### Engineering mathematics

1. Types of matrices: 2011, 2010, 20092. Eigenvalues of matrix: 2016, 2015, 2015, 2014, 2012, 2008, 2007, 2006

3. Eigenvectors of matrix

4. Matrix multiplication: 2014, 2013, 2008

5. Determinant of square matrix and its inverse: 2014, 2007

6. Rank of matrix: 2015, 2014

7. Consistency of non homogeneous equations: 2016, 2015, 2008, 2007, 2006

8. Consistency of homogeneous equations

9. Knowledge about different functions

10. Limit concept of single variables: 2015, 2014, 2014, 2010

11. Limit concept of two variables: 2016

12. Continuity concept: 2011

13. Differentiability concept

14. Angle between two curves: 2016, 2008

15. Mean value theorem

16. Improper integrals: 2016, 2007

17. Definite integrals: 2015, 2013, 2011, 2008

18. Partial derivatives: 2010

19. Taylor series approximation and Maclaurin series: 2016, 2012

20. Maxima and minima of single variable: 2016, 2015, 2010

21. Maxima and minima of double variable

22. Area under curves: 2016, 2016, 2014, 2012, 2006

23. Gradient of scalar function: 2009

24. Directional derivative: 2015, 2009, 2006

25. Divergence of vector function

26. Curl of vector function: 2011

27. Greens theorem

28. Stokes theorem

29. Gauss theorem

30. Fourier series: 2016

31. Order and degree of D.E.: 2010, 2008

32. Differential equation by variable separable method, newtons law of cooling: 2009, 2008, 2007, 2006

33. Differential equations of homogeneous equations

34. Differential equations reducible to homogeneous

35. Leibnitz equation: 2014, 2012

36. Bernoulli equation

37. Integration factor for homogeneous equations

38. Integration factor

39. Integration factors for other types

40. Solution of exact D.E: 2015

41. Second order linear D.E.: 2015

42. Complementary function: 2016, 2010, 2008

43. Particular integral

44.

45. Particular integral of 2016

46. Particular integral of

47. Particular integral of 1

48.

56. Types of PDE: 2016

57. Heat equation : 2016

58. Wave equation

59. Laplace equation: 2013

60. Probability problems: 2016, 2014, 2012, 2011, 2010, 2008, 2006

61. Normal distribution and probability: 2016, 2014, 2014, 2013, 2009, 2008

62. Normal distribution mean and variance: 2016, 2015, 2015

63. Mean, median, mode, and variance, coefficient of variation:2016, 2007, 2006

64. Hypothesis testing error analysis: 2016

65. Binomial distribution

66. Bisection method

67. Regula falsi method

68. Gauss elimination method: 2009

69. Newton Raphson method: 2016, 2015, 2011, 2008

70. Secant method: 2015

71. Simpson’s 1/3 rule: 2015, 2013, 2012, 2010

72. Trapezoidal rule: 2015, 2006

73. Euler’s method: 2006

74. Runge Kutta method

75. Curve fitting by least squares: 2013, 2008

76. Central difference formula: 2012

### Engineering mechanics and strength of material

77. Centroid: 201078. Resultant of forces: 2016

79. Moment of inertia, radius of gyration: 2009, 2006

80. Reaction of determinate beams

81. Shear force and bending moment in statically determinate structures: 2016, 2014, 2012, 2011, 2010, 2010, 2009, 2006

82. Stress, strain and elongation: 2015, 2014, 2008

83. Volumetric strain and Poisson ratio: 2016, 2012

84. Relation between E, G, K, and mu: 2010, 2007

85. Force in composite members: 2008, 2007

86. Thermal stress: 2007

87. Thermal stress in composite bars

88. Normal and shear stress in any plane: 2015, 2009, 2007

89. Principal stresses and Mohr circles: 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2006

90. Theory of simple bending: 2016, 2015, 2014, 2014, 2013, 2008

91. Force in any partial area due to bending: 2006, 2006

92. Shear stress distribution: 2013, 2007, 2006

93. Shear force at any partial area: 2006

94. Shear centre: 2014, 2009

95. Hoop stress, longitudinal stress and shear stress: 2009

96. Hoop strain, longitudinal strain and volumetric strain

97. Torsion problems, polar moment of inertia: 2014, 2010, 2009, 2008, 2007, 2006

98. Power transmitted by shaft

99. Shafts in series

100. Principal stress due to bending and torsion

101. Shear stress due to bending and torsion

102. Helical spring

103. Leaf spring

104. Column buckling: 2014, 2013, 2012, 2012, 2010, 2008, 2008, 2007, 2006

105. Rankine’s formula

106. Combined stresses due to axial and bending: 2007

### Structural analysis

107. Method of joints, method of sections: 2016, 2016, 2016, 2016, 2015, 2014, 2014, 2013, 2010108. Relative displacements by graphical methods: 2014

