GATE 2021 BM – Previous Year Questions with Solutions
All 65 questions of GATE 2021 BM with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Which sentences are grammatically correct? (i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun’s families is here. (iv) Arun’s…
- Question 2 – The word PHYLAXIS is drawn above the X-axis as shown. Which option is its mirror image about the X-axis?
- Question 3 – Two identical fair six-faced dice, numbered 1 to 6, are rolled simultaneously. What is the probability that each die shows an even number?
- Question 4 – Define operators by p⊙q=p−q and p⊕q=p×q. Evaluate (9⊙(6⊕7))⊙(7⊕(6⊙5)).
- Question 5 – Four people P,Q,R,S are seated in a row. R must not sit second from the left. How many distinct arrangements are possible?
- Question 6 – Starting at O, travel 3 units east then 4 units south to P. From P travel northeast to a point 6 units east of O, then northwest to Q, which is 8…
- Question 7 – The author says: “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it…
- Question 8 – Some football players play cricket. All cricket players play hockey. Which statement follows?
- Question 9 – PQRS is a square. The shaded region is the intersection of two circular sectors, each of radius equal to the square’s side, with centres at S and Q.…
- Question 10 – In equilateral triangle PQR, PQ is divided into four equal parts, QR into six equal parts, and PR into eight equal parts. Every subdivided length in…
- Question 11 – For f X(x)=1qex+e-x to be a valid probability density on the real line, find q.
- Question 12 – For V(x,y)=(x2+y2)/2, find its directional derivative at (1,1) in direction 3y i-3x j.
- Question 13 – Three resistors are connected to ideal sources as shown: current source 1.2 A, voltage source 24 V, resistors 10 Ω,20 Ω,30 Ω. Find VAB in V.
- Question 14 – An ideal 1/3 H inductor is connected to a 50 Hz sinusoidal voltage source. The energy stored is stated as 6 J. Find the maximum power delivered to the…
- Question 15 – Let X(jω) be the Fourier transform of x(t), with X(j)=10e-j f( f)/( f) and ω=2πf. Evaluate 12 -X(j)\,d.
- Question 16 – Y=Y₁Y₀ is the two-bit output of the combinational circuit shown. What is the maximum value of Y for digital inputs A₁A₀ and B₁B₀?
- Question 17 – The input Vᵢₙ=sin(2π×10⁶t) is quantized by a 10-bit Nyquist ADC. Four least significant bits are discarded, and the remaining six most significant…
- Question 18 – For a linear stable second-order system, the unit-step peak time is twice its rise time. The system is .
- Question 19 – Which displacement sensor is known for high sensitivity and a relatively large measurement range?
- Question 20 – Which temperature sensor is used in contact-type digital thermometers for measuring body temperature?
- Question 21 – Which range describes blood pH in a healthy human?
- Question 22 – Which is a cranial bone?
- Question 23 – Which gland produces thyroid-stimulating hormone (TSH)?
- Question 24 – Which listed obstruction causes myocardial infarction?
- Question 25 – Treat blood as red cells suspended in a Newtonian fluid. What is the intended effect of flow-induced shear forces on red-cell orientation?
- Question 26 – Water contact angles on surfaces A and B are θA and θB as shown. Which statement is true?
- Question 27 – Which is a bone-resorbing cell?
- Question 28 – Which statements about planar X-ray imaging are correct?
- Question 29 – For equal muscle volume, which comparisons of pennate and parallel-fibre muscles are true?
- Question 30 – Which mechanisms may cause bone-implant failure?
- Question 31 – Find the minimum of f(x 1,x 2,x 3)=12(x 12+x 22+x 32)-2(x 1+x 2+x 3), rounded to the nearest integer.
- Question 32 – H(s)=(1+s/106)/s is converted by a bilinear transform at sampling rate 100 MHz to H(z). At what z is its pole?
- Question 33 – For a type-2 unity-feedback system, the extrapolated initial −40 dB/decade Bode segment crosses 0 dB at 2 rad/s. Find acceleration error constant Kₐ.
- Question 34 – A radionuclide has decay constant 3.22×10⁻⁵ s⁻¹ and activity 6 mCi at 10:30 AM. Find activity at 4:30 PM on the same day, in mCi to two decimals.
- Question 35 – A polymer scaffold for cartilage tissue engineering has initial dry mass 20 mg. After seven days in lysozyme solution it is freeze-dried and has dry…
- Question 36 – A nonsingular 2×2 matrix A has trace 12 and determinant 32. Find the eigenvalues of A⁻¹.
- Question 37 – A unit step is applied at t=0 to a system with H(s)=(1-s/ z)/(1+s/ p). Find y(0⁺).
- Question 38 – Solve y/ t+5 y/ x=0 with y(x,0)=sin x for all real x, and evaluate y at x=π,t=π/6.
