Quiz about X2 M/C TTA Trial22

Question 1

Evaluate $$i^{2022}+i^{2021}+i^{2020}\ .$$

Accepted Answer

$$i$$

Answer

$$-i$$

Answer

$$0$$

Answer

$$1$$

Question 2

If I do play chess then I am smart.

Which statement is the contrapositive?

Accepted Answer

If I am not smart then I do not play chess.

Answer

If I do not play chess then I am not smart.

Answer

If I am not smart then I am not good at chess.

Answer

If I am smart then I play chess.

Question 3

Which of the following is a vector equation of the line joining the points A(1,3) and B(-2,4)

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 4

Question 4.

Accepted Answer

$$36\ \sqrt[]{14}$$

Answer

$$84$$

Answer

$$504$$

Answer

$$6\ \sqrt[]{14}$$

Question 5

A variable force acts on a particle causing it to move in a straight line. At time t seconds its velocity v metres per second and position x metres from the origin are such that $$v=e^x\cos x\ .$$ The acceleration of the particle can be expressed as:

Accepted Answer

$$e^{2x}\cos x\left(\cos x-\sin x\right)$$

Answer

$$-e^x\sin x$$

Answer

$$e^x\left(\sin x+\cos x\right)$$

Answer

$$2e^{2x}\left(\cos^2x\right)$$

Question 6

A ball of mass 12 kg is suspended from a horizontal ceiling by two identical light strings.

Each string makes an angle of $$60\degree$$ with the ceiling as shown.

What is the magnitude, in newtons, of the tension in each string?

Accepted Answer

$$4\ \sqrt[]{3}g$$

Answer

$$6g$$

Answer

$$12g$$

Answer

$$24g$$

Question 7

The integral $$\int\ \frac{1}{x\ \sqrt[]{4+x^2}}dx$$ can be most efficiently solved with which substitution?

Accepted Answer

$$x=2 an\alpha$$

Answer

$$x= an\alpha$$

Answer

$$x=\sec\alpha$$

Answer

$$x=2\sec\alpha$$

Question 8

The algebraic fraction $$\frac{7x-5}{\left(x-4\right)^2\left(x^2+9\right)}$$ is decomposed into partial fractions. What is the correct decomposition?

Accepted Answer

$$\frac{A}{\left(x-4\right)^2}+\frac{B}{x-4}+\frac{Cx+D}{x^2+9}$$

Answer

$$\frac{A}{\left(x-4\right)^2}+\frac{Bx+C}{x^2+9}$$

Answer

$$\frac{A}{x-4}+\frac{B}{x+3}+\frac{C}{x-3}$$

Answer

$$\frac{A}{\left(x-4\right)^2}+\frac{B}{x-4}+\frac{C}{x^2+9}$$

Question 9

On an Argand diagram, a set of points lies on circle of radius 2, centred at the origin.

Which of the following defines this circle?

Accepted Answer

$$\left\{z\in C\ :\ \left(z+\overline{z}\right)^2-\left(z-\overline{z}\right)^2=16\right\}$$

Answer

$$\left\{z\in C\ :\ z\overline{z}=2\right\}$$

Answer

$$\left\{z\in C\ :\ z^2=4\right\}$$

Answer

$$\left\{z\in C\ :\ Re\left(z^2\right)+Im\left(z^2\right)=4\right\}$$

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