Question for GATE Engineering Mathematics - Quiz / Questions / MCQ in English

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Latest GATE Engineering Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : Engineering Mathematics

Question Bank GATE Engineering Mathematics Exam - English

Engineering Mathematics

Q 1 :

Consider the following expression :

where z, y, and t are variables, and   is a complex number. The partial differential equation derived from the above expression is

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Q 2 :

For the equation

the correct description is

1. A.
   an ordinary differential equation of order 3 and degree 2 
2. B.
   an ordinary differential equation of order 3 and degree 3 
3. C.
   an ordinary differential equation of order 2 and degree 3 
4. D.an ordinary differential equation of order 3 and degree â€‹

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Q 3 :

The value of (1 + i)¹², where â€‹ , is.

1. A.
   – 64 i 
2. B.
   64 i
3. C.64 
4. D.– 64

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Q 4 :

Given matrix , the ordered pair (x, y) for which is det (A) = 0 is.

1. A.(1, 1)
2. B.(1, 2) 
3. C.(2, 2)
4. D.(2, 1)

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Q 5 :

Let  where x is real. The value of â€‹ at x = –1 is

1. A.
   – e 
2. B.
   e
3. C.1/e 
4. D.– 1/e

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Q 6 :

The value of the real variable , which maximizes the function ​is.

1. A.
   e 
2. B.
   0
3. C.1/e
4. D.1

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Q 7 :

The partial differential equation

where, and  , is subjected to the following initial and boundary conditions:

u(x, 0) = 

u(0, t) = 0

u(1, t) = 0
The value of t at which is

1. A.1
2. B.e

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Q 8 :

Consider the polynomial on the domain S given by . The first and second derivatives are f'(x) and f"(x). Consider the following statements :
I. The given polynomial is zero at the boundary points x = 1 and x = 3.
II. There exists one local maxima of f(x) within the domain S.
III. The second derivative f"(x) > 0 throughout the domain S.
IV. There exists one local minima of f(x) within the domain S.
The correct option is :

1. A.
   Only statements I, II and III are correct
2. B.
   Only statements I, II and IV are correct
3. C.
   Only statements I and IV are correct
4. D.Only statements II and IV are correct

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Q 9 :

 is equal to

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Q 10 :

The function (x, y) satisfies the Laplace equation ​ on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0 . The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f(0, 0) is :

1. A.
   0
2. B.
   2
3. C.3 
4. D.1

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Q 11 :

Consider a 3 × 3 matrix A whose (i, j)^th element, a_{i, j} = (i – j)³. Then the matrix A will be

1. A.
   symmetric 
2. B.
   skew-symmetric
3. C.unitary
4. D.null

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Q 12 :

e^A denotes the exponential of a square matrix A. Suppose 𝞴 is an eigenvalue and v is the corresponding eigen-vector of matrix A.

Consider the following two statements :

Statement 1 : e^𝞴 is an eigenvalue of e^A.

Statement 2 : u is an eigen-vector of eA.

Which one of the following options is correct ?

1. A.
   Statement 1 is true and statement 2 is false
2. B.
   Statement 1 is false and statement 2 is true
3. C.
   Both the statements are correct
4. D.Both the statements are false

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Q 13 :

Let â€‹. Then f(x) decreases in the interval

1. A.
   x € (1, 3) 
2. B.
   x €(2, 3)
3. C.x €(0, 1) 
4. D.x €(0.5, 1)

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Q 14 :

Consider a matrix . 
The matrix A satisfies the equation 6A^–1 = A² + cA + d I, where c and d are scalars and I is the identity matrix.
​Then (c + d) is equal to

1. A.
   5 
2. B.
   17
3. C.– 6 
4. D.11

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Q 15 :

Let, f(x, y, z) = 4x² + 7xy + 3xz². The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

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Q 16 :

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R ?
​

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Q 17 :

Let The value of , where V is the volume enclosed by the unit cube defined by â€‹ and is.

1. A.
   3 
2. B.8
3. C.10 
4. D.5

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Q 18 :

Consider the following two statements with respect to the matrices A_m×n, B_n×m, C_n×n and D_n×n.
Statement 1 : tr(AB) = tr(BA)
Statement 2 : tr(CD) = tr(DC)
​where tr() represents the trace of a matrix. Which one of the following holds ?

1. A.
   Statement 1 is correct and Statement 2 is wrong
2. B.
   Statement 1 is wrong and Statement 2 is correct
3. C.Both Statement 1 and Statement 2 are correct
4. D.Both Statement 1 and Statement 2 are wrong

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Q 19 :

Consider solving the following system of simultaneous equations using LU decomposition.

where L and U are denoted
​
as Which one of the following is the correct combination of values for L32, U33, and x1 ?

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Q 20 :

Consider the two-dimensional vector field â€‹ , where  denote the unit vectors along the x-axis and the y-axis, respectively. A contour C in the xy-plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral is 
​

1. A.0
2. B.
   1
3. C.​
4. D.– 1

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Q 21 :

Consider a system of linear equations Ax = b, where

This system of equations admits________

1. A.a unique solution for x 
2. B.infinitely many solutions for x 
3. C.no solutions for x 
4. D.exactly two solutions for x

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Q 22 :

The function ​attains its minimum over the interval [1, e] at x = _____ (Here logex is the natural logarithm of x)

1. A.2
2. B.1
3. C.e

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Q 23 :

Let  be two non-zero real numbers and v₁, v₂ be two non-zero real vectors of size 3 × 1. Suppose that v₁ and v₂ satisfy , and  . Let A be the 3 × 3 matrix given by :  
The eigenvalues of A are

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Q 24 :

The Fourier series expansion of x³ in the interval ​with periodic continuation has 

1. A.only sine terms 
2. B.only cosine terms 
3. C.both sine and cosine terms 
4. D.only sine terms and a non-zero constant

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Q 25 :

If â€‹ is a symmetric matrix, the value of k is

1. A.8
2. B.5 
3. C.– 0.4

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