GATE 2020 BM – Previous Year Questions with Solutions
All 65 questions of GATE 2020 BM with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Fill the blanks in the source sentence: “Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a…
- Question 2 – Choose the word completing: “Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are .”
- Question 3 – Choose the word completing the analogy: Cover : Uncover :: Associate : .
- Question 4 – Floods have affected kharif (summer-sown) crops. Officials believe a good rabi (winter-sown) output can recover the production loss, allowing the…
- Question 5 – Find the difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers.
- Question 6 – Repo rate is the rate at which RBI lends money to commercial banks; reverse repo rate is the rate at which RBI borrows from them. Which inference is…
- Question 7 – P,Q,R,S,T,U,V,W sit around a circular table. S is opposite W. U is second to the right of R, T is third to the left of R, and V is a neighbour of S.…
- Question 8 – Delhi and Agra are 233 km apart. Car P leaves Delhi and car Q leaves Agra toward Delhi one hour later. They meet 75 minutes after Q starts. P travels…
- Question 9 – A 4×4 matrix M=[mᵢⱼ] has zero diagonal and mᵢⱼ=−mⱼᵢ. What minimum number of entries determines the full matrix?
- Question 10 – The chart gives annual profit percentages of companies P and Q for 2013–2018. Both invest the same fixed amount every year. Find the ratio of total…
- Question 11 – For roots m₁,m₂ of a second-order characteristic equation, match P real distinct,Q equal,R complex conjugate with K critically damped,L overdamped,M…
- Question 12 – A seated person has feet on the ground and rises to stand. Which listed kinematic motion does NOT occur as part of this rising movement?
- Question 13 – Which equipment measures blood-vessel elasticity in vivo?
- Question 14 – Shape-memory biomaterials are NOT used in which listed application?
- Question 15 – The source asks which MRI contrast results from “long T REP or short T ECHO.”
- Question 16 – In diagnostic X-ray imaging, which is NOT a primary electromagnetic-radiation interaction in soft tissue?
- Question 17 – A 5 MHz ultrasound pulse images a tumor 2 cm deep in soft tissue. Its round-trip echo time is t. If frequency changes to 2.5 MHz, what is the echo…
- Question 18 – X(s) is the Laplace transform of x(t). Assuming x(0)=0, find the Laplace transform of dx(t)/dt.
- Question 19 – Which functions are odd? P=sin t, Q=cos t, R=sin t+cos t, S=sin t cos t.
- Question 20 – A state model is X=pmatrix0&2\&0pmatrixX+pmatrixb\\0pmatrixU, Y=(1\ 0)X. Which condition makes it controllable?
- Question 21 – In a microprocessor system with memory-mapped I/O, which statement is true?
- Question 22 – How many electrodes are used to record a standard 12-lead ECG?
- Question 23 – Which is NOT a constituent bone of the knee joint proper?
- Question 24 – During stethoscopic examination at the left midclavicular line in the fifth intercostal space, a murmur is heard between the first and second heart…
- Question 25 – Which proteins comprise a muscle fibre’s thin filament?
- Question 26 – Evaluate 12 j Cz(z-1)(z-2)\,dz for positively oriented circle z =3/2.
- Question 27 – A nonsingular 3×3 matrix P has eigenvalues 1,2,3. Find trace(P⁻¹), to two decimals.
- Question 28 – Starting at a finite positive value, the iteration xₙ₊₁=(xₙ+1/xₙ)/2 converges to what value?
- Question 29 – NaI crystals detect 120 keV gamma rays. If their half-value layer is 0.2 cm, what percentage of gamma rays passes through 1 cm of NaI, to one decimal…
- Question 30 – An endoscope’s distal end is 1 mm from the gastrointestinal wall. Fibre core and cladding refractive indices are 1.5 and 1.45. Find maximum full…
- Question 31 – Two coils are wound separately on identical ring-shaped ferromagnetic cores. Coil 1 has N turns and wire gauge G, while coil 2 has 2N turns and gauge…
- Question 32 – Two dyes X,Y have concentration ratio cX/cY=0.25 and are measured in identical cuvettes. Their absorbance ratio AX/AY=0.5. Find the ratio of molar…
- Question 33 – The source asks the energy from hydrolysis of one ATP molecule in kilocalories, to one decimal place. Give its conventional biochemical standard…
- Question 34 – An 830 nm laser-Doppler blood-flow probe is at 60° to the flow direction. Mean flow velocity is 3 cm/s. Find Doppler-shift magnitude in kHz to one…
- Question 35 – In the source’s artificial-pacing model, a single 100 mA pulse is delivered through 500 Ω tissue impedance. Delivered energy must not exceed 300 μJ.…
- Question 36 – A mammalian nerve cell initially rests at −80 mV. A drug lowers intracellular K⁺ from 150 to 55 mmol/L while external K⁺ is unchanged. Use R=8.315…
- Question 37 – Four initially equal pressure-catheter resistors are arranged as shown. Pressure lengthens R₂,R₄ and increases cross-sectional area of R₁,R₃,…
- Question 38 – For Vᵢₙ=10sin(2πt) applied to the circuit shown, which output waveform results? Both op-amps have ±12 V supplies. The second stage contains 100 kΩ,0.2…
- Question 39 – Mean arterial pressure is 100 mmHg and systolic pressure is 150 mmHg. Using the usual resting approximation, find diastolic pressure.