109. Horizontal reactions in two hinged and three hinged arches: 2010

110. Tension in cables, funicular arch: 2016, 2014, 2013, 2012, 2010

111. Slope and Deflection using moment area theorem: 2009, 2008, 2006

112. Conjugate beam method

113. Strain energy in members: 2015, 2008, 2007

114. Slope and Deflection by strain energy method, unit load method: 2016, 2013, 2012

115. Double integration method

116. Deflection in trusses: 2008, 2007

117. Propped cantilever, : 2015, 2015, 2015, 2015, 2014, 2011, 2006

118. Static indeterminacy: 2014, 2014, 2009, 2008

119. Kinematic indeterminacy: 2016

120. Indeterminate forces by energy

121. Indeterminate forces by compatibility

122. Indeterminate forces by using symmetry

123. Betti’s theorem, Maxwell’s reciprocal theorem: 2014

124. Reduction of structure by symmetry: 2016

125. Slope deflection method

126. Moment distribution method: 2014, 2013, 2007, 2006

127. Sway analysis of moment distribution

128. ILD for reaction,ILD for shear force,ILD for B.M.: 2014, 2013, 2008, 2007, 2006

129. Maximum B.M. and shear force due to rolling loads or udl: 2015

130. Absolute maximum B.M.

131. flexibility element

132. stiffness element: 2015, 2015, 2015, 2007

### Building materials:

133. Bricks: 2016, 2016134. Cement: 2016

135. Aggregate: 2011

136. Steel: 2011

137. Workability of concrete, slump, compaction factor, veebee test: 2015,

2013, 2007

138. Resonant frequency test, rebound hammer test, split cylinder test: 2009

139. Air entrained concrete, air content: 2015, 2015

### Construction management

140. Floats: 2016141. Critical Duration: 2016

142. PERT: 2016

### Reinforced cement concrete structures

143. Modulus of elasticity of concrete, flexural strength, target mean strength: 2016, 2014, 2009, 2008, 2007, 2006144. Partial safety factors and probability of failure: 2015, 2009

145. Load combinations: 2008

146. Creep: 2013

147. Stress block and strain in concrete beam: 2015

148. Neutral axis depth in singly reinforced beam: 2012

149. Moment of resistance of singly reinforced beam: 2015, 2012, 2006

150. Limiting depth of neutral axis: 2012, 2006

151. Limiting moment of resistance, limiting area of steel: 2007

152. M.R.of doubly reinforced beam: 2010

153. M.R. of T-beam

154. Shear reinforcement and spacing: 2016, 2016, 2014, 2011

155. Maximum and minimum reinforcement: 2016, 2014

156. Equivalent shear

157. Equivalent moment

158. Development length: 2015, 2013, 2011, 2008

159. Bearing strength of concrete: 2014, 2011

160. Load carrying capacity of axially loaded columns

161. Load carrying capacity of spiral reinforced columns

162. Minimum eccentricity of column: 2015

163. Stresses in pre-stressed: 2015, 2013, 2012, 2010, 2008

164. Losses in pre-stressed beam: 2012, 2009, 2007

### Steel structures

165. Net area in tension member: 2016166. Gross section yielding strength in tension member

167. Net section rupture strength in tension member: 2012

168. Block shear strength in tension member

169. Flexural strength of beam: 2016, 2014

170. Maximum force in rivet of bracket connection: 2015, 2014, 2007

171. Shear strength of bolt and Bearing strength of bolt: 2010, 2009, 2007

172. Prying force in bolt stresses in bolt: 2015, 2008

173. Welding strength: 2016, 2012, 2011 2010

174. Slenderness ratio of different members, elastic critical stress: 2015, 2009

175. Plastic modulus, shape factor, plastic hinge, load factor: 2014, 2014, 2009, 2008

176. Plastic capacity of beams and collapse load: 2016, 2016, 2015, 2015, 2014, 2014, 2013, 2013, 2011, 2008, 2007

177. Plate girder elements: 2011

### Soil mechanics

178. Three phase system and interrelationships: 2016, 2015, 2015, 2014, 2013, 2010, 2009, 2007179. Borrow pit and embankment: 2015

