Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

The value of ^{$\lim \limits_{x \rightarrow 0} \frac{sin[\frac{2}{3}x]}{x}is$}

The order and degree of the differential equation ^{$\frac{d^3y}{dx^3} + 4 \sqrt{(\frac{dy}{dx})^3 + y^3 = 0}$} are respectively

The major and minor principal stresses at a point are 3 MPa and -3 MPa respectively. The maximum shear stress at the point is

For the truss shown in the figure, the force in the member QR is

As per India standard code of practice for pre stressed concrete (IS:1343 –1980) the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elements are respectively

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

The effective length of a column of length L fixed against rotation and translation at one end and free at the other end is

A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the plasticity chart, according to IS classification, the soil is represented by the letter symbols

Quicksand condition occurs when

A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at three free ends is

A coastal city produces municipal solid waste (MSW) with high moisture content, high organic materials, low calorific value and low inorganic materials. The most effective and sustainable option for MSW management in that city is

In a compaction test, G, w, S and e represent the specific gravity, water content, degree of saturation and void ratio of the soil sample respectively. If y_w represents the unit weight of water and y_d represents the dry unit weight of the soil, the equation for zero air voids line is

A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in the channel are

The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, the water surface under no-choke condition will

The e-log p curve shown in the figure is representative of

As per IRC: 67-2001, a traffic sign indicating the speed limit on a road should be of

The value of the integral of the function between the limits 0 to 1 using Simpson’s rule is

The correct match of Group-I with Group-II is

Aggregate impact value indicates the following property of aggregates

A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is ^{$y = 4h \frac{x^2}{L^2}$} where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

Group-I gives a list of devices and Group-II gives the list of uses.

The correct match of Group-I with Group-II is

The local mean time at a place located in longitude 90º 40’E when the standard time is 6 hours and 30 minutes and the standard meridian is 82º 30’E is

The partial differential equation that can be formed from z = ax + by + ab has the form $\Big( with p = \frac{\partial z}{\partial x} and q = \frac{\partial z}{\partial y} \Big)$

A double cover butt riveted joint is used to connect two flat plates of 200 mm width and 14 mm thickness as shown in the figure. There are twelve power driven rivets of 20 mm diameter at a pitch of 50 mm in both directions on either side of the plate. Two cover plates of 10 mm thickness are used. The capacity of the joint in tension considering bearing and shear ONLY, with permissible bearing and shear stresses as 300 MPa respectively is

Given a function: (x, y) = 4x² + 6y² − 8x − 4y + 8 The optimal value of f(x, y)

The solution to the ordinary differential equation ^{$\frac{d^2y}{dx^2} + \frac{dy}{dx} - 6y = 0$}is

For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per unit length as shown in the figure, the bending moment (in kN-m) at the mid-span of the beam is

A three-hinged parabolic arch having a span of 20 m and a rise of 5 m carries a point load of 10 kN at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having coefficient of permeability of 10⁻²m/ s. The barrel stands on a saturated bed of gravel. The time required for the water level in the barrel to drop by 0.75 m is

A disc of radius r has a hole of radius ^{$\frac{r}{2}$} cut out as shown. The centroid of the remaining disc (shaded portion) at a radial distance from the centre “O” is

According to the Noise Pollution (Regulation and control) Rules, 2000, of the Ministry of Environment and Forests, India, the day time and night time noise level limits in ambient air for residential areas expressed in dB(A) Leg are

The vertical stress at point P₁ due to the point load Q on the ground surface as shown in figure is s₂. According to Boussinesq’s equation, the vertical stress at point P₂ shown in the figure will be

The ultimate load capacity of a 10 m long concrete pile of square cross-section 500 mm x 500 mm driven into a homogeneous clay layer having undrained cohesion value of 40 kPa is 700 kN. If the cross-section of the pile is reduced to 250 mm x 250 mm and the length of the pile is increased to 20 m, the ultimate load capacity will be

The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 1.5 m, the critical depth is

Consider the following statements in the context of cement concrete pavements. I. Warping stresses in cement concrete pavements are caused by the seasonal variation in temperature. II. Tie bars are generally provided across transverse joints of cement concrete pavements. The correct option evaluating the above statements is

If the BOD3 of a waste water sample is 75 mg/L and reaction rate constant k (base e) is 0.345 per day, the amount of BOD remaining in the given sample after 10 days is

If ^{$\sigma_h, \sigma_w, \sigma_n$} and ^$\sigma_w$ represent the total horizontal stress, total vertical stress, effective horizontal stress and effective vertical stress on a soil element respectively, the coefficient of earth pressure at rest is given by

An air parcel having 40ºC temperature moves from ground level to 500 m elevation in dry air following the “adiabatic lapse rate”. The resulting temperature of air parcel at 500 m elevation will be

A benchmark has been established at the soffit of an ornamental arch at the known elevation of 100.0 m above the sea level. The back sight used to establish height of instrument is an inverted staff reading of 2.105 m. A forward sight reading with normally held staff of 1.105 m is taken on a recently constructed plinth. The elevation of the plinth is

Which of the following options is closest in meaning to the word 'Circuitous'?

