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Test: Engineering Mathematics - 1 - Electronics and Communication Engineering (ECE) MCQ


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15 Questions MCQ Test GATE ECE (Electronics) Mock Test Series 2026 - Test: Engineering Mathematics - 1

Test: Engineering Mathematics - 1 for Electronics and Communication Engineering (ECE) 2025 is part of GATE ECE (Electronics) Mock Test Series 2026 preparation. The Test: Engineering Mathematics - 1 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Engineering Mathematics - 1 MCQs are made for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Engineering Mathematics - 1 below.
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Test: Engineering Mathematics - 1 - Question 1

Detailed Solution for Test: Engineering Mathematics - 1 - Question 1

Test: Engineering Mathematics - 1 - Question 2

Test: Engineering Mathematics - 1 - Question 3

The order of differential equation 

Test: Engineering Mathematics - 1 - Question 4

The order of differential equation  

Test: Engineering Mathematics - 1 - Question 5

Find the rank of matrix 

Test: Engineering Mathematics - 1 - Question 6

The rank of Diag matrix  [− 1 0 1 0 0 4] is ________

Detailed Solution for Test: Engineering Mathematics - 1 - Question 6


Test: Engineering Mathematics - 1 - Question 7

  the third row of R-1 is 

Test: Engineering Mathematics - 1 - Question 8

For what value of k will the matrix given below become singular 

is ___________

Detailed Solution for Test: Engineering Mathematics - 1 - Question 8

Correct Answer :- B

Explanation:- If the matrix is singular, its determinant has to be zero.

[8(0-12) -4(4k-24) +0(24-0)] = 0

-96 -16k +96 = 0

-16k = 0

k = 0

 

 

Test: Engineering Mathematics - 1 - Question 9

The Eigen values of the matrix 

Test: Engineering Mathematics - 1 - Question 10

Test: Engineering Mathematics - 1 - Question 11

Test: Engineering Mathematics - 1 - Question 12

   then find 

Detailed Solution for Test: Engineering Mathematics - 1 - Question 12

Test: Engineering Mathematics - 1 - Question 13

 Given system of linear equations

3x + 2y + z = 0, x + 4y + z = 0, 2x + y + 4z = 0, has 

Detailed Solution for Test: Engineering Mathematics - 1 - Question 13

 

 

 

 

 

 


 

  • Given equations:

    • 3x + 2y + z = 0

    • x + 4y + z = 0

    • 2x + y + 4z = 0


    •  
  • These are homogeneous linear equations of form Ax = 0.
  • Such systems always have at least the trivial solution (x = 0, y = 0, z = 0).
  • To determine if there are more solutions, check the determinant of the coefficient matrix.
  • Coefficient matrix determinant is non-zero, indicating only the trivial solution.
  • Therefore, the correct answer is C: only trivial solution.
Test: Engineering Mathematics - 1 - Question 14

Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two events are independent. Then P(A|B) is:

Test: Engineering Mathematics - 1 - Question 15

The Newton-Raphson method formula for finding the square root of a real number R from the equation x2 − R = 0 is

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