GATE 2023 BM – Previous Year Questions with Solutions
All 65 questions of GATE 2023 BM with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Choose the word that completes: “I cannot support this proposal. My will not permit it.”
- Question 2 – Complete the analogy by word meaning: Courts : :: Parliament : Legislature.
- Question 3 – What is the smallest number with distinct digits whose digits add up to 45?
- Question 4 – In a class of 100 students, 30 like neither romantic movies nor comedy movies. The number who like romantic movies is twice the number who like comedy…
- Question 5 – How many rectangles are present in the given figure?
- Question 6 – Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals, all of whom are ferocious. There…
- Question 7 – Which function represents the given graph?
- Question 8 – “When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and…
- Question 9 – There are 1000 people, of whom 100 have a disease. In pooled testing, samples are divided into groups of five. Each group is tested once; if it is…
- Question 10 – A rectangular sheet of paper is 100 cm × 32 cm. It is folded five times so that the long edge is brought onto its opposite edge, producing a 100 cm ×…
- Question 11 – Find the difference between the mean and median of the dataset 1, 2, 3, 4, 6, 8.
- Question 12 – For a binomial random variable X, which proposed pair of expectation E(X) and variance Var(X) cannot be true?
- Question 13 – For Q=pmatrix1&-2\\2&1pmatrix, which statement is true?
- Question 14 – For A=pmatrix1&1&0\\1&-1&0\\1&-1&1pmatrix, which vector is an eigenvector corresponding to eigenvalue 1?
- Question 15 – For f(x,y)=ex y, evaluate 2 f/( x y) at x=0,y=/2.
- Question 16 – For the shown series circuit with R=1 kΩ, C=100 μF and source 100cos(ω₀t) V, at which angular frequency ω₀ in rad/s is the capacitor-voltage amplitude…
- Question 17 – A two-tap FIR filter has impulse response h[0]=h[1]=1 and all other samples zero. What is the magnitude of its DTFT for ω ≤π?
- Question 18 – An 8-bit successive-approximation ADC uses a 1 MHz clock. Starting and ending each conversion take one clock cycle each, in addition to the comparison…
- Question 19 – In the shown ideal-op-amp circuit, the parallel-plate capacitance is C= A/x, where ε is dielectric permittivity, A is plate area and x=x 0+kt is plate…
- Question 20 – Korotkoff sounds are used in which measurement technique?
- Question 21 – Which describes the oxygenation of blood in the pulmonary artery and pulmonary vein, respectively, in normal postnatal circulation?
- Question 22 – Which bridge is NOT used for inductance measurement?
- Question 23 – A polychromatic X-ray beam has the energy spectrum in Figure P. Which option depicts the energy spectrum after passing through a human body? In every…
- Question 24 – Which dimensions represent dynamic viscosity, using M for mass, L for length and T for time?
- Question 25 – Which sequence lists the materials in decreasing tensile strength?
- Question 26 – A causal discrete-time system obeys y[n]=0.5y[n−1]+x[n]. With initial rest, which statements are correct?
- Question 27 – Which of the following are absent from normal blood serum?
- Question 28 – Q, R and S are Boolean variables and ⊕ denotes XOR. Select the correct statements.
- Question 29 – In the human pancreas, which cell types secrete insulin and glucagon, respectively?
- Question 30 – In the shown circuit, switch S is open for t<0 and closes at t=0. Find the steady-state capacitor voltage in volts after closing, rounded to one…
- Question 31 – A tissue has Young’s modulus 3.6 kPa and Poisson’s ratio 0.2. Find its shear modulus in kPa, rounded to one decimal place.
- Question 32 – In the shown series RC circuit, the resistor- and capacitor-voltage amplitudes are equal. With R=1 kΩ, C=100 μF and source 100cos(ω₀t) V, find ω₀ in…
- Question 33 – A band-limited continuous signal has X(f)=1- f /200 for f 200 Hz and zero otherwise. It is uniformly impulse-sampled at 600 Hz, giving spectrum Xₛ(f).…
- Question 34 – At a given time, a cardiac dipole of magnitude 3 mV is oriented at −45° to the horizontal axis. Assuming Einthoven frontal-plane configuration, find…
- Question 35 – A 5 MHz ultrasound transducer measures blood velocity using an echo frequency shift of 200 Hz. The beam makes 45° with blood flow, and sound speed is…
- Question 36 – A bacterial population satisfies dx/dt=x(1-x/200) with x(0)=100. What population is approached as t tends to infinity?
