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GATE CS Engineering Mathematics questions

Practise Engineering Mathematics questions for GATE CS. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

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Official PYQ1995Engineering MathematicsSets, Relations and FunctionsNAT · 1 mark
Determine the number of divisors of 600.600.
Official PYQ1995Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
If the proposition ¬p→q\lnot p \to q is true, then the truth value of the proposition ¬p∨(p→q)\lnot p \lor \left ( p \to q \right ), where ¬\lnot is negation, ∨\lor is inclusive OR and →\to is implication, is
Official PYQ1995Engineering MathematicsCalculus: Limits, Continuity, DifferentiabilityMCQ · 1 mark
The solution of differential equation y′′+3y′+2y=0y''+3y'+2y=0 is of the form
Official PYQ1995Engineering MathematicsMonoids and GroupsMCQ · 1 mark
Let AA be the set of all non-singular matrices over real number and let ∗* be the matrix multiplication operation. Then
Official PYQ1995Engineering MathematicsProbability: Random Variables and DistributionsMCQ · 1 mark
A bag contains 1010 white balls and 1515 black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is:
Official PYQ1995Engineering MathematicsLinear Algebra: Matrices, Determinants, System of Linear EquationsMCQ · 1 mark
A unit vector perpendicular to both the vectors a=2i−3j+ka=2i-3j+k and b=i+j−2kb=i+j-2k is:
Official PYQ1995Engineering MathematicsCalculus: Limits, Continuity, DifferentiabilityMCQ · 1 mark
If the cube roots of unity are 1,ω1, \omega and ω2\omega^2, then the roots of the following equation are (x−1)3+8=0(x-1)^3 +8 =0
Official PYQ1995Engineering MathematicsGraphs: Connectivity, Matching, ColouringMCQ · 1 mark
The minimum number of edges in a connected cyclic graph on nn vertices is:
Official PYQ1995Engineering MathematicsLinear Algebra: Matrices, Determinants, System of Linear EquationsMCQ · 1 mark
The rank of the following (n+1)×(n+1)(n+1) \times (n+1) matrix, where aa is a real number is …
Official PYQ1995Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
In the interval [0,π][0, \pi] the equation x=cos⁡xx=\cos x has
Official PYQ1995Engineering MathematicsSets, Relations and FunctionsMCQ · 1 mark
The number of elements in the power set P(S)P(S) of the set S={{∅},1,{2,3}}S=\{\{\emptyset\}, 1, \{2, 3\}\} is:
Official PYQ1995Engineering MathematicsSets, Relations and FunctionsMCQ · 1 mark
Let RR be a symmetric and transitive relation on a set AA. Then
Official PYQ1995Engineering MathematicsProbability: Random Variables and DistributionsMCQ · 1 mark
The probability that a number selected at random between 100100 and 999999 (both inclusive) will not contain the digit 77 is:
Official PYQ1994Engineering MathematicsPropositional and First Order LogicNAT · 1 mark
Let pp and qq be propositions. Using only the Truth Table, decide whether p⟺qp \Longleftrightarrow q does not imply p→¬qp \to \lnot q is True or False.
Official PYQ1994Engineering MathematicsSets, Relations and FunctionsNAT · 1 mark
Every subset of a countable set is countable. State whether the above statement is true or false with reason.
Official PYQ1994Engineering MathematicsPartial Orders and LatticesNAT · 1 mark
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
Official PYQ1994Engineering MathematicsProbability: Random Variables and DistributionsNAT · 1 mark
Let A,B,A, B, and CC be independent events which occur with probabilities 0.8,0.5,0.8, 0.5, and 0.30.3 respectively. The probability of occurrence of at least one of the event is _______
Official PYQ1994Engineering MathematicsCombinatorics: Counting, Recurrence Relations, Generating FunctionsMCQ · 1 mark
The number of substrings (of all lengths inclusive) that can be formed from a character string of length nn is
Official PYQ1994Engineering MathematicsMonoids and GroupsMCQ · 1 mark
Some group (G,o)(G, o) is known to be abelian. Then, which one of the following is true for GG?
Official PYQ1994Engineering MathematicsLinear Algebra: Matrices, Determinants, System of Linear EquationsMCQ · 1 mark
The rank of matrix [00−3935311]\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix} is: