level stringclasses 6
values | question stringlengths 33 386 |
|---|---|
### level:
Application
### Response:
| A computer while calculating carrelation coefficient between two variables X and Y from 25 pairs of observations obtained the following results : n = 25, X 125, 2X 650, Y1 0 0 , 2Y 460, XY 508. Later it was discovered that the values (X, Y) = (8, 12) was copied as (6, 14) and the value (8, 6) was copied a... |
### level:
Analysis
### Response:
| If 1ˆ ˆˆ F yzi z x j x yk and 222 2ˆ ˆˆ F x yz i y zx j z xy k then show that 12FF is solenoidal. |
### level:
Application
### Response:
| Verify at 5% level of significance and 4 degrees of freedom if the distribution can be assumed to be poisson given: # defects : 0 1 2 3 4 5 Frequency : 6 13 13 8 4 3 Take 20.135. e in the calculations round off the frequencies to the immediate higher integral value. Take 2 5,0.05 11.07 |
### level:
Application
### Response:
| A filament of a 230V lamp is to be drawn from a wire of having a diameter of 0.025mm and resistivity at 28°C is 5.65×10-6-cm. If the resistance temperature coefficient at 280°C is 5×10-3/°C. Calculate the lenght of the filament to dissipate 40W at filament temperature of at 3003°C. |
### level:
Application
### Response:
| Two identical soil specimens were tested in a triaxial apparatus. First specimen was failed at a deviator stress of 700 kN/m2 when the cell pressure was 200 kN/m2. Second specimen was failed at a deviator stress of 1300 kN/m2 when the cell pressure was 400 kN/m2. Determine cohesion of soil and angle of internal frictio... |
### level:
Application
### Response:
| Find the work done in moving a particle once around the ellipse 22 1, 025 16xyz under the field of force given by 2(2 ) ( ) (3 2 4 ) .Fx y z i x y z jx y z k |
### level:
Application
### Response:
| Solve the one dimensional heat equation 2 2y uktx subject to conditions. i) u is finite .t ii) u (0, t) = 0, iii) u(, t) = 0, iv) u( x, 0) = x – x2 0.x |
### level:
Analysis
### Response:
| Show that 22 22 22ˆˆ ˆ Fi xy xz yx yz j zx zy k is irrotational. Find scalar such that F. |
### level:
Analysis
### Response:
| Compare the crippling loads given by Euler’s and Rankine’s formulae for a steel strut 2.5 m long having outer & inner diameter as 40 mm and30 mm respectively loaded through pin jointed at the ends. Take yield stress as 320 N/mm 2 the Rankine’s constant 1 7500, E = 2 × 105 MPa. |
### level:
Application
### Response:
| Evaluate using Stoke ’s theorem F Sds where 2 F yiz jx y k and S is surface of paraboloid 2240zx y z . |
### level:
Application
### Response:
| Two examiners A and B award marks to seven students as follows: Roll No. : R1R2R3R4R5R6R7 Marks (A) : 40 44 28 30 44 36 30 Marks (B) : 32 39 26 30 28 34 28 Find the coefficient of correlation. |
### level:
Application
### Response:
| Determine the shear strength in terms of effective stress on a plane within a saturated soil mass at a point where the total normal stress is 200 kN/m2 and pore water pressure is 80 kN/m2. The shear strength parameters in terms of effective stress are, c’ = 16 kN/m2 and ’ = 390. |
### level:
Application
### Response:
| Among 64 off springs of a certain cross between European horses 34 were red, 10 were black and 20 were white. According to a genetic model these numbers should be in the ratio 9:3:4. Is the data consistentwith the model at 5% level of significance? Take 2 2;0.05 5.991 |
### level:
Knowledge
### Response:
| 1 – b) 1 + c) 1 + d) 1 – vi) If f (z) is analytic on and within a closed conter C then by Cauchy's Integral theorem () Cfzd zis equal to |
### level:
Application
### Response:
| 2i b)i c) 0 d) 1 Q2) a) Using Newton's forward difference formula, find a polynomial passing through the points (0,1), (1,1), (2,7), (3,25), (4,61), (5,121). Hence find y and dy dxat x = 0.5. |
### level:
Application
### Response:
| In a magnetic material, hysteresis loss is 150 W when maximum flux density of 1.3 tesla and frequency is 50 Hz. What would be hysteresisloss if flux density is decreased to 0.8 tesla and frequency is increased to 60 Hz? Assume that hysteresis loss is proportional to (B m)1.7. |
### level:
Application
### Response:
| Use Green ’s theorem to evaluate 22 222 cxyd x x yd y where ‘C’ is boundary of area enclosed by the axis and circle 2216, 0. xy z |
### level:
Application
### Response:
| The input to 3 phase, 6 pole, 50 Hz, induction motor is 47 kWatt at certain load. The stator losses are 1.5 kWatt and mechanical losses are1k Watt. Determine the HPoutput power of motor when it runs at 970rpm. (Take 1 HP = 746 watt) |
### level:
Application
### Response:
| Consider the following page reference string 1, 2, 3, 1, 4, 5, 6, 2, 1, 3, 2,7, 6, 3, 4, 1, 2, 6 Number of page frame =6. Calculate Page fault andHit ratio using LRU page replacement algorthm. |
### level:
Application
### Response:
| A 1:15 model of a flying boat is towed though water. The prototype is moving in seawater of density 1025kg/m3 at velocity of 21 m/s. Find the corresponding speed of the model. Also, determine the resistance due towaves on model if the resistance due to waves of the prototype is 610N. |
### level:
Application
### Response:
| Assume the mean height of soldiers to be 68.22 inches with a variance of 10.8 inches square. How many soldiers in a regiment of 10,000 would you expect to be over 6 feet? Assume area (0 < z < 1.15) = 0.3749 where z is the standard normal variate. |
### level:
Application
### Response:
| In a normal distribution 31% of the items are under 45 and 8% are above 64. Find the mean and standard deviation of the distribution. Take Area (0 < z <1.4) = 0.42 and Area (0 < z < 0.5) = 0.19 where z is the standard normal variate. |
### level:
Application
### Response:
| A trapezoidal channel has side slope of 3 horizontal to 4 vertical and slope of its bed is 1 in 2000. Determine the optimum dimensions for thechannel sections and show it with neat sketch, if it is carry water at 0.55m 3/s. Take Chezy’s constant as 80. |
### level:
Application
### Response:
| A 250 V DC Shunt motor takes a current of 6 Ampere and runs at 1200 rpm. The armature resistance is 0.05 Ohm and shunt filed resistance is250 Ohm. Determine the speed of motor when it is loaded and taking acurrent of 31 Ampere. |
### level:
Application
### Response:
| Two straights PI and QI meet at chainage of 1250 m. A right handed simple circular curve of 250 m radius joins them. The deflection anglebetween two straights is 30 °. Tabulate the necessary data to layout the curve by Offset from long chord. Take chord interval as 10 m. |
### level:
Application
### Response:
| Mr. Vilas brough an air-conditioner for Rs. 20,000; he paid tax of Rs. 2,000 and Rs. 200 for trnsport. If he sold it to a customer forRs. 22,500, what is the percentage profit or loss? |
### level:
Application
### Response:
| An infinitely long uniform metal plate is enclosed between lines y = 0, and y = l for x > 0. The temperature is zero along the edges y = 0, y = l, and at infinity. If edge x = 0 is kept at a constant temperature 0,v Find the temperature distribution ,.vxy |
### level:
Application
### Response:
| A wall with a smooth vertical back, 10 m high, supports a purely cohesive soil with c = 9.81 kN/m2 and = 17.66 kN/m3. Determine total active earth pressure against the wall and position of zero pressure beforeformation of tension crack. |
### level:
Application
### Response:
| Suppose heights of students follows normal distribution with mean 190 cm and variance 80 cm 2. In a school of 1000 students, how many would you except to be above 200 cm tall? (Given, z = 1.1180, A = 0.3686). |
### level:
Application
### Response:
| A pipe of 110 mm diameter is carrying water. If the velocities at the pipe center and 30 mm from the pipe centre are 2.1 m/s and 1.6 m/srespectively and flow in the pipe is turbulent. Calculate the shear frictionvelocity and wall shearing stress. |
### level:
Application
### Response:
| Compare the project by NPV and B/C ratio method and state its feasibility if project cost is Rs. 2,80,000 and it has net cash flow of Rs. 90,000 fora peiod 4 years. Firm expect returns 10% per annum. |
### level:
Analysis
### Response:
| The resisting force R of a supersonic plane during the flight can be considered as dependent upon the length of the aircaft l, velocity V , air viscosity μ, air density ρ, and bulk modulus of air K. Express the functional relationship between these variables and the resisting force.Use Buckingham’s Π Method |
### level:
Analysis