180. Relative density: 2014

181. Flow index

182. Plastic limit, liquid limit, shrinkage limit: 2008

183. Shrinkage index, plasticity index

184. Consistency index and liquidity index

185. Toughness index

186. Shrinkage ratio

187. Activity: 2015

188. Classification of soil: 2016, 2014, 2012, 2010, 2009, 2008, 2007

189. Clay minerals: 2014, 2009

190. Capillary pressure in soils: 2006

191. Constant head permeability

192. Falling head permeability: 2012, 2010

193. Darcy law, Seepage velocity and discharge velocity: 2016, 2015, 2013

194. Confined aquifer, Unconfined aquifer: 2010, 2006

195. Stratified soil permeability: 2016, 2016, 2015

196. Flownet problems: 2016, 2014, 2013, 2012

197. Anisotropic soil permeability: 2008

198. Non homogeneous soil permeability

199. Effective stress with water table: 2011

200. Effective stress with capillary saturation

201. Effective stress with seepage: 2016, 2014, 2012, 2007

202. Quicksand condition: 2016, 2011, 2010, 2006

203. Relation between change in void ratio and change in thickness

204. Compression index, Recompression index and expansion index

205. Normally consolidated and overconsolidated soil: 2016, 2010

206. Coefficient of Volume change: 2014

207. Consolidated Settlement: 2016, 2015, 2015, 2009, 2007, 2006

208. Time factor and coefficient of consolidation: 2015, 2011, 2008

209. Basics of proctor test: 2016, 2013, 2012, 2008

210. Theoretical dry density in compaction: 2006

211. Relation between normal and shear stress

212. Angle of internal friction in shear box test: 2008

213. Vane shear test: 2014, 2011

214. Unconfined compressive strength: 2010

215. Triaxial shear test, CD, CU and UU tests: 2016, 2016, 2014, 2012, 2011, 2007, 2006

216. Stress and volume relationship: 2015

217. Pore pressure parameters: 2015

218. Stress path: 2015

#### Foundation Engineering

219. Area ratio, SPT, SCPT, pressure meter test: 2015, 2014, 2014, 2009, 2007220. Immediate settlement in sand: 2014, 2013

