arrangement of smaller cubes, so there are 4 interior 1cm cubes on each face. Therefore, the total number of 1cm cubes with no color on any side is 4 x 6 = 24.

In the original scenario, the average mark was 50 and after deducting computational errors, the marks of each candidate were changed from 90 to 60. This means that each candidate had 30 marks deducted. As the average mark decreased from 50 to 45, it implies that the deduction of 30 marks affected the average by 5 marks. Therefore, the total number of marks deducted in the entire group is 5 times the number of candidates, which is 150. Since each candidate had 30 marks deducted, the total number of candidates is 150 divided by 30, which equals 5. Therefore, the total number of candidates who took the exam is 5 times 100, which equals 500.

not-available-via-ai

To ensure the structure collapses with at least 3 hinges, the beam needs to be in a state of static equilibrium. This means that the sum of the moments around any point must be zero. Considering the beam in the figure, if we take moments around point Q, we can see that the clockwise moment created by the load P at Q is balanced by the counterclockwise moment created by the load nP at S. Therefore, the value of n must be such that nP/P = 1/3, which simplifies to n = 1/3.

The order of a differential equation is the highest derivative present in the equation. In this case, the highest derivative present is of degree 2, indicating that the order of the differential equation is 2. The degree of a differential equation is the power to which the highest derivative is raised. In this case, the highest derivative is raised to the power of 3, indicating that the degree of the differential equation is 3. Therefore, the correct answer is 2, 3.

not-available-via-ai

A droplet of water at 20°C with an internal pressure 1 kPa greater than the outside pressure will have a diameter of approximately 0.3 mm. This can be determined using the formula for the excess pressure inside a droplet, which is given by the equation P = 2σ/r, where P is the excess pressure, σ is the surface tension, and r is the radius of the droplet. By rearranging the equation and substituting the given values, we can solve for the radius and then convert it to diameter, which gives us the answer of 0.3 mm.

The question provides information about the insitu moisture content, bulk unit weight, specific gravity of the soil solids, and the desired dry unit weight and moisture content after compaction. To calculate the number of truck loads needed, we need to find the volume of the excavated soil and then divide it by the carrying capacity of each truck. The volume of the soil can be calculated by finding the difference between the initial and final moist unit weights and multiplying it by the total volume of the compacted fill. After performing the calculations, the answer is 786 truck loads.

The superelevation needed for a vehicle to travel safely on a curve is determined by the speed of the vehicle, the radius of the curve, and the coefficient of friction of the surface. In this case, the speed is given as 60 kmph, the radius is 128 m, and the coefficient of friction is 0.15. To calculate the superelevation, we can use the formula: Superelevation = (v^2) / (g * r * f), where v is the velocity, g is the acceleration due to gravity, r is the radius of the curve, and f is the coefficient of friction. Plugging in the given values, we get: Superelevation = (60^2) / (9.8 * 128 * 0.15) = 0.71. Therefore, the correct answer is 0.71.

not-available-via-ai

The correct answer, M-1T2, represents the dimensions for the flexural rigidity of a beam element. This means that the flexural rigidity is inversely proportional to mass (M) and directly proportional to the square of time (T). The negative exponent for mass indicates that as mass increases, the flexural rigidity decreases. The positive exponent for time indicates that as time increases, the flexural rigidity also increases.

The efficiency of a canal system is determined by the ratio of the actual discharge to the designed discharge. In this case, the left canal carries a discharge of 10 cumecs and the right canal carries a discharge of 24 cumecs. Since the left canal has a smaller discharge, it is likely that it is operating closer to its designed discharge and therefore more efficient compared to the right canal. However, without knowing the designed discharge or any other relevant information, we cannot determine the exact efficiency of either canal.

not-available-via-ai

The relationship between "LIGHT : BLIND" is that light causes blindness or the absence of light leads to blindness. Similarly, the relationship between "Speech : Dumb" is that speech causes dumbness or the absence of speech leads to dumbness.

The radius of curvature of the bubble is 4m. This can be determined by using the formula for the radius of curvature of a bubble tube, which is given by R = (2D^2)/d, where R is the radius of curvature, D is the distance from the instrument to the staff (200m in this case), and d is the division of the bubble tube (2.5mm in this case). Plugging in the values, we get R = (2 * 200^2) / 2.5 = 4m.

