Mathematics Majorship Practice Questions — Set 2

Question 1

What is the remainder when x^3 - 2x^2 + 3x - 4 is divided by (x - 2)?

Accepted Answer

2

Answer

6

Answer

-4

Answer

0

Question 2

Solve for x: log2(x) + log2(x-2) = 3.

Accepted Answer

4

Answer

2

Answer

8

Answer

4 and -2

Question 3

Find the eccentricity of the ellipse given by (x^2)/(25) + (y^2)/(9) = 1.

Accepted Answer

0.8

Answer

0.6

Answer

1.25

Answer

0.36

Question 4

What is the derivative of f(x) = ln(sin x)?

Accepted Answer

cot x

Answer

tan x

Answer

1/sin x

Answer

csc x

Question 5

Evaluate ∫ e^x cos x dx.

Accepted Answer

(e^x/2)(sin x + cos x) + C

Answer

e^x sin x + C

Answer

e^x cos x + C

Answer

(e^x/2)(sin x - cos x) + C

Question 6

The probability of hitting a target is 1/3. If 5 shots are fired, what is the probability of hitting the target exactly 2 times?

Accepted Answer

80/243

Answer

10/243

Answer

20/81

Answer

40/243

Question 7

Find the dot product of vectors u = 2i - 3j and v = 4i + j.

Accepted Answer

5

Answer

8

Answer

11

Answer

-1

Question 8

What is the area of a triangle with vertices (0,0), (4,0), and (0,3)?

Accepted Answer

6

Answer

12

Answer

7

Answer

5

Question 9

Which of the following is an even function?

Accepted Answer

cos x

Answer

sin x

Answer

x^3

Answer

e^x

Question 10

What is the order of the differential equation y'' + 3(y')^3 + y = 0?

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Mathematics Majorship Practice Questions — Set 2

What is the remainder when $x^{3} - 2 x^{2} + 3 x - 4$ is divided by $(x - 2)$ ?

Solve for x: $lo g 2 (x) + lo g 2 (x - 2) = 3$ .

Find the eccentricity of the ellipse given by $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$ .

What is the derivative of $f (x) = ln (sin x)$ ?

Evaluate $\int e^{x} cos x d x$ .

The probability of hitting a target is $\frac{1}{3}$ . If 5 shots are fired, what is the probability of hitting the target exactly 2 times?

Find the dot product of vectors $u = 2 i - 3 j$ and $v = 4 i + j$ .

What is the area of a triangle with vertices (0,0), (4,0), and (0,3)?

Which of the following is an even function?

What is the order of the differential equation $y^{''} + 3 (y^{'})^{3} + y = 0$ ?

Mathematics Majorship Practice Questions — Set 2

What is the remainder when x3−2x2+3x−4 is divided by (x−2)?

Solve for x: log2(x)+log2(x−2)=3.

Find the eccentricity of the ellipse given by 25x2​+9y2​=1.

What is the derivative of f(x)=ln(sinx)?

Evaluate ∫excosxdx.

The probability of hitting a target is 31​. If 5 shots are fired, what is the probability of hitting the target exactly 2 times?

Find the dot product of vectors u=2i−3j and v=4i+j.

What is the area of a triangle with vertices (0,0), (4,0), and (0,3)?

Which of the following is an even function?

What is the order of the differential equation y′′+3(y′)3+y=0?

What is the remainder when $x^{3} - 2 x^{2} + 3 x - 4$ is divided by $(x - 2)$ ?

Solve for x: $lo g 2 (x) + lo g 2 (x - 2) = 3$ .

Find the eccentricity of the ellipse given by $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$ .

What is the derivative of $f (x) = ln (sin x)$ ?

Evaluate $\int e^{x} cos x d x$ .

The probability of hitting a target is $\frac{1}{3}$ . If 5 shots are fired, what is the probability of hitting the target exactly 2 times?

Find the dot product of vectors $u = 2 i - 3 j$ and $v = 4 i + j$ .

What is the order of the differential equation $y^{''} + 3 (y^{'})^{3} + y = 0$ ?