221. Settlement of foundation in sand by plate load test: 2014, 2009, 2008

222. Active earth pressure in sandy and clayey soils: 2016, 2015, 2015, 2013, 2012, 2010, 2008, 2006

223. Passive earth pressure in sandy and clayey soils:

224. Stability of retaining wall: 2016

225. Depth of tension crack

226. Unsupported vertical cut: 2016

227. Stability of slopes: 2014, 2014, 2013, 2007

228. Rotational stability

229. Stability number

230. Friction circle method: 2015

231. Bearing capacity of strip, square and circular footings: 2016, 2016, 2015,

2015, 2013, 2012, 2011, 2010, 2009, 2007

232. Boussinesq’s formula: 2010

233. Stress due to line load

234. Stress due to strip load: 2008

235. Stress due to circular load

236. Newmark chart, rectangular load: 2007

237. Stress under rigid and flexible foundations in clay and sand: 2014, 2013, 2011

238. Dynamic formula for pile capacity: 2009

239. Pile capacity in clay and sand: 2015, 2014, 2014, 2011, 2010, 2008

240. Pile group capacity: 2007, 2006

241. Settlement of pile group

### Fluid mechanics

242. Types of fluids: 2016, 2014243. Finding shear stress due to viscosity

244. Capillary rise

245. Pressure inside droplet, soap bubble and liquid jet

246. Continuity equation: 2015, 2014, 2014, 2012, 2006

247. Momentum equation

248. Energy equation: 2015, 2009, 2007

249. Jet propulsion problems

250. Shear stress at any radius in pipe laminar flow, friction factor: 2009

251. Relation between pressure difference and discharge

252. Velocity distribution in laminar flow: 2014

253. Hagen poisselli equation: 2007, 2006

254. Friction and minor losses: 2015, 2014, 2013

255. Pipe network problems: 2015, 2014, 2011

256. Equivalent pipe length

257. Displacement, momentum and energy thickness of boundary layer

258. Drag force

259. Momentum correction factor and energy correction factor

260. Thickness laminar boundary layer

261. Laminar sublayer thickness: 2008

262. Chezy’s formula and Manning’s formula: 2015

263. Most economical rectangular and trapezoidal sections: 2016, 2012, 2010

264. Critical depth condition: 2014, 2011, 2010, 2009, 2008

265. Alternate depths and specific energy, Froude number: 2012

266. Hump problems: 2016, 2011

267. Width constriction problems: 2014, 2010

268. Gradually varied flow concept, water slope: 2015, 2013, 2010

269. Direct step method: 2009

270. Different profiles: 2016, 2007, 2007, 2006

271. Sequent depths in hydraulic jump: 2016, 2015, 2011, 2008

272. Prejump velocity and post jump velocity: 2015

273. Energy loss in hydraulic jump: 2006

274. Total pressure on plane surfaces: 2015

275. Total pressure on curved surfaces: 2016

276. Centre of pressure

277. Buoyancy, Metacentric height: 2011

278. Manometers: 2014, 2010

279. Sharp-crested weirs: 2013

280. Triangular weir: 2007

281. Trapezoidal weir and cipolletti weir

282. Broad crested weir

283. Submerged weir

284. Venturimeter and orifice meter: 2014, 2014, 2010

285. Pitot tube: 2014, 2010

286. Froude model law and Froude number: 2015, 2013, 2008, 2007

287. Raynolds model law and raynolds number: 2015, 2006

288. Acceleration: 2015, 2014

289. Angular velocity: 2015

290. Vorticity and circulation

291. Velocity potential and stream function: 2007

292. Discharge between two stream lines: 2013

293. Force on plate due to jet: 2016, 2014, 2014, 2007

294. Power generation in turbines: 2016

295. Specific speed of pump and turbine

296. Net Positive Suction Head

### Hydrology

297. Water budget: 2015298. Missing rain gauge data estimation: 2015

299. Optimum number of rain gauges

300. Isoheital method: 2013

301. Flow duration curves: 2014

302. Currentmeter, two point method, anemometer: 2012, 2010

303. Theissen polygon method

304. ∅ −index: 2013, 2007

305. Hortons equation: 2012, 2010, 2006

306. Evapotranspiration: 2012, 2010

307. Probability of flood: 2013, 2012

308. Relation between catchment area and hydrograph area: 2016, 2014, 2014, 2012, 2011, 2011, 2010, 2009, 2007

309. Derivation of storm hydrograph from Unit hydrograph: 2016, 2012, 2011, 2009

310. Superposition principle to derive UH: 2007

311. S-hydrograph and its uses: 2015, 2006

312. Dickens and Ryves formula

313. Types of flood routing: 2016, 2008

314. Muskingum equation: 2014, 2010

315. Specific yield, specific retention and porosity: 2016, 2015, 2011, 2009,

2008

### Irrigation:

316. Duty, delta and base period: 2016, 2013, 2009317. Duty, discharge and catchment area: 2015, 2012, 2008, 2007

318. Field capacity, wilting point and depth of water, frequency of irrigation :

2014, 2010, 2007

319. Anemometer, hygrometer, tensiometer: 2014

320. irrigation efficiencies

321. Manning’s, chezy,s, Boundary shear stress: 2007

322. Lacey’s formulae and kennedy: 2009, 2008, 2007

323. Khosla uplift pressures at different points: 2016

324. Piping failure: 2006

325. Flour thickness required to overcome uplift

326. Kosla critical exit gradient: 2008

