Mathematics - (MA) 2018 GATE Paper (Practice Test) - GATE MCQ

 The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?  

The value of the expression  

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

 A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

An unbiased coin is tossed six times in a row and four different such trials are conducted.One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT

(2) TTHHHT

(3) HTTHHT

(4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

The principal value of (-1)(-^2i/π) is

Let  be an entire function with f (0) = 1, f (1) = 2 and f'(0) = 0. If there exists M > 0 such that

In the Laurent series expansion of valid for ; the coefficient of  is

Let X and Y be metric spaces, and let f : X → Y be a continuous map. For any subset S of X; which one of the following statements is true?

The general solution of the differential equation

is given by (with an arbitrary positive constant k)

Let p_n(x) be the polynomial solution of the differential equation 
with p_n(1) = 1 for n = 1; 2; 3; ....If

then n is  

In the permutation group S₆; the number of elements of order 8 is

Let R be a commutative ring with 1 (unity) which is not a field. Let I ⊂ R be a proper ideal such that every element of R not in I is invertible in R: Then the number of maximal ideals of R is

Let be a twice continuously differentiable function. The order of convergence of the secant method for finding root of the equation f (x) = 0 is

The Cauchy problem  when solved using its characteristic equations with an independent variable t; is found to admit of a solution in the form
 
Then f (s; t) =

An urn contains four balls, each ball having equal probability of being white or black. Three black balls are added to the urn. The probability that five balls in the urn are black is

For a linear programming problem, which one of the following statements is FALSE?

Let , where a, b, c, f are real numbers and f ≠ 0. The geometric multiplicity of the largest eigenvalue of A equals .

Consider the subspaces

of

Then the dimension of W₁ + W₂ equals .

Let V be the real vector space of all polynomials of degree less than or equal to 2 with real coefficients. Let T : V→V be the linear transformation given by

T (p) = 2p + p' for p ∈ V

where p' is the derivative of p. Then the number of nonzero entries in the Jordan canonical form of a matrix of T equals ____________.

Let I = [2, 3), J be the set of all rational numbers in the interval [4, 6], K be the Cantor (ternary) set, and let Then the Lebesgue measure of the set I ∪ J ∪ L equals .

Let Then the directional derivative of u in the direction at the point (5, 1, 0) is .

If the Laplace transform of y(t) is given by Y (s) = L(y(t)) =
then y(0) + y'(0) = .

The number of regular singular points of the differential equation in the interval is equal to .

Let F be a field with 7 ⁶ elements and let K be a subfield of F with 49 elements. Then the dimension of F as a vector space over K is .