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QUESTION: 1

Daytime temperature in Delhi can ______ 40°C

Solution:

Daytime temperature in Delhi can reach 40°C

QUESTION: 2

The growth rate of ABC Motors in 2017 was the same ________ XYZ Motors in 2016 .

Solution:

The growth rate of ABC Motors in 2017 was the same as that of XYZ Motors in 2016.

QUESTION: 3

Suresh wanted to lay a new carpet in his new mansion with an area of 70 × 55 sq. mts. However an area of 550 sq. mts had to be left out for flower pots. If the cost of carpet is Rs. 50 per sq. mts, how much money (in Rs.) will be spent by Suresh for the carpet now?

Solution:

Area of mansion = 70 × 55 = 3850 m^{2} Area for flower pots = 550 m^{2}

∴ Area left for carpet = 3850 – 550 = 3300m^{2}

∴ Cost = 3300 × 50 = 165000

QUESTION: 4

A retaining wall with measurements 30 m × 12 m × 6 m was constructed with bricks of dimensions 8 cm × 6 cm×6cm. If 60% of the wall consists of bricks used for the construction is ___________ lakhs.

Solution:

QUESTION: 5

Hima Das was _______ only Indian athlete to win _____________ gold for India.

Solution:

Hima Das was the only Indian athlete to win a gold for India.

QUESTION: 6

Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of the population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is_____________

Solution:

Let population of X is ‘A’ in 2001 and

Population of Y is ‘B’ in 2001

∴ Population of A in 2011

& Population of B in 2011

Given, A/B = P

% increase in P

QUESTION: 7

The Newspaper report that over 500 hectares of tribal land spread across 28 tribal settlements in Mohinitampuram forest division have already been “alienated’. A top forest official said, “First the tribals are duped out of their land holdings. Second, the families thus rendered landless are often forced to encroach further into the forests”.

On the basis of the information available in the paragraph, _______ is/are responsible for duping the tribals.

Solution:

“it cannot be inferred who”

From given information, nobody can be held responsible.

QUESTION: 8

An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.

If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)

Solution:

Pipe X will fill how much in one hour = 1/5 tank

Pipe Y will fill how much in one hour = 1/4 tank

Drainage will drain out how much water in 1 hour = 1/20 tank

∴ Total tank filled in one hour

2/5 tank gets filled in = 1 hour

∴ Full (i) tank gets filled in

= 5/2 = 2.5 hr

QUESTION: 9

Mohan, the manager, wants his four workers to work in pairs. No paper should work for more than 5 hours. Ram and Johan have worked together for 5 hours. Krishna and Amir have worked as a team for 2 hours. Krishan does not want to work with Ram whom should mohan allot to work with Johan, if we wants all the workers to continue working?

Solution:

Conditions given:

(i) Ram & John have worked for 5 hours.

(ii) Krishna doesn’t want to work with Ram.

(iii) No pair should work beyond 5 hours.

Hence, Krishna should work with John to satisfy the above conditions.

QUESTION: 10

“Popular Hindi fiction, despite – or perhaps because of – its wide reach, often does not appear in our cinema. As ideals that viewers are meant to look up to rather than identify with, Hindi film protagonisits usually read books of apsirational value: textbooks, English books, or high value literature”.

Q. Which one of the following CANNOT be inferred from the paragraph above?

Solution:

People do not look up to writers of textbooks, English book or high value literature.

QUESTION: 11

What is curl of the vector field 2x^{2}yi + 5z^{2}j - 4yzk?

Solution:

QUESTION: 12

Analysis of a water sample revealed that the sample contains the following species.

Q. Concentrations of which of the species will be required to compute alkalinity?

Solution:

H_{2}CO_{3} and HCO_{3}^{- }never come together

QUESTION: 13

The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x* using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by I_{L}, and then by the Newton polynomial, denoted by I_{N}.

Q. Which one of the following statements is correct?

Solution:

Lagrange’s form is more efficient when you have to interpolate several data sets on the same data point.

Newton’s form is more efficient when you have to interpolate data incrementally. So no relationship between both.

QUESTION: 14

If the fineness modulus of a sample of the fine aggregates is 4.3, the mean size of the particles in the sample is between

Solution:

150 μm, 300 μm, 600 μm, 1.18 mm, 2.36 mm, 4.75 mm, 10 mm, 20 mm, 40 mm, 80 mm

150 – 1

300 – 2

600 – 3

4.75 - 6

*Answer can only contain numeric values

QUESTION: 15

The command area of a canal grows only one crop, i.e., wheat. The base period of wheat is 120 days and its total water requirement, Δ, is 40 cm. If the canal discharge is 2 m^{3}/s, the area, in hectares, rounded off to the nearest integer, which could be irrigated (neglecting all losses) is ______________

Solution:

B = 120 days

Δ = 0.4 m and

Δ = 8.64B/D

⇒ D = 2592 ha per (m^{3}/s)

∴ For 2m^{3}/sec water, area will be 5184 ha

*Answer can only contain numeric values

QUESTION: 16

The characteristic compressive strength of concrete required in a project is 25 MPa and standard deviation in the observed compressive strength expected at site is 4 MPa. The average compressive strength of cubes tested at different water-cement (w/c) ratios using the same material as is used for the project is given in the table.

The water-cement ratio (in percent, round off to the lower integer) to be used in the mix is________

Solution:

f_{ck} = 25 ; σ = 4 MPa

f_{m} = f_{ck} + 1.65σ = 31.6 MPa

Using interpolation

= 46.7 (Rounded off to the lowest integer).

QUESTION: 17

A solid sphere of radius, r, and made of material with density ρ_{s}, is moving through the atmosphere (constant pressure, p) with a velocity, ν. The net force ONLY due to atmospheric pressure (F_{p}) acting on the sphere at any time, t, is

Solution:

Force = area × P

Net force will be zero as pressure acts from all sides.

QUESTION: 18

An earthen dam of height H is made of cohesive soil whose cohesion and unit weight are c and γ, respectively. If the factor of safety against cohesion is F_{c}, the Taylor’s stability

Solution:

Taylor’s stability number,

QUESTION: 19

A closed thin walled tube has thickness, t, mean enclosed area within the boundary of the centrline of tube’s thickness, A_{m}, and shear stress τ. Torsional moment of resistance, T of the section would be

Solution:

QUESTION: 20

For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web?

Solution:

*Answer can only contain numeric values

QUESTION: 21

The degree of static indeterminancy of the plane frame is shown in the figure is ________

Solution:

D_{s} = 3C – R'

C = 6

D_{s} = (3 × 6 – 2) – 1 (due to hinge)

= 15

QUESTION: 22

Structural failures considered in the mechanistic method of bituminous pavement design are

Solution:

As per IRC66:2012

QUESTION: 23

Which one of the options contains ONLY primary air pollutants?

Solution:

Ozone and PAN are secondary air pollutants.

QUESTION: 24

The following inequality is true for all x close to 0.

What is the value of

Solution:

It is 0/0 form

L’s hospital rule (differentiate)

Putting 0 everywhere ⇒ still 0/0 form.

Differentiating numerator and denominator again,

QUESTION: 25

The velocity field in a flow system is given by v = 2i + (x + y)j + (xyz)k. The acceleration of the fluid at (1, 1, 2) is

Solution:

= 2 + (x + y) + (xyz)(0) + 0

= 2(yz) + (x + y)(xz) + (xyz)(xy) + 0

a_{z} = 2(1 × 2) + (1 + 1)(1 × 2) + (1 × 1 × 2) (1×1)

= 10k

Therefore,

QUESTION: 26

A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design (IS: 800 – 2007) values, respectively, of effective length factor of the column are

Solution:

As per IS:800-2007

QUESTION: 27

Euclindean norm (length) of the vector [4 –2 – 6]^{T} is

Solution:

The Euclidean norm assigns to each vector the length of its arrow. Because of this, the Euclidean norm is often known as the magnitude. So,

Length

QUESTION: 28

An inflow hydrograph is routed through a reservoir to produce an outflow hydrograph. The peak flow of the inflow hydrograph is P_{I} and the time of occurrence of the peak is t_{I}. The peak flow of the outflow hydrograph is P_{0} and the time of occurance of the peak is t_{0}. Which one of the following statements is correct?

Solution:

P_{l} > P_{o} ; t_{l} < t_{o}

*Answer can only contain numeric values

QUESTION: 29

Construction of a new building founded on a clayey soil was completed in January In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be _____________

Solution:

Ultimate consolidation = 40 mm Recorded consolidation = 10 mm

∴ Total recorded consolidation

⇒ 40 × 0.375

QUESTION: 30

The notation “SC” as per Indian standard Soil Classification System refers to

Solution:

SC : clayey sand

QUESTION: 31

The speed-density relationship in a mid-block section of a highway follows the Greenshield’s model. If the free flow speed is vf and the jam density is kj, the maximum flow observed on this ection is

Solution:

⇒

∴

QUESTION: 32

An anisotropic soil deposit has coefficient of permeability in vertical and horizontal directions as kz and kx, respectively. For constructing a flow net, the horizontal dimension of the problem’s geometry is transformed by a multiplying factor of

Solution:

Flow net for anisotropic soil.

If we transformed geometry in x direction let x cordinate be transformed to the new coordinate xt by the transformation.

⇒

From eq. (i) & (ii),

Hence prove

So, multiplied factor

QUESTION: 33

The Laplace transform of sinh (at) is

Solution:

Laplace transform of sinh (at) =

*Answer can only contain numeric values

QUESTION: 34

The data from a closed traverse survey PQRS (run in the clockwise direction) are given in the table

The closing error for the traverse PQRS (in degrees) is________

Solution:

n = 4 (number of sides of closed traverse)

(2n – 4) × 90° = 360°

so, error in included angle

= (88 + 92 + 94 + 89) – 360 = +3°

*Answer can only contain numeric values

QUESTION: 35

A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s^{2}. On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______.

Solution:

Given: grade = +4%

V_{1} = 20 m/sec.

f = 0.46

g = 10 m/sec.

V_{1} = 10 m/sec.

We know,

⇒

*Answer can only contain numeric values

QUESTION: 36

A broad gauge railway line passes through a horizontal curved section (radius = 875 m) of length 200 m. The allowable speed on this portion is 100 km/h. For calculating the cant, consider the gauge as centre-to-centre distance between the rail heads, equal to 1750mm, The maximum permissible cant (in mm, round off to 1 decimal place) with respect to the centretocentre distance between the rail heads is ______.

Solution:

Given data:

R = 875 mm

Allowable speed = 100 kmph

Gauge length G = 1750 mm

Allowable cant

*Answer can only contain numeric values

QUESTION: 37

When a specimen of M25 concrete is loaded to a stress level of 12.5 MPa, a strain of 500 × 10^{–6} is recorded. If this load is allowed to stand for a long time, the strain increases to 1000 × 10^{–6}. In accordance with provisions of IS: 456-2000, considering the long-term effects, the effective modulus of elasticity of the concrete (in MPa) is ________

Solution:

Short term strain = 500 × 10^{–6} Long term strain = 1000 × 10^{–6}

So, creep coefficient,

θ = 1

Long-term effective modulus

= 12500 N/mm^{2} = 12500 MPa

or

QUESTION: 38

The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is

Solution:

Probability density function of a uniformly distributed random variable.

*Answer can only contain numeric values

QUESTION: 39

The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minutes, respectively. For this signal, the red time is 30 s, the effective green time is 30 s, and the cycle length is 60s. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s, round off to 2 decimal places) is _______

Solution:

Average delay per vehicle

= 12.5 sec

*Answer can only contain numeric values

QUESTION: 40

A rolled I-section beam is supported on a 75 mm wide bearing plate as shown in the figure. Thickness of flange and web of the I-section are 20 mm and 8mm, respectively. Root radius of the I-section is 10mm. Assuming: material yield stress, f_{y} = 250 MPa and partial safety factor for material, γ_{mo} = 1.10

As per IS: 800-2007, the web bearing strength (in kN, round off to 2 decimal places) of the beam is _______

Solution:

Effective area in bearing = [75 + 2.5 (flange thickness + root radius)] × 8

= [75 + 2.5 (20 + 10)] × 8

= 1200 mm^{2}

so, web bearing strength

QUESTION: 41

The critical bending compressive stress in the extreme fibre of a structural steel section is 1000 MPa. It is given that the yield strength of the steel is 250 MPa, width of flange is 250 mm and thickness of flange is 15 mm. As per the provisions of IS: 800-2007, the nondimensional slendeness ratio of the steel crosssection is

Solution:

Non-dimensional slenderness ratio

*Answer can only contain numeric values

QUESTION: 42

At the foot of a spillyway, water flows at a depth of 23 cm with a velocity of 8.1 m/s, as shown in the figure.

