MA Mathematics - 2013 GATE Paper (Practice Test) - GATE MCQ

Friendship, no matter how _________it is, has its limitations

Select the pair that best expresses a relationship similar to that expressed in the pair: Medicine: Health

Q. 6 to Q. 10 carry two marks each.

Q. X and Y are two positive real numbers such that 2X + Y ≤ 6 and X + 2Y ≤ 8. For which of the following values of (X, Y) the function /(X, Y) = 3X + 6Y will give maximum value?

If |4X−7|=5 then the values of 2 |X|− |−X| is:

Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011.

In 2011, which of the following two categories have registered increase by same percentage?

A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level.

Abhishek is elder to Savar. Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements?

Q. 11 – Q. 35 carry one mark each.

Q. The possible set of eigen values of a 4 × 4 skew-symmetric orthogonal real matrix is

The coefficient of (z−π)² in the Taylor series expansion of 

 around π is

Consider R² with the usual topology. Which of the following statements are TRUE for all A,B ⊆ R²?

Let f:R →R be a continuous function with then  g′ (0) is equal to ______

(Important : you should answer only the numeric value)

Let P be a 2×2 complex matrix such that trace(P)=1 anddet(P)=−6. Then, trace(P⁴−P³) is ______

(Important : you should answer only the numeric value)

Suppose that R is a unique factorization domain and that a,b ∈ R are distinct irreducible elements. Which of the following statements is TRUE?

Let X be a compact Hausdorff topological space and let Y be a topological space. Let f:X→Y be a bijective continuous mapping. Which of the following is TRUE?

Consider the linear programming problem:

If S denotes the set of all solutions of the above problem, then

Which of the following groups has a proper subgroup that is NOT cyclic?

The value of the integral

 is _________________

(Important : you should answer only the numeric value)

Suppose the random variable u has uniform distribution on [0,1] and X=−2logu. The density of X is

Let f be an entire function on C such that |f(z)|≤100log|z|for each z with|z|≥2. If f(i)=2i, then f(1)

The number of group homomorphisms from Z₃ to Z₉ is ______

(Important : you should answer only the numeric value)

Let u(x,t) be the solution to the wave equation

Then, the value of u(1,1) is ______

(Important : you should answer only the numeric value)

Let 

Suppose X is a random variable with (0,1). For the hypothesis testing problem

consider the test “Reject H₀ if X ≤ A or if X ≥ B”, where A < B are given positive integers. The type-I error of this test is

Let G be a group of order 231. The number of elements of order 11 in G is ______

(Important : you should answer only the numeric value)

Let  The area of the image of the region  under the mapping f is

Which of the following is a field?

Let x₀=0. Define xn+1=cosxn for every n≥0. Then