Mathematics In Physics Test

Result

Mathematics In Physics Test - 3

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Weekly Quiz Competition

Question 1
4 / -1

The particular integral of (4D² + 4D + 1) y = 8e^-x/2 is

A
x²e^-x/2

B
x²/ 2

C
e^-x/2

D
x³e^-x/2

Solution
Question 2
4 / -1

The vector [1, 2, 3], [1, 0, 0], [0, 1, 0], [0, 0, 1] are

A
linearly dependent

B
linearly independent

C
orthogonal

D
none of these

Solution

Let a = [1, 2, 3], b = [1, 0, 0], c = [0, 1, 0]
d = [0, 0, 1]
a = b + 2c + 3d
Therefore, vector a, b, c, d are linearly dependent.
Question 3
4 / -1

Find

A

B
1/S

C

D

Solution
Question 4
4 / -1

The projection of vector on vector

A
5/8

B
8/3

C
8/7

D
8/9

Solution

Projection of vactor
Question 5
4 / -1

Find a_n of a Fourier series for |x|, -π < x < π

A

B
0

C

D

Solution
Question 6
4 / -1

Consider a vector v = (v₁, v₂, v₃) in three dimensional complex vector space c³. A linear operator T is designed as follows
T( v₁, v_2, v₃) = ( v_1, v₂ - v_3,iv₂)
Find T⁺matrix representation using orthonormal basis

A

B

C

D

Solution
Question 7
4 / -1

Given the Legendre polynomial P₀(x) = 1, P₁(x) = x and then polynomial (3x² + x -1)

A
P₂(x) - P₁(x)

B
2P₂(x) +P₁(x)

C
P₂(x) +P₁(x)

D
2P₂(x) +P₁(x)+P₀(x)

Solution

Polynomial, 3x² + x - 1
Question 8
4 / -1

The matrix A defined by is orthogonal if

A
a = 1, b = -1

B

C

D
a = 1, b = 1

Solution

A square matrix A is said to be orthogonal if AA^T = A^TA = 1

for orthogonal a² + b² = 1
Therefore,
Question 9
4 / -1

Find the inverse Laplace transform of f(s) =

A
1 - x + sinx + cos x

B
1 + x - cosx - sin x

C
x + sinx - cos x

D
1 + x - 2cosx - sin x

Solution
Question 10
4 / -1

Find the complex coefficient Cn of the fourier series of the function for n is odd.

A
C_n = 0

B
C_n = 1/nπ

C
C_n = 1/inπ

D
C_n = 1/in

Solution

C_n = 1/ inπ
Question 11
4 / -1

The equation of the plane that is tangent to the surface xyz = 8 at point (1,2,4) is

A
x + 2y + 4z = 12

B
4x + 2y + z = 12

C
x + 4y + 2z = 12

D
x + y + z = 7

Solution

Suppose T(x,y,z) be any point on tangent plane is normal to surface at point P(1,2,4). Therefore, is perpendicular to vector lying in the tangent plane of the given surface.