MA Mathematics - 2016 GATE Paper (Practice Test) - GATE MCQ

The number that least fits this set: (324, 441, 97 and 64) is ________.

Note: Question may have more than one correct answer)

It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.

Q. 6 – Q. 10 carry two marks each.

Q.

The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m)?

The overwhelming number of people infected with rabies in In dia has been flagged by the World  Health Organization as a source of concern. It is estimated that inoculating 70% of pets and stray  dogs against rabies can lead to a significant reduction in the number of people infected w ith rabies.

Which of the fo llowing can be logically inferred from the above sentences?

A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat?

Find the area bounded by the lines 3x+2 y=14, 2x-3y =5 in the first quadrant

A straight line is fit to a data set (ln x, y) . This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?

Q. 11 – Q. 35 carry one mark each.

Q.

Let {X,Y,Z} be a basis of . Consider the following statements P and Q:
(P) : {X+Y, Y+Z,X-Z} is a basis of .
(Q) : {X+Y+Z, X+2Y-Z, X-3Z} is a basis of .
Which of the above statements hold TRUE?

Consider the following statements P and Q:
(P) : If  M= then M is singular

(Q) : Let S be a diagonalizable matrix. If T is a matrix such that S + 5 T = Id, then T is
diagonalizable

Which of the above statements hold TRUE?

Consider the following statements P and Q:

(P) : If M is an n x n complex matrix, then  

(Q) : There exists a unitary matrix with an eigenvalue λ such that |λ| <1.

Which of the above statements hold TRUE?

Consider a real vector space V of dimension n and a non-zero linear transformation
T : V → V. If dimension(T(V)) < n and T² = λ T, for some then which of the following statements is TRUE?

Let  and  and   be a strictly increasing function such that f(S) is connected. Which of the following statements is TRUE?

Let a₁=1 and   then

 is equal to _____________________

Maximum   is equal to _________________

Let a,b,c such that c²+d² 0. Then, the Cauchy problem

has a unique solution if

Let u(x,t)  be the d'Alembert's solution of the initial value problem for the wave
equation

where c is a positive real number and f, g are smooth odd functions. Then, u(0,1) is
equal to ___________

Let the probability density function of a random variable X be

Then, the value of c is equal to ________________________

Let V be the set of all solutions of the equation y" +a y'+by=0 satisfying  y(0) =y(1), where a, b are positive real numbers. Then, dimension(V ) is equal to
_____________________

Let  where p(x) and q(x)are continuous functions. If   cos(x) are two linearly independent solutions of the above equation, then |4p(0)+2q(1)| is equal to ____________________

Let P_n(x) be the Legendre polynomial of degree n and   where k
is a non-negative integer. Consider the following statements P and Q:

(P) : I = 0 if k < n.
(Q) : I = 0 if n - k is an odd integer.
Which of the above statements hold TRUE?

Consider the following statements P and Q:

(P) :   has two linearly independent Frobenius series
solutions near x=0.

(Q) : has two linearly independent Frobenius series
solutions near x=0.

Which of the above statements hold TRUE?

Let the polynomial x⁴ be approximated by a polynomial of degree 2, which
interpolates x⁴ at x=-1, 0 and 1. Then, the maximum absolute interpolation error
over the interval [-1, 1] is equal to ______________________

Let  (z_n)be a sequence of distinct points in  with    

Consider the following statements P and Q:

(P) : There exists a unique analytic function f on D(0,1) such that f(z_n) = sin(z_n) for
all n.
(Q) : There exists an analytic function f on D(0,1) such that f(zn) = 0 if n is even
and f(z_n) = 1 if n is odd.

Which of the above statements hold TRUE?

Let be a topological space with the cofinite topology. Every infinite subset of
is

Let 

Then, dimension(C₀/M) is equal to _______________________

Which of the following statements is TRUE for the function f(x)  =x-x²/2 ?

Note: Question may have more than one correct answer)