Skip to content
GATETECH

GATE EC Engineering Mathematics questions

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

Subject, topic, year and type filter the full library. Match any choice within a filter, and all selected filter categories. Search, source and sort apply to this page.

20 on this page
Official PYQ2014Engineering MathematicsLinear AlgebraMCQ · 1 mark
For matrices of same dimension M,NM, N and scalar cc, which one of these properties DOES NOT ALWAYS hold?
Official PYQ2014Engineering MathematicsProbability and StatisticsNAT · 1 mark
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
Official PYQ2014Engineering MathematicsComplex AnalysisMCQ · 1 mark
CC is a closed path in the zz-plane given by ∣z∣=3.\mid z \mid = 3. The value of the integral ∮C(z2−z+4jz+2j)dz\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz is
Official PYQ2014Engineering MathematicsLinear AlgebraNAT · 1 mark
A real (4×4)(4 \times 4) matrix AA satisfies the equation A2=IA^{2} = I, where II is the (4×4)(4 \times 4) identity matrix. The positive eigen value of AA is ______.
Official PYQ2014Engineering MathematicsProbability and StatisticsNAT · 1 mark
Let X1,X2,X_{1},X_{2}, and X3X_{3} be independent and identically distributed random variables with the uniform distribution on [0,1].[0,1]. The probability P{X1 is the largest}P\{X_{1}\: \text{is the largest}\} is ________.
Official PYQ2014Engineering MathematicsCalculusMCQ · 2 marks
The Taylor series expansion of 3sin⁡x+2cos⁡x3\sin x + 2 \cos x is
Official PYQ2014Engineering MathematicsCalculusMCQ · 2 marks
For a function g(t),g(t), it is given that ∫−∞+∞g(t)e−jωt dt=ωe−2ω2\int_{- \infty}^{ + \infty} g(t)e^{-j\omega t}\:dt = \omega e^{-2\omega^{2}} for any real value ω.\omega. If y(t)=∫−∞t g(τ) dτ,y(t) = \int_{- \infty}^{t}\:g(\tau)\:d\tau, then ∫−∞+∞y(t)dt\int_{- \infty}^{ + \infty}y(t)dt is
Official PYQ2014Engineering MathematicsCalculusNAT · 2 marks
The volume under the surface z(x,y)=x+yz(x,y) = x + y and above the triangle in the x–yx – y plane defined by {0≤y≤x and 0≤x≤12}\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\} is _______.
Official PYQ2014Engineering MathematicsLinear AlgebraNAT · 2 marks
Consider the matrix J6=[000001000010000100001000010000100000]J_{6} = \begin{bmatrix} 0&0 &0 &0 &0 &1 \\ 0& 0& 0& 0& 1&0 \\ 0& 0& 0& 1& 0&0 \\ 0&0 & 1& 0&0 &0 \\0 &1 &0 &0 &0 &0 \\1 &0 &0 &0 & 0& 0\end{bmatrix} which is obtained by reversing the order of the columns of the …
Official PYQ2014Engineering MathematicsComplex AnalysisMCQ · 2 marks
Let x[n]=(–19)nu(n) –(–13)nu(−n−1).x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1). The Region of Convergence (ROC) of the zz-transform of x[n]x[n]
Official PYQ2014Engineering MathematicsDifferential EquationsMCQ · 2 marks
A system is described by the following differential equation, where u(t)u(t) is the input to the system and y(t)y(t) is the output of the system. y(t)+5y(t)=u(t)y(t) + 5y(t) = u(t) When y(0)=1y(0) = 1 and u(t)u(t) is a unit step function, y(t)y(t) is
Official PYQ2014Engineering MathematicsLinear AlgebraMCQ · 2 marks
Consider the state space model of a system, as given below …
Official PYQ2014Engineering MathematicsDifferential EquationsMCQ · 2 marks
For the following feedback system G(s)=1(s+1)(s+2).G(s) = \dfrac{1}{(s+1)(s+2)}. The 2%2\%-settling time of the step response is required to be less than 22 seconds. Which one of the following compensators C(s)C(s) achieves this?
Official PYQ2014Engineering MathematicsProbability and StatisticsMCQ · 2 marks
Let XX be a real-valued random variable with E[X]E[X] and E[X2]E[X^{2}] denoting the mean values of XX and X2,X^{2}, respectively. The relation which always holds true is
Official PYQ2014Engineering MathematicsProbability and StatisticsMCQ · 2 marks
Consider a random process X(t)=2sin⁡(2πt+φ),X(t) = \sqrt{2}\sin(2\pi t + \varphi), where the random phase φ\varphi is uniformly distributed in the interval [0,2π].[0,2\pi]. The auto-correlation E[X(t1)X(t2)]E[X(t_{1})X(t_{2})] is
Official PYQ2014Engineering MathematicsVector AnalysisNAT · 2 marks
In spherical coordinates, let aθ^,aϕ^\hat{a_{\theta}},\hat{a_{\phi}} denote unit vectors along the θ,ϕ\theta,\phi directions. E=100rsin⁡θcos⁡(ωt–βr)aθ^ V/m\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t – \beta r)\hat{a_{\theta}}\: V/m and H=0.265rsin⁡θcos⁡(ωt–βr)aϕ^ A/m\textbf{H} = \dfrac{0.265}{r}\sin\theta \cos (\omega t – \beta r)\hat{a_{\phi}} \:A/m represent the electric and magnetic field components …
Official PYQ2014Engineering MathematicsLinear AlgebraNAT · 1 mark
The determinant of matrix AA is 55 and the determinant of matrix B is 4040. The determinant of matrix ABAB is ________
Official PYQ2014Engineering MathematicsProbability and StatisticsNAT · 1 mark
Let XX be a random variable which is uniformly chosen from the set of positive odd numbers less than 100100. The expectation, E[X]E[X], is ________.
Official PYQ2014Engineering MathematicsCalculusMCQ · 1 mark
For 0≤t<∞,0 \leq t < \infty , the maximum value of the function f(t)=e−t−2e−2tf(t)= e^{-t}-2e^{-2t} occurs at
Official PYQ2014Engineering MathematicsCalculusMCQ · 1 mark
The value of lim⁡x→∞(1+1x)x\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x} is