### Response:
| Let 7,1 3 XB be the Binomial distribution with parameters n = 7 and p = 1/3. Then 25 px px is |
### level:
Application
### Response:
| Two wattmeters connected to measure the input to a balanced 3-phase circuit indicate 2000 W and 500 W respectively. Find the power factorof circuit: i) When both the readings are positive ii) When the latter reading is obtained after reversing the connections to the current coil of first instrument. |
### level:
Application
### Response:
| Evaluate 2. sxiy j z k d s Where S is the surface of cylinder 224 xy bounded by planes z = 0 and z = 2. |
### level:
Application
### Response:
| Evaluate F cdr along the straight line joining points (0, 0, 0) and (2, 1, 3) where 2= F = 3 2 xix z y j z k |
### level:
Application
### Response:
| Apply Stoke ’s theorem to evaluate F cdr where Fyzi zxj xyk and S is upper part of sphere 22 21 xyz above XOY plane. |
### level:
Application
### Response:
| A 6 pole, 3 phase induction motor is connected to 400 volt, 50 Hz ac supply. Calculate- i) the speed of rotating magnetic field of the motor ii) Speed of motor at 3% slip iii) the ro tor emf frequency at 3% slip |
### level:
Application
### Response:
| Solve the differential equation 2 2() ()32 ( ) 4t dx t d x txtedt dt , where x (0–) = 1, 1(0 ) 1x. |
### level:
Application
### Response:
| A tightly stretched string with fixed ends x = 0 and x = l is initially at rest in its equilibrium position is set to vibration by giving each point a velocity 3x(l – x) for 0 < x < l. Find the displacement y(x, t) at any time t. |
### level:
Application
### Response:
| A symmetric I section of flanges 120 mm × 20 mm and web of thickness 20 mm and 100 mm depth, carrying uniformly distributed load ofmagnitude 80 kN/m over 4 m span. Calculate the maximum bendingcompressive stress. |
### level:
Application
### Response:
| A rectangular simply supported beam of 5m span is subjected to a central point load of 100 kN. The given beam is 300 mm wide and 500mm deep. Determine maximum bending stress induced in the section.Draw Bending Stress Distribution diagram. |
### level:
Application
### Response:
| A rectangular column of 240 mm × 150 mm is subjected to a vertical load of 110 kN, acting at an eccentricity of 60 mm in a plane bisecting150 mm side. Determine the maximum and minimum stresses. |
### level:
Application
### Response:
| A DC Shunt motor develops output power of 7355 watt and runs at 700 rpm. It is connected across 400 volt DC supply and draws a current of23 Ampere. The mechanical and iron losses are 735.5 Watt. |
### level:
Application
### Response:
| In the network shown in Fig. 3, switch is closed at t = 0. Find the value of 2 2(0 ) (0 )(0 ), ,di d iidt dt Assume the initial current of inductor to be zero. |
### level:
Application
### Response:
| Determine normal, tangential and resultant stresses on a plane at 25º with major principal plane. The principal stresses of 120 MPa tensile onmajor principal plane and 50 MPa compressive on minor principal planeare acting at a point on the member. |
### level:
Application
### Response:
| A flat plate 1.5 m×1.5 m moves at 51 m/hr in stationary air of density 1.16 kg/m 3. If the co-efficient of drag and lift are 0.16 and 0.76 respectively, determine: |
### level:
Application
### Response:
| A symmetric I section is having two flanges, each of 300 mm × 20 mm and vertical web of 20 mm thickness and 160 mm depth. The beam issubjected to shear force 200 kN. Draw Shear Force Distribution diagram. |
### level:
Application
### Response:
| A solid circular shaft transmits 220 kW at 160 rpm. The maximum allowable shear stress is 60 MPa and angle of twist permitted is 2º in 3mlength. Design suitable shaft. Take G = 78 GPa. |
### level:
Application
### Response:
| A string stretched and fastened between two points L a part. Motion is started by displacing the string in the form y = a sin Lx from which it is released at time t = 0. Find the displacement ,.yxt |
### level:
Knowledge
### Response:
| 3 vdv b) 21 vdvr c) vdv d) 0 v) Inverse shifting operator is equivalent to. |
### level:
Application
### Response:
| Evaluate CFdr⋅ for 2 ˆ ˆˆ F 2 xi xyj z k =+ + along the curve C x = t, y = t2, z = t3 from t = 0 to t = 1. |
### level:
Knowledge
### Response:
| An orifice meter with orifice diameter 15cm is inserted in a pipe of 30cm diameter the pressure difference measured by a mercury oil differentialmanometer on the two sides of the orifice meter gives a reading of 50 cmof mercury. |
### level:
Application
### Response:
| A ‘T’ beam, subjected to shear force of 200 kN. The flange is 200 mm × 30 mm and the web is 30 mm thick and 180 mm deep. Drawshear stress distribution diagram. |
### level:
Application
### Response:
| Evaluate Sxiy j z k d s over the surface of sphere 22 21 xyz |
### level:
Application
### Response:
| Determine the range of output voltage for adjustable voltage regulator LM317 for R1 = 240, R2 = 4.7 k Assume Iadj = 100 A. |
### level:
Application
### Response:
| Design the adjustable voltage regulator for the following specification output voltage = 5V – 10V I0 = 1.2 A, Iadj = 100A, R1 = 240 |
### level:
Application
### Response:
| Using Routh’s & Hurwitz’s criteria, comment on the stability if characteristic equation is: S6 + 2S5 + 8S4 + 12S3 + 20S2 + 16S + 16. |
### level:
Application
### Response:
| A concentrated load of 25 kN acts on the surface of homogenous soil mass of large extent. Find the stress intensity at a depth of 8 m by usingBoussinesq’s theory at a horizontal distance of 2.5 m. |
### level:
Application
### Response:
| If the directional derivative of axy byz czx at (1, 1, 1) has maximum magnitude 4 in a direction of x-axis. Find a, b and c. |
### level:
Application
### Response:
| Calculate the machining time required for 3 passes while reducing 60 mm diameter shaft to 50 mm diameter for a length of 1200 mm with depth ofcut of 2 mm for rough cut and 1 mm for finish cut. |
### level:
Analysis
### Response:
| Prove that 242( )(l o g ) () .ba a rba r b rrr |
### level:
Application
### Response:
| Use Runge Kutta second order method of find an approximate value of y correct to three places of decimal when x = 0.1, given that y = 1.2 when x = 1 and dy dx = 3x + y2. |
### level:
Application
### Response:
| A fluid of viscosity 8 poise and specific gravity 1.2 is flowing through a circular pipe of diameter 100 mm. The maximum shear stress at the pipewall is 211 N/m 2. Find: |
### level:
Application
### Response:
| The random variable X has a Poisson distribution.If P(X = 1) = 0.01487, P(X = 2) = 0.04461. Then find P(X = 3). |
### level:
Application
### Response:
| A 3 - phase, 500 V motor load has a power factor of 0.4. Two wattmeters are connected to measure the input. They show the input to be 30 kW.Find the reading of each instrument. |
### level:
Application
### Response:
| Find directional derivative of = e2x cos ( yz) at the origin in the direction tangent to the curve r = a sin t + i + a cos t j + at k at t = 4. |
### level:
Application
### Response:
| A steel rod 6m long and 30 mm diameter is used as a column. One end is fixed and other is free. Determine the crippling load by Euler’s formula.Take E = 200 GPa. |
### level:
Application
### Response:
| Find f(10) of the cubic function passing through the points (4,–43) (7,83) (9,327) and (12,1053) using Newtons divided difference formula. |
### level:
Application
### Response:
| Use 4th order RK method to estimate approximate value of y for x = 0.1 with step size is 0.1, if dy/dx = x + y2 given that y = 1 when x = 0. |
### level:
Application
### Response:
| The beam is supported and loaded as shown in figure. Determine the position and value of Maximum deflection EI = 1.4 × 1011 kN-mm2. Use Macauly’s method. |
### level:
Application
### Response:
| Write a program to generate square wave of 50Hz frequency with 50% duty cycle on pin 2.3. Assume XTAL=11.0592 MHz & use timer 0 inmode l. |
### level:
Application
### Response:
| 14 b) 2 c) 12 d) 8 ii) If f (x) = x2, h = 1, f (x) is given by |
### level:
Application
### Response:
| –2 b) 1 c) 2 d) –1 iii) The value of 21 2Czdzz where C is | z | = 1, |
### level:
Application
### Response:
| A circular bar of diameter 80 mm diameter is subjected to axial compression force of 200 kN. Determine shear stress on a plane, onwhich the normal stress is 100 MPa. |
### level:
Application
### Response:
| A T section with 200 mm X 50 mm and web 200 mm X 50 mm as shown in figure 1 is subjected to vertical shear force of 200 KN. |
### level:
Application
