MA Mathematics - 2014 GATE Paper (Practice Test) - GATE MCQ

If y = 5x² + 3, then the tangent at x = 0, y = 3

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,
where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily
production of 100 tonnes?

(Important : you should answer only the numeric value)

Q. 6 – Q. 10 carry two marks each.

Q.

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building
(the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered
floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors
below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor
immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the
following floor-person combinations is correct?

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The
ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its
smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the
largest angle of the quadrilateral?

(Important : you should answer only the numeric value)

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y
are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both
countries together, what is the percentage of people taller than 6 ft?

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure.
Which of the following are true? (k percentile is the value such that k percent of the data fall below
that value)

(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall

Q. 1 – Q. 25 carry one mark each.

Q.

The function  is differentiable at

The radius of convergence of the power series  is _____________

Let   E₁ and E₂ be two non empty subsets of a normed linear space X and let 

Then which of the following statements is FALSE:

Let y(x) be the solution to the initial value problem   subject to y(1.2) 2. Using the Euler method with the step size h = 0.05, the approximate value of ??(1.3), correct to two
decimal places, is _____________________

Let α ∈ R. If αx is the polynomial which interpolates the function f (x) = sinπ x on [−1,1]at all the zeroes of the polynomial 4x³ − 3x , then α is ___________

If u(x,t) is the D’Alembert’s solution to the wave equation  with
the condition u(x,0) = 0  is _________________

The solution to the integral equation  

The general solution to the ordinary differential equation  in
terms of Bessel’s functions, ??_v(x), is

The inverse Laplace transform of 

If  X₁ , X₂ is a random sample of size 2 from an N (0,1) population, then follows

 Let be a random variable. Then the value of E[max{Z,0}] is

The number of non-isomorphic groups of order 10 is ___________

Let a,b,c,d be real numbers with a < c < d < b. Consider the ring C[a,b] with pointwise
addition and multiplication. If  then

Let ?? be a ring. If R[x]is a principal ideal domain, then R is necessarily a

Consider the group homomorphism   given by φ ( A) = trace(A) . The kernel of φ
is isomorphic to which of the following groups?

Let X be a set with at least two elements. Let τ and τ′ be two topologies on X such that   Which of the following conditions is necessary for the identity function id : to be
continuous?

Let  be such that det(A− I ) = 0 , where I denotes the 3×3 identity matrix. If the
trace(A) =13 and det(A) = 32, then the sum of squares of the eigenvalues of A is ______

Let V denote the vector space . Then

Let V be a real inner product space of dimension 10 . Let x, y∈V be non-zero vectors such that
= 0 . Then the dimension of   is _________________

Consider the following linear programming problem:
Minimize x₁ + x₂
Subject to:
2x₁ + x₂ ≥ 8
2x₁ + 5x₂ ≥ 10
x₁, x₂ ≥ 0
The optimal value to this problem is _________________________