GATE 2020 MA – Previous Year Questions with Solutions
All 65 questions of GATE 2020 MA with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world boxing champion, recently in a ceremony the Rashtrapati Bhawan in New Delhi.
- Question 2 – Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are .
- Question 3 – Complete the analogy: Cover : Uncover :: Associate : .
- Question 4 – Floods affected the summer-sown kharif crops. Officials believe this loss can be recovered through winter-sown rabi crops so the country can achieve…
- Question 5 – Find the difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers.
- Question 6 – Repo rate is the rate at which RBI lends to commercial banks; reverse repo is the rate at which RBI borrows from them. Which statement follows?
- Question 7 – P,Q,R,S,T,U,V,W sit around a circular table. S is opposite W; U is second to the right of R; T is third to the left of R; V neighbours S. Which must…
- Question 8 – Delhi and Agra are 233 km apart. P travels from Delhi to Agra; Q starts from Agra to Delhi one hour later. They meet 75 minutes after Q starts. Both…
- Question 9 – A 44 matrix M=[m ij] has all diagonal entries zero and satisfies m ij=-m ji. What is the minimum number of elements needed to specify it?
- Question 10 – The chart shows profit percentages of companies P and Q during 2013–2018. Both invest a fixed, equal amount every year. Find the ratio of P’s total…
- Question 11 – Topologies T 1, T 2 on X are induced by metrics d 1,d 2, with T 1 T 2. Which is true?
- Question 12 – On D=[-1,1]2, define f(x,y)=casesx2-y2(x2+y2)2,&(x,y)(0,0),\\0,&(x,y)=(0,0).cases Which is true?
- Question 13 – The IVP is y=y3/5, y(0) = b. It has
- Question 14 – Consider I: z is harmonic on C\0\. II: it has a harmonic conjugate on that entire domain.
- Question 15 – Let G= C\x+iy:x0,y=0\ and H= C\x+iy:x Z,x0,y=0\. Suppose f:G→C and g:H→C are analytic. I: f\,dz is independent of paths in G joining −i and i. II:…
- Question 16 – Let f(z)=e1/z on C\0\ and R n=\x+iy: x <1/n, y <1/n\\0\. Bars denote closure in C. Which relation is stated correctly?
- Question 17 – Let U= R2 Q2 and V= R2\(x,y):x>0,y=1/x\ with Euclidean metric. Then
- Question 18 – Let D1,D2 be duals of P1,P2. Both primal objectives are to minimize x 1-2x 2 with x 1,x 20. P1 has constraint -x 1+x 2=10. P2 additionally has x 1-x…
- Question 19 – For f(x,y)=5-(+)x2+ y2+(+1)y3+x3, suppose (4,0) and (0,−1/2) are critical points. Which holds?
- Question 20 – For x 0>0, define x n=x n-1/2+3/x n-1 for n ≥ 1. The sequence
- Question 21 – On C[0,1] with supremum norm, define Tf(x)= 0xe-yf(y)dy. Which statement is true?
- Question 22 – A real 55 matrix M has characteristic polynomial p(x) = det(xI − M). Which is true?
- Question 23 – Let f∈C[0,1] satisfy f(x)-f(y) M x-y for all x,y and some M > 0. Set f n(x)=f(x1+1/n) and S=\f n:n N\ in the supremum norm. Then
- Question 24 – The heat-equation IVP u t=u xx, u(x,0) = f(x), x∈R, t > 0, has solution u(x,t)= RK(x-y,t)f(y)dy for every bounded continuous f. Find RK(x,t)dx.
- Question 25 – Find the number of cyclic subgroups of the quaternion group Q 8= a,b a4=1,a2=b2,ba=a3b.
- Question 26 – Find the number of elements of order 3 in the symmetric group S₆.
- Question 27 – A field F has 4096 elements. Find its number of proper subfields.
- Question 28 – The primal minimizes x 1+2x 2 subject to 4x 1-x 28, 2x 1+x 210, -x 1+x 27, x 1,x 20. Let x* and λ* be optimal primal and dual solutions. Find x 1*+x…
- Question 29 – The quadrature rule -11f(x)dx af(-1)+bf(0)+cf(1) is exact for polynomials of degree at most 2. Find b, to two decimal places.
- Question 30 – For f(x) = x⁴, let p be its interpolating polynomial at nodes 1,2,3. Find p(0).
- Question 31 – For n ≥ 2, define x n=(2)-1 0/21/nt\,dt. Find its limit, to two decimal places.
- Question 32 – On real L2[0,10] with its usual norm, define T(f)= 02f(x)dx- 310f(x)dx. Find its operator norm.
- Question 33 – A balanced minimum-cost transportation problem has basic variables \x 13,x 22,x 23=10,x 31,x 32,x 34\. The cost rows for destinations D1,D2,D3,D4 are…
- Question 34 – In the ring Z₂₂₅, let x be the number of prime ideals and y the number of nontrivial units. Find x + y.
- Question 35 – Let u solve u tt-u xx=0 on R for t > 0, with u(x,0) = f(x), uₜ(x,0) = 0 and twice continuously differentiable f. If f(−2) = 4, f(0) = 0 and u(2,2) =…
- Question 36 – Let (e n) n1 be an orthonormal basis of a separable Hilbert space H and set f n=e n-e n+1/(n+1). Which is true?
- Question 37 – On a nonzero finite-dimensional complex vector space V, a linear T satisfies Range(T) = Nullspace(T). Which statement is FALSE?
- Question 38 – Let P∈Mₘ×ₙ(R). I: if XPY = 0 for every row X∈M₁×ₘ(R) and column Y∈Mₙ×₁(R), then P = 0. II: if m = n, P is symmetric and P² = 0, then P = 0.
- Question 39 – For n∈N define bounded operators Tₙ,T from ℓ¹ to ℓ∞ by T n(x 1,x 2,)=(x 1,,x n,x n,x n,) and T(x)=x. Which is true?
- Question 40 – Equip the power set P(R) with d(U,V)= x R U(x)- V(x) . The set \\m\:m Z\ is
- Question 41 – Let f(x)= n=02-n (n,n+1](x) on R, and define S =\x:f(x)>\. Which is true?
- Question 42 – On (0,1), define f n(x)=xn and g n(x)=xn(1-x). Then
- Question 43 – Let u solve u′ + xu = 0 and suppose φ = uβ solves +2x+(x2+2)=0, with φ(0) = 1 and φ′(0) = 0. Find φ(x).
- Question 44 – For n∈N∪0, let yₙ satisfy xy n+(1-x)y n+ny n=0 and yₙ(0) = 1. Which weight w gives 0 y p(x)y q(x)w(x)dx=0 for p ≠ q?
- Question 45 – With Euclidean induced metrics, let X=\(0,0)\\(x,(1/x)):x0\ and Y=\(0,0)\\(x,x(1/x)):x0\. Let Bₓ,Bᵧ be their open unit balls about the origin. I: the…
- Question 46 – Let f:C\0→C satisfy f(z)=f(z/ z ) and have a continuous restriction to the unit circle. Then
- Question 47 – For a subset S of a topological space, let Int(S) and S denote interior and closure. Which is true?
- Question 48 – Let T 1, T 2, T 3 be the smallest topologies on R containing, respectively, S 1=\(a,a+/n):a Q,n N\, S 2=\(a,b):a,b Q,a<b\ and S 3=\(a,b):a,b R,a<b\.…
- Question 49 – Let M=pmatrix&3&0\\&3&1\\0&1&2pmatrix. I: there is a real lower-triangular L with M = LLᵀ. II: Gauss–Seidel iteration for Mx = b converges for every…
- Question 50 – In R= Z[10]=\a+b10:a,b Z\, let I and J be ideals generated by \5,10\ and \4,10\ respectively. Which statement holds?
- Question 51 – Let W₁,W₂,W₃ be subspaces of a finite-dimensional real vector space V. Which statement is TRUE?
- Question 52 – For α ≠ 0, the nonnegative system x 1-2x 2+ x 3=8, x 1-x 2+x 4=, x 1,x 2,x 3,x 40, has NO basic feasible solution if
- Question 53 – Let 0 < p < 1 and let X=\f: R R:f continuous, R f p<\. Define f p=( f p)1/p. Which holds?
- Question 54 – Let φ₁,φ₂ be independent solutions of 2x2y-(x+x2)y+(x2-2)y=0, with φ₁(0) = 0. Find the smallest positive integer n for which x0xn 2(x)/ 1(x)=0.
- Question 55 – Let f(z)= n=117(z-/n) and (t)=e2it for 0 ≤ t ≤ 2π. If f(z)/f(z)\,dz= i, find α.
- Question 56 – For (t)=12e3 it, 0 ≤ t ≤ 2, suppose [z2(ez-1)]-1dz= i. Find β, to one decimal place.
- Question 57 – Let K= Q(3+22,), where ω is a primitive cube root of unity. Find [K:Q].
- Question 58 – For α∈R, (3,0,0,β) is optimal for minimizing x 1+x 2+x 3- x 4, subject to 2x 1-x 2+x 3=6, -x 1+x 2+x 4=3, all variables nonnegative. Find the maximum…
- Question 59 – A linear map T:R⁴→R[x] satisfies T(-1,1,1,1)=x2+2x4, T(1,2,3,4)=1-x2 and T(2,-1,-1,0)=x3-x4. Find the coefficient of x⁴ in T(−3,5,6,6).
- Question 60 – Let F=(2x-2y x) i+(2y-y2 x) j+4z k. S is the closed surface of the tetrahedron bounded by x = 0,y = 0,z = 0,x+y+z = 1, with outward normal. Find S F…
- Question 61 – Let F=(x+2y)ez i+(yez+x2) j+y2z k. S is x2+y2+z=1, z ≥ 0, with either unit normal. If S( F) n\,dS =, find α.
- Question 62 – G is a noncyclic group of order 57. Find its number of elements of order 3.
- Question 63 – For F(x)= 1x[ t/(t-1)]dt, 0 < x < 2, find the coefficient of (x−1)⁵ in its Taylor expansion about x = 1, to two decimal places.
- Question 64 – Let u solve u x+ u\,u y=0 with u(x,0) = 1 + x². Find u(0,1), to three decimal places.
- Question 65 – Evaluate n 01nxnex\,dx, to three decimal places.