- Question 40 – Two parallel loads draw 10 kW at unity power factor and 10 kVA at 0.6 lagging power factor. What nearest capacitor-bank rating in kVAr gives overall…
- Question 41 – Find the nearest power dissipated in the 3 Ω resistor of the shown circuit, with 2 A current source, 2 V voltage source and resistors 2 Ω,2 Ω,4 Ω,3 Ω.
- Question 42 – Two first-order low-pass filters H 1(j)=1/(1+j/ 1) and H 2(j)=1/(1+j/ 2) are cascaded. Find the resulting second-order undamped natural frequency ωc.
- Question 43 – Match bridges P Maxwell,Q Kelvin double,R Hay,S Schering to applications K low-resistance measurement,L medium-Q coil inductance,M capacitance,N…
- Question 44 – A non-unity-feedback system has G(s)=12/(s+2) and H(s)=2/(s+3). Find the magnitude of steady-state tracking error for a unit step.
- Question 45 – Match Boolean expressions P= X Y Z+ XY Z+ XYZ, Q=XYZ+X YZ+XY Z, R=XY+XYZ+XY Z+ XYZ, S= X YZ+ XYZ+X YZ+XYZ to K=X(Y+Z), L= X(Y+ Z), M=Z, N=Y(X+Z).
- Question 46 – Glomerular filtration is modeled as flow through a flat membrane with cylindrical pores of radius 1 nm and length 60 nm. Fluid viscosity is 0.002 Pa…
- Question 47 – At rest, extracellular voltage relative to the inside of a mammalian cell is . Intracellular and extracellular regions have higher and concentrations,…
- Question 48 – A degradable surgical suture loses 40% of its original tensile strength after 10 days and 50% after 20 days. Assuming exponential decay, what closest…
- Question 49 – A 60 kg person stands on one foot on a force plate. Ground reaction acts 40 mm anterior to the ankle joint. The foot centre of mass is 60 mm from the…
- Question 50 – During femoral arthroplasty, bone cement warms from 37°C to 87°C and has thickness 20 mm. Bone, cement and implant are concentric cylinders;…
- Question 51 – An MRI RF coil at 1 T has induced voltage magnitude V =2 0V sM 0()Br, with γ₀ the Larmor frequency, Vₛ slice volume, M₀ equilibrium magnetization and…
- Question 52 – A 3 MHz transducer sends a three-cycle pulse normally toward a fat–liver boundary. Use tissue speed 1500 m/s, fat speed 1450 m/s,liver speed 1570 m/s,…
- Question 53 – A silicon diode obeys the exponential V–I model. Its current is 1 mA at 0.7 V. With thermal voltage 25.3 mV, find nearest current when voltage is 0.8…
- Question 54 – A continuous random variable has normalized density f(x)=e-a x for all real x, where a is a real constant. Find its variance to one decimal place.
- Question 55 – Find the magnitude of the gradient of f(x,y)=x²+y² at (1,1), to two decimals.
- Question 56 – Evaluate Rxy\,dx\,dy over the first-quadrant part of the unit disc, to three decimals.
- Question 57 – Recorded pairs (age in years,diastolic BP in mmHg) are (23,65),(24,60),(25,62),(26,70),(28,70),(29,73),(31,75),(35,83),(40,90). Using linear…
- Question 58 – A standing person flexes the hip by 50° from the initial trochanter–knee–ankle line and then flexes the knee by 20°. Hip-to-knee length is 400 mm and…
- Question 59 – A 36 cm ×48 cm chest radiograph is digitized to preserve 6 cycles/mm at 8-bit quantization. Find approximate image size in MB to two decimals, using…
- Question 60 – In the shown 50 keV X-ray path, incident photon count is 2×10⁶. The ray crosses 2 cm soft tissue,0.5 cm blood and 1 cm soft tissue. Attenuation…
- Question 61 – Find the de Broglie wavelength in nm of an electron accelerated through 1 V, to two decimals. Use electron mass 9.11×10⁻³¹ kg,h=6.63×10⁻³⁴ J s and…
- Question 62 – A PMMC instrument has magnetic flux density 1.5 T, torsional spring constant 2×10⁻⁶ N m/degree, coil area 2.5 cm² and 500 turns. Find angular…
- Question 63 – The source gives blood oxygen partial pressure 40 mmHg, oxygen solubility 0.003 mL/(mmHg dL), hemoglobin saturation 95%, oxygen capacity 1.34 mL/g and…
- Question 64 – A C-clamp magnetic arterial-flow probe records 3.75 nV between diametrically opposite vessel points. Inner diameter is 0.5 cm and magnetic flux…
- Question 65 – A cell is driven by current i(t)=u(t). Its linear membrane model has impulse response h(t)=Ae-t/u(t), with A=−34 V/s and τ=3 ms. Find membrane-voltage…