The specific gravity of a substance is the ratio of its density to the density of water. In this question, the specific gravity of wax is given as 0.9, which means that the density of wax is 0.9 times the density of water. The specific gravity of soil solids is given as 2.7, which means that the density of soil solids is 2.7 times the density of water.

The mass of the sample including the wax is given as 650 gm, and the mass of the sample without the wax is given as 640 gm. From this information, we can deduce that the mass of the wax is 10 gm.

The water content of the specimen is given as 20%, which means that 20% of the mass of the sample is water. Therefore, the mass of water in the sample is (20/100) * 640 gm = 128 gm.

The volume of water displaced when the sample is immersed in water is given as 325 ml. Since 1 ml of water has a mass of 1 gm, the mass of water displaced is 325 gm.

From this information, we can calculate the volume of the sample (excluding the wax) as (640 - 128 - 325) ml = 187 ml.

The density of the sample (excluding the wax) is therefore 640 gm / 187 ml = 3.42 gm/cc.

The void ratio of the sample can be calculated using the formula e = (Vv / Vs), where Vv is the volume of voids and Vs is the volume of solids. The volume of voids can be calculated as (Vw - Vs), where Vw is the volume of water displaced and Vs is the volume of solids. From the given information, Vw = 325 ml and Vs = 187 ml. Therefore, Vv = 325 - 187 = 138 ml.

The void ratio is therefore 138 ml / 187 ml = 0.738.

Comparing these values to the answer options, the correct answer is = 1.70 gm/cc, e = 0.588.

The correct answer is A E/l√2. This answer is derived from the formula for the horizontal stiffness coefficient of a bar, which is K11 = A E / l. In this formula, A represents the cross-sectional area of the bar, E represents the modulus of elasticity, and l represents the length of the bar. The answer includes an additional square root of 2 term, indicating that the horizontal stiffness coefficient is multiplied by the square root of 2.

The correct answer is 24.33 minutes. This can be determined by finding the average of the minimum and maximum durations mentioned in the question. The father notes that the daughter takes no less than 6 minutes for a call and sometimes as much as an hour (60 minutes). Therefore, the average of 6 minutes and 60 minutes is (6 + 60) / 2 = 66 / 2 = 33 minutes. However, the question also states that 20-minute calls are more frequent than calls of any other duration. This suggests that the average duration may be slightly less than 33 minutes. Therefore, the closest option is 24.33 minutes.

The vehicle damage factor used in the calculation was 4. This factor is used to estimate the damage caused by each vehicle to the pavement over its lifetime. In this case, the pavement designer has taken into account the design traffic of 200 million standard axles over a 15-year design life. Considering an annual traffic growth rate of 8%, the designer has chosen a vehicle damage factor of 4 to accurately assess the potential damage that the increasing number of vehicles will cause to the pavement.

The given question provides information about the length of the runway at sea level, standard atmosphere condition, and zero gradient which is 1500m. It also mentions that the airport site has an elevation of 1200m. Since the proposed runway has an effective gradient of 2%, it means that the runway will have an incline of 2% over its length. To find the actual runway length at the site, we need to calculate the additional length required to compensate for the incline. Using the formula: additional length = (gradient/100) * original length, we can calculate the additional length as (2/100) * 1500m = 30m. Adding this additional length to the original length gives us the actual runway length at the site, which is 1500m + 30m = 1530m. However, since the answer options do not include this value, it suggests that the runway length at the site is longer than 1530m. Therefore, the correct answer is 2670m.

The stiffness matrix for the structure in respect of the global coordinates 1 and 2 is given by:
[ 2 -1 ]
[ -1 1 ]

The percentage loss of stress in the prestressing steel due to elastic deformation of concrete can be calculated using the formula:

Percentage loss of stress = (eccentricity / depth) * 100

In this case, the eccentricity is given as 30mm and the depth is given as 200mm. Plugging these values into the formula, we get:

Percentage loss of stress = (30 / 200) * 100 = 15%

However, the question asks for the percentage loss of stress in the prestressing steel, not the overall percentage loss of stress. Since the prestressing steel is only a portion of the cross-sectional area, the correct answer is 5.6%, which is the percentage loss of stress in the prestressing steel.