- Question 37 – A 20 mV DC signal is superimposed with 10 mV RMS Gaussian noise whose spectrum is flat up to 5 kHz. An integrating voltmeter measures the DC signal.…
- Question 38 – In the shown circuit, the DC sources have voltages V₁ and V₂. To which expression is the power dissipated in the 60 kΩ resistor proportional?
- Question 39 – The bilateral Laplace transforms of x₁(t)=e⁻ᵗu(t) and x₂(t)=eᵗu(−t) are X₁(s) and X₂(s), respectively. Which statement is true?
- Question 40 – A parallel X-ray beam traverses a uniform circular disc of radius R and linear attenuation coefficient 1 unit⁻¹. A ray is offset by distance t from…
- Question 41 – In MRI, s(t)= m(x,y)e-j2[K x(t)x+K y(t)y]dx\,dy, where Kₓ and Kᵧ are proportional to time integrals of gradients Gₓ and Gᵧ. The gradients are in phase…
- Question 42 – For the shown series RLC circuit, R=10 kΩ, L=10 mH and C=1 μF. The resistor-voltage amplitude equals the source-voltage amplitude. Find ω₀ in rad/s.…
- Question 43 – In a biomaterial, formation of hydrogen bonds involving alcoholic groups leads to which infrared spectral change?
- Question 44 – In the shown circuit the sinusoidal input is 2.5 V peak to peak. Both capacitors are 20 μF, diode knee voltage is zero, and Rₗ is almost infinite.…
- Question 45 – An ultrasonic wave of incident pressure amplitude P₀ strikes a boundary normally from acoustic impedance Z₁ toward Z₂. What is the total pressure…
- Question 46 – In the shown 10 V circuit, what load resistance R gives maximum power dissipation in R?
- Question 47 – Sequences x₁[n] and x₂[n] have samples [1,2,1] and [1,1,2] respectively for n=0,1,2 and are zero elsewhere. Let x=x₁*x₂. Which statements are correct?
- Question 48 – For f(z)=1/(z−1), which counterclockwise circular contours yield contour integral 2πj?
- Question 49 – Let x(t)=1 for 0≤t≤1 and zero otherwise, and y(t)=x*x. Which statements are correct?
- Question 50 – Which relations between lung-volume measurements are correct?
- Question 51 – For the shown ideal-op-amp circuit, which properties are true? The inverting terminal is grounded and the output is fed directly to the non-inverting…
- Question 52 – By which mechanisms can a water-insoluble polymeric biomaterial become water-soluble in vivo?
- Question 53 – For f(x)=x⁴−x² on the real line, which statements are correct?
- Question 54 – A system initially at rest satisfies 0.01y(t)+0.2y(t)+y(t)=6x(t), with t in seconds. A unit step is applied at t=0. Find y(1) to two decimal places.
- Question 55 – A thermistor has resistance 1 kΩ at 25°C and 500 Ω at 50°C. Find its temperature coefficient of resistance at 35°C, in °C⁻¹ to three decimals.
- Question 56 – A normally incident X-ray of energy 140 keV passes through the tissue phantom shown. Tissue P has attenuation coefficient 1 cm⁻¹ and thickness 1 cm;…
- Question 57 – A two-dimensional square plate of side 20 mm contains a homogeneous circular inclusion of diameter 5 mm. A parallel X-ray beam of width 30 mm is used…
- Question 58 – Expand sin z as a Taylor series about z=0. What is the reciprocal of the coefficient of z³?
- Question 59 – In a 24-hour cell-viability assay with 10000 cells and absorbance measured at 570 nm, control absorbance is 0.8, treated absorbance 0.5 and blank…
- Question 60 – Inspired air contains 20% oxygen and expired air 16%. A person breathes 12 times per minute with tidal volume 500 mL and cardiac output 5 L/min. Find…
- Question 61 – For a membrane at 27°C, use the Goldman–Hodgkin–Katz equation to find the magnitude of membrane potential in mV to one decimal. Ion concentrations…
- Question 62 – A metallic strain gauge has resistance 200 Ω, Young’s modulus 80 GPa and Poisson’s ratio 0.42. It experiences longitudinal strain 50×10⁻⁶. Neglect…
- Question 63 – A total hip-joint prosthesis has L₁=40 mm, L₂=60 mm, θ₁=45° and θ₂=90°, as shown. While the subject stands symmetrically on both feet, a joint…
- Question 64 – A diaphragm full-Wheatstone-bridge strain transducer has R₁,R₄ in compression and R₂,R₃ in tension. Every resistor is 200 Ω unloaded and changes by 20…
- Question 65 – A stone is thrown from height 2 m above the ground at 30° to the horizontal. It lands 6 m horizontally from its release point. Neglect air resistance…