MA Mathematics - 2012 GATE Paper (Practice Test) - GATE MCQ

One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the
following is INCORRECT?

I requested that he should be given the driving test today instead of tomorrow.

Which one of the following options is the closest in meaning to the word given below?
Latitude

Q. 6 - Q. 10 carry two marks each.

Q.

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number
of weighings required to identify the heavier bag is

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed
and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting,
even when the odds and conditions were against them.
Which one of the following statements best sums up the meaning of the above passage?

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a
condition that whoever arrives first will not wait for the other for more than 15 minutes. The
probability that they will meet on that day is

The data given in the following table summarizes the monthly budget of an average household.

The approximate percentage of the monthly budget NOT spent on savings is

Q. 11 – Q. 35 carry one mark each.

Q.

The straight lines  are mapped by the transformation
 w= z² into the curves C₁ , C₂ and C₃ respectively. The angle of intersection between the curves at
w =0 is

In a topological space, which of the following statements is NOT always true :

C onsider the following statements:
P: The family of subsets  satisfies the finite intersection property.
Q: On an infinite set X , a metric 

The metric space (X,d) is compact.
R: In a Frechet ( T₁ ) topological space, every finite set is closed.
S: If f : R→X is continuous, where R is given the usual topology and (X, ) is a Hausdorff
( T₂ ) space, then f is a one-one function.
Which of the above statements are correct?

L et H be a Hilbert space and  denote the orthogonal complement of a set  . Which of
the following is INCORRECT?

L et H be a complex Hilbert space, T :H →H be a bounded linear operator and let T * denote
the adjoint of T . Which of the following statements are always TRUE?

L et X = {a,b,c} and let  be a topology defined on X . Then which of
the following statements are TRUE?

C onsider the statements
P: If X is a normed linear space and is a subspace, then the closure  is also a subspace
of X.

Q: If X is a Banach space and  is an absolutely convergent series in X , then  is convergent.

R: Let  M₁ and M₂ be subspaces of an inner product space such that  Then

S: Let f :X →Y be a linear transformation from the Banach Space X into the Banach space Y .
If f is continuous, then the graph of f is always compact.
The correct statements amongst the above are:

A continuous random variable X has the probability density function

The probability density function of Y= 3X + 2 is

A simple random sample of size 10 from  gives 98% confidence interval (20.49, 23.51).
Then the null hypothesis H₀ : μ = 20.5 against H_A :μ  20.5

F or the linear programming problem

W hich one of the following statements is TRUE?

Let α =e^2πi/5  and the matrix

Then the trace of the matrix  I +M +M² is

L et V = C² be the vector space over the field of complex numbers and B={(1, i), (i,1)}be a given
ordered basis of V. Then for which of the following,   is a dual basis of B over C?

Let R = ZxZxZ and I = ZxZx{0}. Then which of the following statement is correct?

T he function u(r,θ) satisfying the Laplace equation

subject to the conditions  u(e,θ )=1, u(e² ,θ)=0

The functional

is path independent if k equals

If a transformation y = uv transforms the given differential equation

f (x)y"- 4 f '(x)y'+ g(x)y = 0 into the equation of the form v''+ h(x)v = 0, then

The expression  is equal to

The function φ (x) satisfying the integral equation

 is

Given the data:

If the derivative of y(x) is approximated as: hen the value
of y'(2) is