### Response:
| Find the greatest length of a mild steel rod 25 mm X 25 mm which can be used as a compression member with one end fixed and the other endfree to carry a working load of 35 kN. |
### level:
Application
### Response:
| Use residue theorem to evaluate (1 ) (2 )z Cedzzzwhere C is the contour |z + 1| = 1 2. |
### level:
Application
### Response:
| A coin is tossed three times. Write the sample space which gives all possible out comes. A random variable X. Which represents the numberof heads obtained on any tripple toss. Calculate and draw the CDF andPDF. |
### level:
Application
### Response:
| Find the directional derivative of = x2 – y2 – 2z2 at the point p(2,–1,3), in the direction PQ where Q is (5,6,4). |
### level:
Application
### Response:
| A coil which has an inductance of 40mH and a resistance of 2 is connected to form an LR series circuit. If they are connected to a 20VDC supply. Find |
### level:
Application
### Response:
| Show that the vector field F = (8xy + z4) i (4x2 – 2) j + (4xz3 – y) kis irrotational. Find scalar potential function . |
### level:
Application
### Response:
| For an Unity feedback System with open loop transfer function 4G(S)(2 )ss. Determine Damping factor, Undamped natural frequency, reason peak, resonant frequency. |
### level:
Application
### Response:
| Consider the following page reference string A,B,C,D,A,B,E,A,B,C,D,E. Calculate page fault with FIFO page replacement algorithm when framesize is 4. |
### level:
Application
### Response:
| Determine the transition matrix of state equation 03X( )14xt. |
### level:
Application
### Response:
| Compute the intensity of active earth pressure at a depth of 8 m in dry cohesionless sand with an angle of internal friction 300 and unit weight of 18 kN/m3. |
### level:
Application
### Response:
| A rectangular beam 150 mm wide and 300 mm deep is subjected to maximum shear force of 80 KN Determine Average shear stress andMaximum shear stress. |
### level:
Application
### Response:
| Find the directional derivative of 2xyy z at the point (1, –1, 1) to wards point (2, 1, 2). |
### level:
Application
### Response:
| The first four moments of a distribution about the value 4 are –1.5, 17, –30, 108. Find the moments about the mean and β1 and β2. |
### level:
Analysis
### Response:
| A site is proposed for excavation of tunnel is A-B and M-N, which is passing through axis and limb region of fold respectively. Justify thesuitability of tunnel is such conditions. |
### level:
Knowledge
### Response:
| State any four assumptions in Boussinesq's theory. Mention the formula for calculation of stress in soil by point load and circular load byBoussinesq’s theory, with description of each term. |
### level:
Application
### Response:
| A quantity of air having a volume of 400 m 3 at 30ºC DBT and 25ºC WBT is heated to 50 ºC DBT. |
### level:
Application
### Response:
| Using IC 741 op-amp with supply voltage of ±15V design an inverting schmitt trigger circuit to have VUTP = +3V , VLTP = –3V . |
### level:
Application
### Response:
| Apply Green's theorem to evaluate : 2() Cxdx xydy Where C is the curve of region enclosed by y = x2 and the line y = x. |
### level:
Application
### Response:
| Obtain the state model for the system with transfer function 2Y( ) 3S 4 U( ) 5S 6s ss. |
### level:
Application
### Response:
| Find the directional derivative of xy yz xzφ=++ at (1, 1, 1) along line 111 212x yz −−−== . |
### level:
Application
### Response:
| Consider the following processes arrival time and burst time as shown below in table. Calculate average waiting time and average turn aroundtime if Quantum time is 2. Use Round Robin Algorithm. Draw GANTTchart. |
### level:
Application
### Response:
| Design constant K-low pass filter to have a cut-off frequency of 796 Hz when terminated in a 600 resistance in both the T and π configurations. |
### level:
Application
### Response:
| Show that the transformation w = z + 1 z–2i maps the circle | z| = 2 into an ellipse. Find centre, semi-major and semi-minor axes of ellipse |
### level:
Application
### Response:
| Random sample of 400 men and 600 women were asked whether they would have a school near their residence 200 men and 325 womenwere in favour of proposal. |
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