- Question 39 – In the shown bridge, Vₛ=100 V, R₁=30 Ω,R₂=60 Ω,R₃=90 Ω,R₄=45 Ω,R₅=30 Ω. Find current through R₃ in the indicated left-to-right direction, in A to two…
- Question 40 – The shown x[n] and h[n] are convolved to give y[n]. If y[2]=1 and y[3]=0, find h[0]. The graph amplitudes are not drawn to scale.
- Question 41 – The shown infinite-tap feedforward realization gives H(z)=1/(1-0.5z-1). Its successive delayed tap weights are α²,α⁴,α⁶,… . Find positive α.
- Question 42 – An analog signal sampled at 100 MHz produces 1024 samples. Only those samples are used for a 1024-point FFT. Find adjacent frequency-bin separation in…
- Question 43 – All op-amps in the shown circuit are ideal with infinite gain and bandwidth. Find Vout/Vin.
- Question 44 – The shown saturated NMOS has μₙCox=200 μA/V²,W=40 μm,L=1 μm, threshold 0.4 V and gmb/gm=0.1. A small input is applied at the bulk terminal. Neglect…
- Question 45 – An ideal 5 V source drives two series 100 Ω resistors, and voltmeters V1,V2 measure the drop across one. At five times, V1 readings are…
- Question 46 – The closed-loop characteristic equation is s⁴+2s³+8s²+8s+16=0. Find its steady-state oscillation frequency in rad/s.
- Question 47 – Match techniques P SEM,Q FTIR,R XPS,S AFM with properties K elemental composition,L roughness,M functional groups,N topography.
- Question 48 – Compared with ECG amplifiers, surface-EMG amplifiers have which typical characteristics?
- Question 49 – Match organs P stomach,Q liver,R pancreas,S gallbladder with functions K insulin/glucagon secretion,L bile storage,M bile synthesis/secretion,N…
- Question 50 – An axial MR slice at the isocentre of a 1.5 T scanner has thickness 2.5 mm. Slice-selection gradient is 2 gauss/cm and proton gyromagnetic ratio is…
- Question 51 – A longitudinal ultrasound wave meets a muscle–kidney boundary at 60°. Acoustic impedances are 1.70×10⁵ and 1.62×10⁵ g cm⁻² s⁻¹; sound speeds are 1590…
- Question 52 – A cylindrical biomaterial sample is 10 cm long and 1 cm in diameter. A 50 kN tensile force elongates it by 4 mm. Compare its tensile modulus with bone…
- Question 53 – The shown ladder has R₁=2 Ω,R₂=1 Ω,L₁=2 H,L₂=0.5 H, with output across R₂. Which descriptions apply?
- Question 54 – A clinician estimates cardiac output by thermodilution. A 2.0 mL saline injection at 7°C enters the right atrium, and the pulmonary-artery…
- Question 55 – Which statements about smooth muscle are true?
- Question 56 – A unity-feedback system has closed-loop transfer function C(s)/R(s)=(s+90)/(s2+10s+90). Find steady-state error to a unit ramp, to one decimal place.
- Question 57 – A renal artery has lumen diameter 5 mm and mean blood speed 40 cm/s. Blood density is 1060 kg/m³ and viscosity 3 cP. Find Reynolds number to the…
- Question 58 – A drug has approval probability 0.95 if tests show no side effects and 0.50 if tests show side effects. A physician assigns probability 0.20 that…
- Question 59 – Group A has 10 measurements with mean 35 and standard deviation 0.4. Group B has 15 measurements with mean 38 and standard deviation 0.6. Find the…
- Question 60 – In the shown circuit, Vₛ=50 V and L=0.1 H. Let the circuit reach steady state with the SPDT switch at position 1, then move it to position 2. Both…
- Question 61 – The shown op-amp has ±10 V supplies. Its non-inverting node connects to ground through 2R and output through R; its inverting node connects to +10 V…
- Question 62 – A pacemaker has a 2.4 Ah battery and delivers rectangular 1.5 V pulses lasting 1 ms once each second into electrode–heart resistance 150 Ω. Neglect…
- Question 63 – An 80 kVp X-ray system uses a 2.5 mm aluminium filter, replaced by copper for equal attenuation. Mass attenuation coefficients are 0.02015 m²/kg for…
- Question 64 – A radioisotope has activity 2 mCi, decay constant 3.22×10⁻⁵ s⁻¹ and atomic molar mass 98 g/mol. Avogadro constant is 6.02×10²³ mol⁻¹. Find isotope…
- Question 65 – A PZT crystal has thickness 1 mm and sound speed 4000 m/s. Its longitudinal ultrasound beam meets blood flow at 30°. Blood speed is 10 cm/s and tissue…