Attempt the ISRO Mechanical & Aerospace 2012 previous year paper in real CBT exam mode or practice mode with verified answers and explanations.
All ISRO Mechanical & Aerospace papers
80 questions.
Area moment of inertia for the quadrant shown is
Answer: D. \pi r^4 / 16
Explanation: For a full circle, I = \pi r^4 / 4. A quadrant is 1/4th. With respect to diametric axes, I = 1/4 * (\pi r^4 / 4) = \pi r^4 / 16.
A column of length 'L' is fixed at bottom end and hinged at the other end. This column is restrained from lateral displacement at 1/3rd height. The buckling load is given by
Answer: A. 9\pi² EI / (4L^2)
Explanation: The restraint creates two segments. Top segment (2L/3) is hinged-hinged: P = \pi² EI / (2L/3)^2 = 9\pi² EI / 4L^2. Bottom segment (L/3) is fixed-hinged: P approx 2\pi² EI / (L/3)^2 = 18\pi² EI / L². Failure occurs at the lower load.
A shaft has two heavy rotors mounted on it. The transverse natural frequency considering each rotor separately is 100 hz & 200 hz respectively. The lowest critical speed is
Answer: B. 5367 rpm
Explanation: Dunkerley's Formula: 1/f² = 1/f1^2 + 1/f2^2. 1/f² = 1/100^2 + 1/200^2 = 5/40000. f = $\sqrt{8000}$ = 89.44 Hz. N = 60f = 5366.4 rpm.
A mass 'M' is suspended from a ceiling through a string of length 'L'. This mass moves in a circle of horizontal radius 'r' at constant speed such that it is a conical pendulum. The tension in the string will be
Answer: D. mgL / \sqrt{L²-r²}
Explanation: T cos(theta) = mg. cos(theta) = h/L = $\sqrt{L²-r²}$/L. T = mgL / $\sqrt{L²-r²}$.
The stress in the rod AB in the pin jointed truss ABCD (where P acts at C downwards) is
Answer: B. 4P / \pi d²
Explanation: Force in AB balances P. Stress = Force/Area = P / (\pi d² / 4) = 4P / \pi d².
The number of degrees of freedom for a mechanism with 6 links and 7 binary joints is
Answer: B. 1
Explanation: F = 3(N-1) - 2J. F = 3(6-1) - 2(7) = 15 - 14 = 1.
A plate is held by a chain AB through hinge joints. The plate is pulled with a force T. The tension in the chain is given by
Answer: D. 3\sqrt{2}T
Explanation: Based on moment equilibrium and geometry (often 45 degree angle implied by L,L dimensions), T_chain = 3 * $\sqrt{2}$ * T.
In a turn buckle joint, both mating rods will have
Answer: C. Right hand and left hand threads
Explanation: Opposite threads allow the turnbuckle to tighten or loosen both rods simultaneously when rotated.
In a flat belt drive, the belt can be subjected to a maximum tension (T) and centrifugal tension (Tc). The condition of transmission of maximum power is given by
Answer: C. T = 3Tc
Explanation: For maximum power, centrifugal tension is 1/3rd of maximum tension.
The diameter of a soap bubble with has an inside pressure of 2.5 N/m² over the atmospheric pressure and a surface tension of 0.0125 N/m is
Answer: A. 40 mm
Explanation: P = 8*sigma / d. d = 8*0.0125 / 2.5 = 0.04 m = 40 mm.
Find the loss of head due to friction in a smooth pipe of rectangular cross section of 1m x 0.5 m and 10m long. Velocity of flow is 10 m/s and the friction coefficient is 0.01962.
Answer: B. 6m
Explanation: Hydraulic mean depth m = Area/Perimeter = 0.5/3 = 1/6. hf = f L v² / (2 g m) = 0.01962 * 10 * 100 / (2 * 9.81 * 1/6) = 19.62 / (3.27) = 6 m.
When a supersonic flow is admitted into a convergent duct, the flow will
Answer: B. Decelerate
Explanation: A converging duct acts as a diffuser for supersonic flow, decreasing velocity and increasing pressure.
Which configuration measures the stagnation pressure?
Answer: B. Pitot tube facing flow
Explanation: A tube opening facing directly upstream brings the fluid to rest, measuring stagnation pressure.
The maximum lift in a centrifugal pump would be close to 'X' if the pump is handling cold water (25 C) from an open tank at sea level with no friction and turbulence loses, where 'X' is equal to
Answer: A. 10 m
Explanation: Theoretical suction lift is limited by atmospheric pressure, approx 10.3m.
Both pressure and velocity of steam drops in the moving blades of
Answer: C. Reaction turbine
Explanation: In reaction turbines, expansion (pressure drop) occurs in both fixed and moving blades.
A model of a golf ball is to be studied to determine the effects of the dimples. A sphere 10 times larger in diameter than an actual golf ball is used in the wind tunnel study. What speed should be selected for the model to simulate a prototype speed of 50 m/s?
Answer: B. 5m/s
Explanation: Reynolds number similarity: Vm Dm = Vp Dp. Vm (10 Dp) = 50 Dp. Vm = 5 m/s.
The sound of explosion on a ship located 10km away from the beach was heard 28.6 seconds after the explosion was seen. Estimate the temperature of air at that time.
Answer: A. 31 C
Explanation: c = 10000/28.6 = 349.65 m/s. c = $\sqrt{1.4 * 287 * T}$. T = 304 K = 31 C.
A spherical balloon is filled with helium at sea level. Helium and balloon material together weight 500 N. If the net upward lift force on the balloon is also 500 N, what is the diameter of the balloon?
Answer: A. 5.42m
Explanation: Buoyant force = Weight + Lift = 500 + 500 = 1000 N. 1000 = rho_air * g * V. V = 83.2 m³. D = 5.42 m.
Air at 20 C and 10^5 Pa enters the bottom of an angle of 85 degree conical flow meter duct at 0.3 kg/s. Estimate the weight of the body in Newton's
Answer: A. 2.5N
Explanation: Force balance using momentum equation yields approx 2.5N.
A jet of water issues from a nozzle with a velocity 20 m/s on a flat plate moving away from it at 10 m/s. The cross-sectional area of the jet is 0.01 m². The force developed on the plate is
Answer: A. 1000 N
Explanation: F = rho A (V - u)^2 = 1000 * 0.01 * (20 - 10)^2 = 1000 N.
The laminar boundary layer thickness varies as
Answer: C. x^(1/2)
Explanation: Delta varies as $\sqrt{x}$ for laminar boundary layer.
An increase in pressure of a liquid from 7.5 MPa to 15 MPa results into 0.2 percent decrease in its volume. The coefficient of compressibility of the liquid in m²/N is
Answer: A. 0.267 * 10^-9
Explanation: Beta = (dV/V) / dP = 0.002 / (7.5 * 10^6) = 0.267 * 10^-9.
A reservoir of capacity 0.01 m³ is completely filled with a fluid of compressibility 0.75 * 10^-9 m²/N. The amount of fluid that will spill over if pressure is reduced by 2 * 10^7 N/m² is
Answer: B. 1.5 * 10^-4
Explanation: dV = V * Beta * dP = 0.01 * 0.75e-9 * 2e7 = 1.5e-4 m³.
The extent of pressure produced due to water hammer depends on
Answer: D. All the above
Explanation: Water hammer pressure is a function of fluid velocity, pipe characteristics, and closure time.
Rank of the matrix A = [[1, 1, 2], [1, 2, 3], [0, -1, 1]] is
Answer: D. 3
Explanation: Determinant is non-zero, so rank is 3.
The value of t for which A + tB is perpendicular to C where A = i + 2j + 3k, B = -i + 2j + k and C = 3i + j
Answer: A. 5
Explanation: Dot product of (A+tB) and C is zero. Solving gives t=5.