327. Uplift force under dam: 2016, 2008

### Environmental engineering:

328. Water treatment processes: 2014, 2011329. Total dissolved solids, toxic metals: 2015, 2014, 2006

330. Ph of water: 2016, 2012, 2008

331. Alkalinity: 2013

332. Hardness: 2016, 2014, 2010, 2009, 2007, 2007, 2006

333. Nitrates, kjedhal nitrogen: 2015

334. Settling velocity, surface overflow rate and design: 2016, 2014, 2013,

2012, 2011

335. Efficiency of sedimentation tank, dia of particles: 2015, 2015, 2009, 2007

336. Alum dose and alkalinity requirement: 2014

337. Velocity gradient and power required in coagulation mixing tank

338. Sand filters: 2015, 2013

339. Lime and soda requirements

340. Ion Exchange process and bypass flow ratio: 2016

341. Disinfectin, proportion of Hocl and ocl ions: 2014, 2014, 2011, 2011

342. COD test: 2012

343. BOD determination: 2006

344. BOD at different temperatures and different times: 2016, 2016, 2015,

2014, 2013, 2010

345. Efficiency of trickling filter

346. Efficiency of high rate trickling filter

347. Activated sludge process: 2016, 2014, 2009

348. Rising of sludge: 2016

349. Nitrification: 2016

350. Biological nitrogen removal: 2016

351. Methane production: 2014, 2009

352. Food to micro organism ratio, Sludge age (MCRT), HRT, SVI: 2012, 2007

353. Sludge recirculation ratio

354. Sludge volume reduction, Sludge solids unit weight, moisture content and

density of sludge: 2011

355. Dilution

356. Critical time in river

357. Critical deficit

358. Deficit at any time

359. Sewer lines, pipes, slope, discharge, corrosion: 2016, 2012

360. Density of MSW: 2015, 2015, 2010, 2008, 2007, 2006

361. Primary and secondary air pollutants: 2016, 2015, 2011, 2008

362. Environmental meteorology: 2016, 2013, 2010, 2009, 2007

363. Concentration conversion: 2015, 2006

364. Fabric filter design: 2016, 2014, 2011, 2009

365. ESP design: 2016, 2007

366. Measurement of sound pressure level: 2016, 2009

367. Addition of two sounds

368. Averaging of sounds

369. Equivalent noise level

370. Ln concept: 2006

371. Reduction of sound level with distance: 2016

372. Noise level standards: 2010

### Transportation engineering:

373. Stopping sight distance: 2016, 2015, 2014, 2011, 2007, 2006374. Overtaking sight distance: 2015

375. Bump integrator: 2012

376. Super Elevation: 2015, 2015, 2009

377. Ruling minimum radius of curve: 2014

378. Extra widening at curves: 2016, 2010, 2007

379. Length of transition curve: 2011, 2006

380. Shift of curve

381. Set back distance: 2012

382. Grade compensation: 2007

383. Length of summit curve: 2010, 2009

384. Length of valley curve: 2013

385. Properties and tests of bitumen: 2015, 2008, 2007

386. Properties and tests of aggregates: 2015, 2008, 2007, 2006

387. CBR test: 2009, 2006

388. Marshal mix design parameters and curves: 2016, 2015, 2014, 2013, 2011

389. Cumulative standard axles: 2014, 2012, 2007, 2006

390. Radius of relative stiffness: 2016

391. IRC -37 code provisions : 2016

392. IRC- 58 code provisions: 2013

393. Equivalent radius of resisting section

394. Frictional stress

395. Thermal stress: 2014, 2010, 2009

396. Load stresses: 2009, 2006

397. Critical Load combinations

398. Design of expansion joint: 2007

399. Design of contraction joint

400. Design of dowel bar

401. Design of tie bar

402. Poisson distribution: 2014, 2014, 2011

403. Exponential distribution: 2013

404. Flow and headway, spacing and density: 2016, 2014

405. Traffic studies: 2006

406. Traffic density, phf: 2014

407. Moving car method: 2016, 2014

408. Speed density , flow density relationships: 2015, 2015, 2014, 2014, 2012,

2011, 2009, 2006

409. Capacity of lane: 2008

410. Capacity of rotary, intersections, conflicts: 2015, 2013, 2012, 2009, 2007

411. Webster optimal signal time, green splitting:2016 2014, 2014, 2007, 2006

412. Total delay and average delay at signal: 2011

413. Traffic signs: 2010, 2008

### Geomatics:

414. Types of surveying: 2014, 2008415. Shape of earth, MSL, plumb line , time: 2015, 2010

416. Scales: 2007

417. Curvature, refraction and combined correction: 2015, 2013, 2011, 2009

418. WCB to QB: 2009

419. Declination, local attraction: 2015, 2013, 2009, 2007,2006

420. Latitudes and departures in traverse and Bowditch rule: 2016, 2015, 2015,

2013, 2007

421. Missing measurement: 2011

422. Height of instrument, Rise and fall method: 2015

423. Contours: 2014

424. Reciprocal leveling: 2015, 2012, 2007

425. Determination height of tower from two angles: 2016, 2012

426. Staff held inverted: 2016, 2014, 2010, 2006

427. Tacheometer problems: 2014

428. Tacheometer tangential method

429. Errors in measurements

430. Weights and precision: 2015

431. Elements of simple curve: 2016, 2014, 2007

432. Photogrametry no. of photographs required and laps: 2016

433. Relief displacement and tower height: 2016

434. Remote Sensing: 2016

435. GIS

436. GPS: 2016

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