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed : Worker

Choose the most appropriate word from the options given below to complete the following sentence. If we manage to ____________ our natural resources, we would leave a better planet for our children.

Direction: The moisture holding capacity of the soil in a 100 hectare farm is 18 cm/m. The field is to be irrigated when 50 percent of the available moisture in the root zone is depleted. The irrigation water is to be supplied by a pump working for 10 hours a day, and water application efficiency is 75%. Details of crops planned for cultivation are as follows:

The area of crop Y that can be irrigated when the available capacity of irrigation system is 40 litres/sec is

There are 25 persons in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. The number of persons playing neither hockey nor football is

For a rectangular channel section, Group I lists geometrical elements and Group II gives proportions for hydraulically efficient section.

y_e is the follow depth corresponding to hydraulically efficient section. The correct match of Group I with Group II is

Choose the most appropriate word from the options given below to the complete the following sentence. His rather casual remarks on politics ___________ his lack of seriousness about the subject.

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage?

Direction: Ion concentrations obtained for a groundwater sample (having pH = 8.1) are given below.

concentration (mg/L)| 100| 6| 15| 250| 45| 39| | Atomic Weight| Ca = 40| Mg = 24| Na = 23| H = 1, C = 12, O = 16| S = 32, O = 16| Cl = 35.5|

Total hardness (mg/L as CaCO₃) present in the above water sample is

If 137 + 276 = 435, how much is 731 + 672?

Direction: The moisture holding capacity of the soil in a 100 hectare farm is 18 cm/m. The field is to be irrigated when 50 percent of the available moisture in the root zone is depleted. The irrigation water is to be supplied by a pump working for 10 hours a day, and water application efficiency is 75%. Details of crops planned for cultivation are as follows:

The capacity of irrigation system required to irrigate crop X in 36 hectares is

Consider the following statements in the context of geometric design of roads. I: A simple parabolic curve is an acceptable shape for summit curves. II: Comfort to passengers is an important consideration in the design of summit curves. The correct option evaluating the above statements and their relationship is

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings, i.e. brothers and sisters.

All were born on 1^st January. The age difference between any two successive siblings (that are born one after another) is less than 3 years. Given are the following facts:

i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest. iii. There are no twins.

In what order were they born (oldest first)?

Direction: Ion concentrations obtained for a groundwater sample (having pH = 8.1) are given below.

concentration (mg/L)| 100| 6| 15| 250| 45| 39| | Atomic Weight| Ca = 40| Mg = 24| Na = 23| H = 1, C = 12, O = 16| S = 32, O = 16| Cl = 35.5|

Carbonate hardness (mg/L as CaCO₃) present in the above water sample is

A wall of diameter 20 cm fully penetrates a confined aquifer. After a long period of pumping at a rate of 2720 litres per minute, the observations of drawdown taken at 10 m and 100 m distances from the centre of the wall are found to be 3 m and 0.5 m respectively. The transmissivity of the aquifer is

Direction: The unconfined compressive strength of a saturated clay sample is 54 kPa.

If a square footing of size 4 m x 4 m is resting on the surface of a deposit of the above clay, the ultimate bearing capacity of the footing (as per Terzaghi’s equation) is

Given digits: 2, 2, 3, 3, 4, 4, 4, 4. How many distinct 4-digit numbers greater than 3000 can be formed?

The design speed for a two-lane road is 80 kmph. When a design vehicle with a wheelbase of 6.6 m is negotiating a horizontal curve on that road, the off-tracking is measured as 0.096 m. The required widening of carriageway of the two-lane road on the curve is approximately

Two plates, subjected to direct tension, each of 10 mm thickness and having widths of 100 mm and 175 mm, respectively are to be fillet welded with an overlap of 200 mm. Given that the permissible weld stress is 110 MPa and the permissible stress in steel is 150 MPa, then length of the weld required using the maximum permissible weld size as per IS: 800-1984 is

Direction: A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm² of steel in tension and 628 mm² of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250 respectively. The stress lock parameters (rounded off to first two decimal places) for concrete shall be as per IS 456:200.

The moment of resistance of the section is

Direction: The unconfined compressive strength of a saturated clay sample is 54 kPa.

The value of cohesion for the clay is

Direction: A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm² of steel in tension and 628 mm² of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250 respectively. The stress lock parameters (rounded off to first two decimal places) for concrete shall be as per IS 456:200.

The depth of neutral axis is

5 skilled workers can build a wall in 20 days, 8 semi-skilled workers can build a wall in 25 days, 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

The inverse of matrix^{$\begin{bmatrix} \ 3+ 2i & i \ \ -i & 3-2i \ \end{bmatrix}$}is

Two people weighing W each are sitting on a plank of length L floating on water at ^{$\frac{L}{4}$} from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is