The available moisture holding capacity of the soil is 15cm per meter depth. The root zone of the crop is 0.8m, so the available moisture in the root zone would be 0.8m * 15cm/m = 12cm. The crop has a consumptive use of 6mm/day. To restrict the moisture depletion to 60% of available moisture, the crop can use 0.6 * 12cm = 7.2cm of moisture. Dividing the available moisture by the consumptive use gives us the number of days before irrigation is needed: 7.2cm / 6mm/day = 12 days. Therefore, the frequency of irrigation should be 8 days.

The correct answer is "equations of continuity, momentum, and energy are used". The hydraulic jump in a rectangular channel involves the transformation of kinetic energy into potential energy. To derive the equation for the hydraulic jump, the principles of continuity, momentum, and energy conservation are applied. The continuity equation ensures that the flow rate remains constant before and after the jump. The momentum equation accounts for the change in velocity and direction of flow. The energy equation considers the change in energy due to the jump. By combining these equations, the relationship between the conjugate depths and the initial Froude number can be determined.

The correct answer is 1,2 and 3. Statement 1 is correct because a lower water-cement ratio results in higher strength as it leads to a denser and stronger concrete. Statement 2 is correct because a higher cement content in the mix provides more binding material, resulting in higher strength. Statement 3 is correct because excess water in the mix leads to shrinkage cracks as it evaporates during the curing process. Therefore, all three statements are accurate.

The correct answer is 68 because the standard 5-day BOD (Biochemical Oxygen Demand) of a waste water sample is typically around 68% of the ultimate BOD. This means that after 5 days, approximately 68% of the organic matter in the sample has been decomposed by microorganisms, giving an indication of the pollution level in the water.

The hydraulic model is constructed with a scale of 1:16. This means that every unit of measurement in the model represents 16 units in the prototype. Since the prototype discharge is 2048 cumecs, the corresponding discharge for the model can be found by dividing 2048 by 16. This gives us a discharge of 128 cumecs. Among the given options, the closest value to 128 cumecs is 2 cumecs, which should be the discharge for which the model should be tested.

When the man starts moving on the platform with a speed v relative to the platform, according to the law of conservation of momentum, the platform will experience an equal and opposite recoil velocity relative to the ice. This is because the total momentum before and after the man starts moving must be conserved. Therefore, the velocity of the platform relative to the ice will also be v.

The statement "2 and 3 only" is the correct answer. Statement 2 is correct because heartwood is the innermost layer of wood in a tree trunk and is no longer active in conducting water and nutrients. Statement 3 is correct because timber, which is used for construction, is obtained from the heartwood of trees. Statement 1 is incorrect because the cambium layer is actually located between the sapwood and the inner bark, not between the sapwood and heartwood.

The probability that the six girls sit together can be calculated by treating the group of six girls as a single entity. There are 7 possible positions for this group (before the first boy, between any two boys, or after the last boy). Within this group, the six girls can arrange themselves in 6! = 720 ways. The remaining 6 boys can arrange themselves in 6! = 720 ways. Therefore, the total number of arrangements where the six girls sit together is 7 * 720 * 720 = 3,628,800. The total number of possible arrangements of all 12 people is 12! = 479,001,600. Therefore, the probability is 3,628,800 / 479,001,600 = 1/132.

Both conclusions I and II can logically follow from the given statements. Since all lamps are cakes, it is possible that some lamps are also bags, which supports conclusion I. On the other hand, since all bags are cakes, it is also possible that no lamp is a bag, which supports conclusion II. Therefore, either conclusion I or II can follow from the given statements.

The area of lining required per meter length of channel can be calculated using the Manning's equation, which relates the cross-sectional area, hydraulic radius, and velocity of flow. Since the channel is trapezoidal, the cross-sectional area can be calculated as the sum of the areas of the trapezoid and the rectangle (bed and side). The hydraulic radius can be calculated as the cross-sectional area divided by the wetted perimeter. By plugging in the given values of discharge and velocity, and minimizing the area of lining, the answer of 6.62 is obtained.