The flow enters as an M-3 profile in the long wide rectangular channel with bed slope = 1/1800 and Manning’s n = 0.A hydraulic jump is formed at a certain distance from the foot of the spillway. Assume the acceleration due to gravity, g = 9.81 m/s^{2}. Just before the hydraulic jump, the depth of flow y_{1} (in m, round off to 2 decimal places) is _________

Solution:

Given data:

y = 0.23 m

V = 8.1 m/sec.

Slope, s = 1/1800

h = 0.015

g = 9.81 m/sec^{2}

q = yV = 8.1 × 0.23

= 1.863 m^{3}/sec/m

It is given that flow enters as an M-3 profile in the long wide rectangular channel with bed slope = 1/1800

From manning equation at M_{3} profile section.

[for wide channel R = y]

The flow profile will follow normal depth (y_{n}) after jump.

For wide rectangular channel,

Here, y_{n} = y_{2} = 1.11 m

⇒ y_{1} = 0.417 m < y_{c} [supercritical]

*Answer can only contain numeric values

QUESTION: 43

Consider the reactor shown in the figure. The concentration (in mg/l) of a compound in the influent and effluent are C_{0} and C, flow rate through the reactor is Q m^{3}/h respectively. The compound is degraded in the reactor following the first order reactions. The mixing condition of the reactor Complete Mix Flow Reactor (CMFR) or a plug-flow reactor (PFR). The length of the reactor can be adjusted in these two mixing conditions to L_{CMFR} and L_{PER} while keeping the cross-section of the reactor constant. Assuming steady state and for C/C_{0} = 0.8, the value of L_{CMFR}/L_{PER} (round off to 2 decimal places) is _______

Solution:

A = constant

Q = AL

For plug flow

detention time for plug flow reaction]

For completely mix =

detention time for completely mix reaction]

*Answer can only contain numeric values

QUESTION: 44

A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of 6 m are 1.22, 1.67, 2.04, 2.34, 2.14, 1.87, and 1.15 m. The area (in m^{2}, round off to 2 decimal places) boundary by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is _______.

Solution:

Area by simpson’s rule

*Answer can only contain numeric values

QUESTION: 45

A water treatment plant treats 6000 m^{3} of water per day. As a part of the treatment process, discrete particles are required to be settled in a clarifier. A column test indicates that an overflow rate of 1.5 m per hour would produce the desired removal of particles through settling in the clarifier having a depth of 3.0 m. The volume of the required clarifier, (in m^{3}, round off to 1 decimal place) would be

Solution:

Given data:

Flow rate = 6000 m3/day

Over flow rate = 1.5 m/hour

= 1.5 × 24 m/day = 36 m/day

Volume required for clarifier = Flow area × depth = 166.67 × 3 = 500 m^{3}

QUESTION: 46

A flexible pavement has the following class of loads during a particular hour of the day.

i. 80 buses with 2-axles (each axle load of 40 kN);

ii. 160 trucks with 2-axles (front and rear axle loads of 40 kN and 80 kN, respectively)

The equivalent standard axle load repetitions for this vehicle combination as per IRC:37-2012 would be

Solution:

= 5 + 5 + 10 + 160

= 180

*Answer can only contain numeric values

QUESTION: 47

Constant head permeability tests were performed on two soil specimens, S_{1} and S_{2}. The ratio of height of the two specimens (L_{S1}: L_{S2}) is 1.5, the ratio of the diameter of specimens (D_{S1}:D_{S2}) is 0.5, and the ratio of the constant head (h_{s1}:h_{s2}) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (k_{s1}:k_{s2}) is ________

Solution:

For constant head permeability test,

k = QL/ah

Q → discharge

L → length of specimen

a → area of cross-section of specimen

h → constant head

Given,

*Answer can only contain numeric values

QUESTION: 48

A long uniformly distributed load of 10 kN/m and a concentrated load of 60 kN are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in kN, round off to the nearest integer) caused at the internal hinge B due to the two loads is __________

Solution:

Maximum

*Answer can only contain numeric values

QUESTION: 49

A square footing of 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m^{3}. Terzaghi’s bearing capacity factor ϕ = 25° are N_{c} = 25.1, N_{q} = 12.7, N_{γ} = 9.7, N’_{c} = 14.8, N’_{q} = 5.6, and N_{’γ} = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.

