GATE - Data Science and Artificial Intelligence (DA)

India · IITs and IISc on rotation (2026: IIT Guwahati) · pg

291practice questions written to this syllabus
18subjects

Format

Computer-based, 3 hours, 100 marks (15 General Aptitude + 85 subject). MCQ, MSQ and NAT; negative marking on MCQ only.

Sections

Over the years

Paper introduced in GATE 2024. Relevant to agricultural data-science MTech/PhD admission and to Computer Application candidates. Sections read from the 2026 syllabus.

Official source: https://gate2026.iitg.ac.in/doc/GATE2026_Syllabus/DA_2026_Syllabus.pdf

Subjects this exam draws on

Linear Algebra & Matrix Theory for Statistics12 questionsExploratory Data Analysis & Statistical Graphics54 questionsProgramming for Statistics & Data (R and Python)18 questionsComputer Science Fundamentals: Architecture, Data Structures, Networks & Operating Systems10 questionsProbability Theory4 questionsProbability Distributions & Sampling Distributions1 questionsStochastic Processes2 questionsStatistical Inference II: Testing of Hypotheses & Sequential Analysis3 questionsLinear Models & Regression Analysis10 questionsMultivariate Analysis7 questionsCategorical Data Analysis & Generalized Linear Models5 questionsBayesian Inference5 questionsBioassay, Survival & Epidemiological Statistics1 questionsOptimization Techniques for Statisticians3 questionsStatistical Computing: Simulation, Resampling & Algorithms20 questionsStatistical & Machine Learning for Agriculture104 questionsSpatial Statistics, Geostatistics & Remote Sensing for Agriculture10 questionsDatabases, Big Data & Agricultural Information Systems22 questions

Five practice questions, worked

Original questions written to this exam's published syllabus and pattern. Not past papers.

1. In regression, the vector of fitted values ŷ lies in:

  1. The null space of X
  2. The row space of y
  3. The column space of X
  4. The null space of X′
Answer and working

C. The column space of X

ŷ = Xβ̂ is a linear combination of the columns of X; residuals lie in the null space of X′.

Linear Algebra & Matrix Theory for Statistics · Vector spaces, subspaces, linear independence, basis and dimension

2. For which variable is the coefficient of variation a meaningful summary?

  1. Milk yield per cow in litres per day
  2. Air temperature in degrees Celsius
  3. Calendar date of sowing
  4. Soil series coded 1 to 6
Answer and working

A. Milk yield per cow in litres per day

The CV divides the SD by the mean, which is meaningful only on a ratio scale with a true zero. With Celsius or dates, moving the zero changes the CV arbitrarily; codes for soil series are nominal.

Exploratory Data Analysis & Statistical Graphics · Types of data and measurement scales

3. About how many comparisons does binary search need, at most, in a sorted list of one million items?

  1. 1,000
  2. 20
  3. 500,000
  4. 1,000,000
Answer and working

B. 20

Each step halves the range; 2²⁰ ≈ 1.05 million, so about 20 steps.

Programming for Statistics & Data (R and Python) · Algorithms, flowcharts and pseudocode

4. By De Morgan's law, (A + B)′ equals:

  1. A′B′
  2. A′ + B′
  3. AB
  4. A + B′
Answer and working

A. A′B′

The complement of an OR is the AND of the complements.

Computer Science Fundamentals: Architecture, Data Structures, Networks & Operating Systems · Number systems, Boolean algebra and logic circuits

5. Among all functions g, which choice minimises the mean squared prediction error E[Y − g(X)]²?

  1. g(X) = the conditional median of Y given X
  2. g(X) = E(Y), the unconditional mean of Y
  3. g(X) = the least-squares straight line in X
  4. g(X) = E(Y | X), the conditional mean of Y given X
Answer and working

D. g(X) = E(Y | X), the conditional mean of Y given X

E[Y − g(X)]² = E[Y − E(Y | X)]² + E[E(Y | X) − g(X)]², minimised by g = E(Y | X). The conditional median minimises mean absolute error; the best straight line is optimal only among linear predictors, and coincides with E(Y | X) when (X, Y) is bivariate normal.

Probability Theory · Joint, marginal and conditional distributions; conditional expectation

Practise it, and prove it

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