GATE Engineering - General Aptitude & Engineering Mathematics

Linear Algebra, Calculus, Differential Equations & Probability question bank (Engineering Mathematics)

Practice 40 free GATE Engineering - General Aptitude & Engineering Mathematics Engineering Mathematics - Linear Algebra, Calculus, Differential Equations & Probability questions with answers and step-by-step solutions.

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Q1.

Numerical Methods: In 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem', what is the local truncation error order of Simpson's $1/3$ rule for numerical integration with step size $h$?

(A)

$O(h^5)$ for local step, $O(h^4)$ global composite error (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

$O(h^2)$

(C)

$O(h^3)$

(D)

$O(h)$

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Q2.

General Aptitude (Spatial & Logical): A solid regular cube with edge length 3 cm is painted blue on all outer faces and cut into 27 identical $1\text{ cm}$ unit cubes in 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem'. How many unit cubes have EXACTLY TWO painted faces?

(A)

12 cubes (located along the 12 edges, excluding corners: $12 \times (3-2) = 12$) (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

8 cubes (corner cubes with 3 painted faces)

(C)

6 cubes (face center cubes with 1 painted face)

(D)

1 cube (unpainted internal core)

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