Mathematics Test

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Mathematics Test - 43

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Weekly Quiz Competition

Question 1
5 / -1

I₂ is the matrix

A

B

C

D

Solution

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context
Question 2
5 / -1

Let A be any m×n matrix, then A² can be found only when

A
m < n

B
m = n

C
m > n

D
none of these.

Solution

The product of any matrix with itself can be found only when it is a square matrix.i.e. m = n.
Question 3
5 / -1

A
-1

B
2

C
0

D
1

Solution

To find the determinant we have to cross mutliply the elements and then subtract it.

cos²θ - (-sin²θ) = 1
Question 4
5 / -1

A
an increasing function

B
neither increasing nor decreasing

C
a decreasing function

D
none of these

Solution
Question 5
5 / -1

Let f (x) = x⁴ – 4x, then

A
f is increasing in [−∞,1)

B
f is decreasing in [1,∞)

C
f is increasing in [1,∞)

D
none of these.

Solution
Question 6
5 / -1

The function f (x) = x³ has a

A
point of inflexion at = 0

B
local minima at x = 0

C
local maxima at x = 0

D
none of these

Solution

f ‘(0) = 0 , f ‘’ (0) = 0 and f ‘’’(0) = 6 . So, f has a point of inflexion at 0.
Question 7
5 / -1

A

B

C

D

Solution

By cross checking the options, we can find the answer.

Hence option 3 is the correct answer and we can check the other choices by the similar argument.
Question 8
5 / -1

A

B
d/dx (g(x)) = f(x)

C
g (x) + f (x) = constant.

D
g (x) = f (x)

Solution
Question 9
5 / -1

A
second order, third degree equation.

B
third order, second degree equation.

C
third order, third degree equation.

D
second order, second degree equation

Solution

To calculate the degree or the order of a differential equation, the powers of derivatives should be an integer.

On squaring both sides, we get a differential equation with the integral power of derivatives.

⇒ Order (the highest derivative) = 2

⇒ Degree (the power of highest degree) = 2
Question 10
5 / -1

A

B

C

D

Solution

y = Acos(αx) + Bsin(αx)

dy/dx = -Aαsin(αx) + Bαcos(αx)

d²y/dx² = -Aα²cos(αx) - Bα²sin(αx)

= -α²(Acos(αx) + Bsin(αx))

= -α² * y

d²y/dx² + α²*y = 0