Solution:

Here, ϕ < 29^{o }

Footing rests on the ground

Hence, q = 0

*Answer can only contain numeric values

QUESTION: 50

The dimensions of a soil sampler are given in the table.

For this sampler, the outside clearance ratio (in percent, round off to 2 decimal places) is _________.

Solution:

Given:

D_{4} = 90 mm

D_{2} = 100 mm

*Answer can only contain numeric values

QUESTION: 51

A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are k_{x} = k_{y} = 5 × 10^{5} kN/m^{3} and kθ = 3 × 10^{5} kNm/rad.

For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is ________

Solution:

QUESTION: 52

Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be

Solution:

Disinfection eff.

⇒ t = 19.93 min.

*Answer can only contain numeric values

QUESTION: 53

A confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale)

The heads indicated by two piezometers P and Q are 55.2 m and 34.1 m, respectively. The aquifer has a hydraulic conductivity of 80 m/ day and its effective porosity is 0.If the distance between the piezometers is 2500 m, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) is ______.

Solution:

Given,

= 9.259 × 10^{–4} m/s

h = 55.2 – 34.1 = 21.1 m

L = 2500 m

n = 0.25

B = 15 m

As per Darcy’s law,

V = ki

Seepage velocity

QUESTION: 54

For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in the figure.

By how much angle (θ) in degrees the stress element should be rotated in order to get the planes of maximum shear stress?

Solution:

= (30, 0)

In ΔABC,

BC = 80 – 30 = 50 MPa

AB = 25 MPa

Angle to be rotated

QUESTION: 55

The inverse of the matix

Solution:

Det. of matrix, |A| = 2 (12 – 2) – 3(16 – 1) + 4(8 – 3)

= 20 – 45 + 20

= –5

(adj A) = (cof A)'

cof of A_{11} = 12 – 2 = 10

cof of A_{12} = –(16 – 1) = –15

cof of A_{13} = 8 – 3 = 5

cof of A_{21} = –(12 – 8) = –4

cof of A_{22} = (8 – 4) = 4

cof of A_{23} = –(4 – 3) = –1

cof of A_{31} = (3 – 12) = –9

cof of A_{32} = –(2 – 16) = 14

cof of A_{33} = (6 – 12) = –6

adj A = (cof A)'

*Answer can only contain numeric values

QUESTION: 56

Two identical pipes (i.e. having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series and also discharge freely into the atmosphere. In the second case, they are attached in parallel and friction factor is same in both the cases, the ratio of the discharge in the parallel arrangement to that in the series arrangement (round off to 2 decimal places) is _____

Solution:

Case (1): Series connection,

then from equation (i) and (ii)

QUESTION: 57

A camera with a focal length of 20 cm fitted in an aircraft is used for taking vertical aerial photographs of a terrain. The average elevation of the terrain is 1200 m above mean sea level (MSL). What is the height above MSL at which an aircraft must fly in order to get the aerial photographs at a scale of 1:8000?

Solution:

Given that

f = 0.2 m

h = 1200 m

s = 1/8000

*Answer can only contain numeric values

QUESTION: 58

Raw municipal solid waste (MSW) collected from a city contains 70% decomposable material that can be converted to methane. The water content of the decomposable material is 35%. An elemental anlysis of the decomposable material yields the following mass percent.

C : H : O: N : other = 44 : 6 : 43 : 0.8 : 6.2

The methane production of the decomposable material is governed by the following stoichiometric relation

C_{a}H_{b}O_{c}N_{d} + nH_{2}O → mCH_{4} + sCO_{2} + dNH_{3}

Given atomic weights: C = 12, H = 1, O = 16, N = The mass of methane produced (in grams, round off to 1 decimal place) per kg of raw MSW will be _______

Solution:

For the MSW, the phase diagram is as follows

From the mass percent given,

12a = 44x

b = 6x 16c = 43x

14d = 0.8x

∑ = 100x

100x = wt of decomposable waste

= 0.455 kg

⇒ a = 16.683, b = 27.3,

c = 12.228, d = 0.26

From the balance of reaction we have

a = m + s …(A)

b + 2n = 4m + 3d …(B)

c + n = 2s …(C)

⇒ 2c + 2n = 4s …(D)

⇒ b – 2c = 4m – 4s + 3d

⇒ m - s = 0.516

⇒ m + s = 16.683

⇒ m = 8.6

⇒ Methane produced = 8.6 × 16 g = 137.6 g

QUESTION: 59

In the context of provisions relating to durability of concrete, consider the following assertion:

Assertion (1): As per IS 456-2000, air entrainment to the extent of 3% to 6% is required for concrete exposed to marine environment.