A x B is a vector
Answer: C. Perpendicular to both A & B
Explanation: Cross product yields a vector perpendicular to the plane of the operands.
The equation of the plane through the line (x-1)/3 = (y-4)/2 = (z-4)/-2 and parallel to the line (x+1)/2 = (y-1)/-4 = (z+2)/1 is
Answer: C. 6x + 7y + 16z = 98
Explanation: Normal is cross product of direction vectors. Equation derived is 6x + 7y + 16z = 98.
Let E and F be any two events with P (E U F) = 0.8, P (E) = 0.4 and P(E/F) = 0.3. Then P (F) is
Answer: B. 4/7
Explanation: Using P(E U F) = P(E) + P(F) - P(E n F) and P(E n F) = P(E/F)P(F).
The approximate value of y (0.1) from dy/dx = x^2y-1, y(0) = 1 is
Answer: A. 0.900
Explanation: Euler's method: y1 = 1 + 0.1 * (0 - 1) = 0.9.
1 + i is equivalent to
Answer: B. $\sqrt{2}$ e^(i pi/4)
Explanation: Magnitude $\sqrt{2}$, angle 45 degrees.
In a class of 45 students, the mean mark of 25 girls is 32 and the mean mark of 20 boys is 27.5. What is the class mean?
Answer: D. 30
Explanation: (25*32 + 20*27.5)/45 = 30.
If L {f(t)} = F(s), then the value of L {e^(-at) f(t)} is
Answer: B. F (s+a)
Explanation: Shifting theorem.
The probability that A happens is 1/3. The odds against happening of A are
Answer: A. 2 : 1
Explanation: P(not A) / P(A) = (2/3) / (1/3) = 2.
Draft on pattern for casting is provided for
Answer: C. Taper to facilitate removal
Explanation: Draft allows pattern removal without mold damage.
Welding spatter is
Answer: A. Welding defect
Explanation: Spatter is the splashing of metal droplets.
Which of the following statements is false about annealing? (Annealing is done to)
Answer: A. Harden Steel slightly
Explanation: Annealing softens metal, it does not harden it.
The property of corrosion resistance of chromium Stainless Steel is due to
Answer: C. Formation of thin film of Cr2O3
Explanation: Passive oxide layer protects the steel.
Hot working operation is carried out at
Answer: D. Above re-crystallization
Explanation: Hot working is deformation above the recrystallization temperature.
The engineering and true strains for a bar which is doubled in length during tension test are
Answer: A. e = 1.0 epsilon = 0.693
Explanation: e = (2L-L)/L = 1. epsilon = ln(2L/L) = ln(2) = 0.693.
The purpose of adding wood flour to the moulding sand is to improve
Answer: C. Collapsibility
Explanation: Wood flour burns out allowing sand to collapse as casting cools.
Stretch forming is a process in which
Answer: C. Advantage is taken of plastic state
Explanation: Material is stretched to yield point to facilitate forming.
In which type of welding, a pool of molten metal is used?
Answer: B. Electro slag welding
Explanation: ESW uses a conductive slag pool to melt filler and base metal.
A mild steel block... straight slab cutter... value of maximum uncut chip thickness?
Answer: D. 0.00563 mm
Explanation: Using formula for slab milling chip thickness.
Match List I (Instruments) with List II (Applications)
Answer: B. A-4, B-3, C-1, D-2
Explanation: Talysurf-Roughness; Telescopic gauge-Internal Dia; Transfer Calipers-Slots; Autocollimator-Flatness.
A shaft has dimension 35 -0.009/-0.025, fundamental deviation and tolerance are
Answer: D. -0.009, 0.016
Explanation: Fund dev is upper limit (-0.009). Tolerance is difference (0.016).
Deformation under constant load over time is
Answer: A. Creep
Explanation: Time-dependent deformation is creep.
Which is a wrong statement?
Answer: B. Lining of open hearth furnace controls impurities
Explanation: Though lining affects chemistry, the statement is flagged as wrong in context.
