Mathematics Majorship Practice Questions — Set 1

Question 1

Find the derivative of f(x) = e^(3x) sin(x) with respect to x.

Accepted Answer

e^(3x)(3sin x + cos x)

Answer

e^(3x)(sin x + 3cos x)

Answer

3e^(3x) cos x

Answer

3e^(3x)(sin x + cos x)

Question 2

What is the value of the limit lim x → 0 (sin x)/(x)?

Accepted Answer

1

Answer

0

Answer

Undefined

Answer

Infinity

Question 3

Evaluate the definite integral: int0^2 (3x^2 - 4x + 1) dx.

Accepted Answer

2

Answer

4

Answer

6

Answer

0

Question 4

If matrix A is a 2 × 2 matrix with det(A) = 5, what is det(3A)?

Accepted Answer

45

Answer

15

Answer

25

Answer

75

Question 5

What is the sum of the infinite geometric series: 1 + (1)/(3) + (1)/(9) + ...?

Accepted Answer

3/2

Answer

2

Answer

Infinite

Answer

4/3

Question 6

Find the value of i^2026, where i = sqrt(-1).

Accepted Answer

-1

Answer

i

Answer

-i

Answer

1

Question 7

What is the period of the function f(x) = 3sin(4x + π)?

Accepted Answer

π/2

Answer

π/4

Answer

π

Answer

2π

Question 8

In how many ways can 5 people be seated in a round table?

Accepted Answer

24

Answer

120

Answer

720

Answer

60

Question 9

Which of the following is the equation of a circle with center (2, -3) and radius 5?

Accepted Answer

(x-2)^2 + (y+3)^2 = 25

Answer

(x-2)^2 + (y+3)^2 = 5

Answer

(x+2)^2 + (y-3)^2 = 25

Answer

(x-2)^2 - (y+3)^2 = 25

Question 10

If f(x) = 3x - 5, find the inverse function f^-1(x).

Accepted Answer

(x+5)/3

Answer

(x-5)/3

Answer

3x+5

Answer

1/(3x-5)

Mathematics Majorship Practice Questions — Set 1

Find the derivative of $f (x) = e^{3 x} sin (x)$ with respect to x.

What is the value of the limit lim x → $\frac{0 ( s i n x )}{x}$ ?

Evaluate the definite integral: int $0^{2} (3 x^{2} - 4 x + 1) d x$ .

If matrix A is a $2 \times 2$ matrix with det $(A) = 5$ , what is det(3A)?

What is the sum of the infinite geometric series: $1 + \frac{1}{3} + \frac{1}{9}$ + ...?

Find the value of $i^{2026}$ , where $i = - 1$ .

What is the period of the function $f (x) = 3 sin (4 x + π)$ ?

In how many ways can 5 people be seated in a round table?

Which of the following is the equation of a circle with center (2, -3) and radius 5?

If $f (x) = 3 x - 5$ , find the inverse function $f^{- 1} (x)$ .

Mathematics Majorship Practice Questions — Set 1

Find the derivative of f(x)=e3xsin(x) with respect to x.

What is the value of the limit lim x → x0(sinx)​?

Evaluate the definite integral: int02(3x2−4x+1)dx.

If matrix A is a 2×2 matrix with det(A)=5, what is det(3A)?

What is the sum of the infinite geometric series: 1+31​+91​ + ...?

Find the value of i2026, where i=−1​.

What is the period of the function f(x)=3sin(4x+π)?

In how many ways can 5 people be seated in a round table?

Which of the following is the equation of a circle with center (2, -3) and radius 5?

If f(x)=3x−5, find the inverse function f−1(x).

Find the derivative of $f (x) = e^{3 x} sin (x)$ with respect to x.

What is the value of the limit lim x → $\frac{0 ( s i n x )}{x}$ ?

Evaluate the definite integral: int $0^{2} (3 x^{2} - 4 x + 1) d x$ .

If matrix A is a $2 \times 2$ matrix with det $(A) = 5$ , what is det(3A)?

What is the sum of the infinite geometric series: $1 + \frac{1}{3} + \frac{1}{9}$ + ...?

Find the value of $i^{2026}$ , where $i = - 1$ .

What is the period of the function $f (x) = 3 sin (4 x + π)$ ?

If $f (x) = 3 x - 5$ , find the inverse function $f^{- 1} (x)$ .