Assertion (2): The equivalent alkali content (in terms of Na_{2}O equivalent) for a cement containing 1% and 0.6% of Na_{2}O and K_{2}O, respectively, is approximately 1.4% (rounded to 1 decimal place).

Q. Which one of the following statements is correct?

Solution:

As per IS-456, where freezing and thawing actions under wet conditions exit, inhance durability can be obtained by the use of suitable air entraining admixture.

The entrained air percentage can vary from 4 ± 1 to 5 ± 1 (i.e. 3 to 6%) depending on size of aggregate. Hence, Assertion (1) is correct.

Equivalent alkali content (in terms of Na_{2}O equivalent)

= Na_{2}O + 0.658 × K_{2}O

Molecular ratio of Na_{2}O to K_{2}O = 0.658 = 1% + 0.658 × 0.6% = 1.39

≃ 1.4 (rounded to 1 decimal place).

*Answer can only contain numeric values

QUESTION: 60

The ordinates, u of a 2-hour unit hydrograph (i.e. for 1 cm of effective rain), for a catchment are shown in the table.

A 6-hour storm occurs over the catchment such that the effective rainfall intensity is 1 cm/hour for the first two hours, zero for the next two hours, and 0.5 cm/hour for the last two hours. If the base flow is constant at 5 m^{3}/s, the peak flow due to this storm (in m^{3}/s, round off to 1 decimal place) will be ________

Solution:

0–2 hr — total rainfall = 1 × 2 = 2 cm

2–4 hr — total rainfall = 0 cm

4–6 hr — total rainfall = 2 × 0.5 = 1 cm

Maximum ordinate is 92 m^{3}/sec.

Maximum flood discharge = 92 + 5

= 97 m^{3}/sec

*Answer can only contain numeric values

QUESTION: 61

The speed-density relationship of a highway is given as

u = 100 – 0.5 k

where, u = speed in km per hour, k = density in vehicles per km. The maximum flow (in vehicles per hour, round off to the nearest integer) is ______

Solution:

Given that,

u = 100 – 0.5 k

u = u_{f} (1- k / k_{j})

u = 100(1- (0.5k/100))

= 100(1- k/200) therefore, u_{f }= 100 and k_{j} = 200

= 5000 vehicles/hr

QUESTION: 62

Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m^{3}) when the depth of water at the centre of the tank is 6 m?

Solution:

Volume generated by the Y axis revolution equation of circle

⇒ (x + 0)^{2} + (y - 13)^{2} = 13^{2}

*Answer can only contain numeric values

QUESTION: 63

A timber pile of length 8m and diameter of 0.2m is driven with a 20 kN drop hammer, falling freely from a height of 1.5m. The total penetration of the pile in the last 5 blows is 40 mm. Use the engineering news record expression. Assume a factor of safety of 6 and empirical factor (allowing reducing in the theoretical set, due to energy losses) of 2.5 cm. The safe load carrying capacity of the pile (in kN, round off to 2 decimal places) is ______

Solution:

Engineering news record expression

s = Penetration of pile per hammer blow.

C = 2.5 cm = 0.025 m

then safe load carrying capacity

*Answer can only contain numeric values

QUESTION: 64

A 2 m × 4 m rectangular footing has to carry a uniformly distributed load of 120 kPa. As per the 2:1 dispersion method of stress distribution, the increment in vertical stress (in kPa) at a depth of 2 m below the footing is __________.

Solution:

Increment in the vertical stress

QUESTION: 65

An ordinary differential equation is given below:

The solution for the above equation is

(Note: K denotes a constant in the options)

Solution:

taking ℓnx = t

### CBSE Past Year Paper Session (2016), Math Class 12

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