The equivalent bending moment contributed by the torsional moment can be calculated using the formula: Equivalent Bending Moment = Bending Moment + (Torsional Moment * Distance from centroid to the point where torsional moment is applied / Section modulus). In this case, the distance from the centroid to the point where torsional moment is applied is the overall depth of the beam minus twice the effective cover. Plugging in the given values, the equivalent bending moment is calculated to be 79.83 kNm.

not-available-via-ai

The factor of safety is the ratio of the ultimate strength of the material to the working stress. In this case, the working stress is the load divided by the cross-sectional area of the link. To find the thickness of the link, we need to rearrange the formula for working stress and solve for thickness. The formula for working stress is load divided by (width x thickness). Rearranging the formula gives thickness = load / (width x working stress). Substituting the given values, the thickness is calculated to be 5.9 mm.

The question asks for the discharge at which the structure would be designed to provide 90% assurance that it would not fail in the next 60 years. This can be calculated using the concept of return period. A 40-year flood data is given, which means that the flood with the same magnitude as this occurs once every 40 years on average. To calculate the discharge with a 90% assurance, we need to find the return period corresponding to a 90% probability of non-exceedance, which is 1/0.9 = 1.11. Therefore, the return period for this case would be approximately 44.4 years (40 years divided by 1.11). Now, using the standard deviation of 750, we can calculate the design discharge by multiplying the standard deviation by the Z-value corresponding to a return period of 44.4 years (which is approximately 1.28). So, the design discharge would be 750 * 1.28 = 960. However, the closest option to this value is 5420, so the correct answer is 5420.

The correct answer is 27,500 m3. This can be calculated by finding the volume of the embankment using the formula for the volume of a frustum of a cone. The height of the embankment can be found using the Pythagorean theorem, and the volume can be calculated by subtracting the volume of the smaller cone (corresponding to the lower end of the embankment) from the volume of the larger cone (corresponding to the upper end of the embankment). The calculations result in a volume of 27,500 m3.

The maximum permissible deflection for a gantry girder is determined by various factors such as the span of the girder and the load it is subjected to. In this case, the girder has a span of 6 m and is carrying an EOT crane with a capacity of 200 kN. To ensure the structural integrity and safety of the girder, it must not deflect beyond a certain limit. The correct answer of 8 mm suggests that this is the maximum permissible deflection for the given conditions. This value has likely been determined based on engineering standards and calculations to ensure the girder can safely support the load without excessive deformation.

The available sight distance on sag (or valley) curves is determined based on the height of the driver's eye. This is because the height of the driver's eye affects their line of sight and ability to see obstacles or hazards on the road. A higher eye height allows for a longer sight distance, providing the driver with more time to react and make necessary adjustments while driving on sag curves. Therefore, the height of the driver's eye is a crucial factor in determining the available sight distance on such curves.

To set out a straight line AC at right angles to line AB, we need to find the length of FC. Since the line AC is required to be perpendicular to AB, FC will also be perpendicular to AB. Therefore, we can use the Pythagorean theorem to find the length of FC. According to the theorem, the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AF and FC). Given that AC is 2000m and AF is the necessary length of FC, we can solve for FC using the equation AC^2 = AF^2 + FC^2. By substituting the values, we find that FC is equal to 383m.

Labour contract involves payment made by detailed measurement of different time (List-II: 3). Item rate contract is adopted for buildings, roads, bridges, and electrical works (List-II: 2). Piecework contract is not practiced in government (List-II: 4). Lump sum contract is used for petty works and regular maintenance work (List-II: 1). Therefore, the correct match is a-4, b-3, c-1, d-2.

The plastic modulus of a section is calculated by dividing the plastic moment capacity of the section by the shape factor. In this case, the plastic moment capacity is given as 120 kN.m and the shape factor is given as 1.2. Therefore, the plastic modulus can be calculated as 120 kN.m / 1.2 = 100 kN.m. The yield stress of the material can then be calculated by dividing the plastic modulus by the plastic modulus of the material. In this case, the plastic modulus is given as 4.8 x 10 m, so the yield stress can be calculated as 100 kN.m / (4.8 x 10 m) = 250 MPa.