18:4:1 High Speed Steel contains
Answer: A. 18W, 4Cr, 1V
Explanation: Tungsten 18%, Chromium 4%, Vanadium 1%.
Water boiled in coffee maker... power rating?
Answer: C. 1.05 kW
Explanation: Calculation yields approx 1.05 kW.
Adiabatic heat exchanger... exit temperature of cold water?
Answer: C. 85 C
Explanation: Energy balance indicates 85 C.
Log mean area 'A' is
Answer: B. (A2-A1)/ln(A2/A1)
Explanation: Formula for log mean area.
Nusselt number is ratio of
Answer: B. Conductive/Convective resistances
Explanation: Nu = hL/k = (L/k) / (1/h) = R_cond / R_conv.
Zeroth law not valid for
Answer: D. Mixing water and acid
Explanation: Chemical reaction heat release violates simple thermal equilibrium premise.
Work obtained is greatest for PV^n = C when
Answer: C. n=0
Explanation: Isobaric (n=0) gives maximum area under curve for expansion.
Air compressed to half volume at constant pressure, entropy change
Answer: B. Decrease
Explanation: Volume decrease at constant P means Temperature decrease, thus Entropy decreases.
Cycle on P-V diagram represented in T-S diagram by
Answer: B. b
Explanation: Matching process curves.
If 2 bar air at 27 C heated to 177 C at constant volume, pressure is
Answer: B. 3 bar
Explanation: P2 = P1 * T2/T1 = 2 * 450/300 = 3 bar.
Frictionless heat engine 100% efficient only if exhaust temp is
Answer: C. 0 K
Explanation: Carnot efficiency = 1 - TL/TH. 100% implies TL=0.
Ideal engine absorbs heat at 127 C and rejects at 77 C. Efficiency is
Answer: A. 13%
Explanation: 1 - 350/400 = 1/8 = 12.5%.
Francis turbine power output at 100m head (from 5000kW at 25m)
Answer: C. 40000
Explanation: Power proportional to H^1 May 5000 * (100/25)^1.5 = 40000.
Steam turbine mean diameter
Answer: B. 4.73 m
Explanation: Calculation based on velocity triangles.
Refrigerator power input
Answer: B. 33W
Explanation: COP calculation yielding 33W.
Efficiency order for same compression ratio
Answer: B. Otto > Dual > Diesel
Explanation: Standard comparison for same compression ratio.
Section modulus of triangular section
Answer: C. bh²/24
Explanation: Z = I/y = (bh³/36) / (2h/3) = bh²/24.
Stress diagram for eccentric load on rectangular column
Answer: A. a
Explanation: Combined bending and direct stress.
Shaft A radius half of B. Power of A is ... of B
Answer: A. 1/8
Explanation: Power proportional to r³.
Natural frequency of 4 spring system
Answer: A. $\sqrt{4k/m}$
Explanation: Parallel springs.
Lowest friction bearing
Answer: C. Aero-static
Explanation: Air has very low viscosity.
Velocity at point P on rolling disc
Answer: B. $\sqrt{3}$V
Explanation: Vector addition of velocities.
Viscous damping factor from log decrement
Answer: B. 25%
Explanation: Calculation gives 0.25.
Elevator cable tension
Answer: D. 11800
Explanation: T = m(g+a).
Block friction cable tension
Answer: C. 481
Explanation: Equilibrium calculation.
Suspension damping factor
Answer: A. 0.471
Explanation: Zeta calculation.
Balancing mass radial position
Answer: C. 150
Explanation: Balancing equation.
Gear tooth tangential load
Answer: B. 22.1
Explanation: Power/Velocity calculation.
Steel rod length change
Answer: B. -10
Explanation: Sum of PL/AE.
Planetary gear rotations
Answer: B. 4
Explanation: Epicyclic gear train calculation.
Mohr circle reduces to point when
Answer: C. equal axial stress...
Explanation: Radius is zero.
Shear stress distribution rectangular beam
Answer: D. d
Explanation: Parabolic profile.