Explanation

(a) 5 men, 3 women

Number of ways of forming the committee = \(^{8}C_{3}\)

= \(\frac{8!}{(8 - 3)! 3!}\)

= 56 ways.

(b) p(no woman) = \(\frac{^{5}C_{3}}{^{8}C_{3}}\)

= \(\frac{10}{56}\)

\(\therefore\) p( at least one woman) = 1 - p(no woman)

= \(1 - \frac{10}{56}\)

= \(\frac{46}{56}\)

= \(\frac{23}{28}\).

Explanation

(a) Net force is the effective or resultant force resulting from the actions of a system of forces on a body.

(b) The principle ofconservation of linear momentum explains that in an isolated or closed system of colliding bodies the total linear momentum in a fixed direction remains constant, e.g. the recoil of gun, colliding trolleys, rocket propulsion, etc.

(c) V\(_1^2\) = \(U_1^2 + 2gh_1\) = 0 + 2 x 10 x 2

= 40

\(V_1 = \sqrt{40}\) = 6.325m/s

\(v_2^2 = u_2^2 - 2gh_2\)

O = \(U^2_2\) - 2 x 10 x 1.8

u = \(\sqrt{36}\)

= 6ms\(^{-1}\)

Impulse Change in momentun

mv\(_1\) - (-mu\(_2\)) = m (v\(_1\) + u\(_2\))

= 0.2(6.325 + 6.000)

= 2.46 Ns

(d) v = \(\omega \sqrt{r^2 - y^2}\)

2\(\pi\)f\(\sqrt{r^2 - y^2}\)

2 = 2 x 3.14 x 5 x \(\sqrt{r^2 - 0.1^2}\)

r = 0.12m

(ii) Vmax = \(\omega\)r = 2\(\pi\)fr

= 2 x 3.142 x 5 x 0.12

= 3,77 m/s

(iii) P.E = \(\frac{1}{2}m \omega^2e^2 = \times \frac{1}{2}m(2 \pi f)^2r^2\)

= \(\frac{1}{2} \times 0.02(2 \times 3.142 \times 5)^2 \times (0.12)^2\)

= 1.42 x 10\(^{-1}J\)

Correct Answer: C. 4/5 π

Explanation

Phase difference = \(\frac{2\pi x}{\lambda}\)

= \(\frac{2\pi \times 20}{50}\)

= \(\frac{4}{5} \pi\)

Correct Answer: A. dumping

Explanation

(a) Process of conversion of food to chyme in the stomach of a mammal

The stomach is a large thick-walled muscular sac; made of three layers of muscles; that contracts in different directions when food enters into it; bringing about a twisting/squeezing/churning effect; enabling food to mix with digestive juice; and HCL; this movement then converts food to the semi-liquid called chyme.

(b)Table

(c) Experiment to show that carbon dioxide is necessary for photosynthesis

Two potted plants are de-starched by placing them in a dark cupboard for 24hours;

a leaf each from both plants are then tested for starch to ensure they have no starch/have been de-starched; the potted plants are placed on a board each; a beaker containing caustic soda is placed beside plant A; to absorb carbon dioxide; while a beaker containing water is placed beside plant B as control; they are both covered with bell jars labelled A and B respectively; the rim/edge is smeared with vaseline/petroleum jelly to make it air tight; the setup is exposed to sunlight/light for 4-6 hours; a leaf each from both plants are plucked and tested for starch.

Observation:It is observed that leaf from plant A is negative/does not contain starch/remains brown in colour while leaf from plant B is positive/contains starch/turns blue - black.

Conclusion: Carbon dioxide is necessary for photosynthesis.

OR

De-starch a well-watered potted plant by putting it in darkness for 48 hours; insert a leaf into a flask containing water which serves as a control experiment; and another leaf into another flask containing KOH/ potassium hydroxide/ caustic potash; ensure both flasks are air tight by smearing the split corks with Vaseline; leave the potted plant in a well-lit place for

Correct Answer: A. q = \(\frac{rt^2}{(p - r^3)}\)

Explanation

t = √pq/r - r\(^2\)q

multiply both sides by the L.C.M, r

r\(^2\) = pq - qr\(^3\)

collect like terms on the RHS

q(p - r3) = rt\(^2\)

q = \(\frac{rt^2}{(p - r^3)}\)

Explanation

(a) Fundamental Human Rights are inalienable freedoms and privileges that individuals are entitled to in a State e.g. right to life, right to fair hearing, right to freedom of movement, etc.

(b)(i) Entrenchment of Fundamental Human Rights in the State's constitution.

(ii) Existence of an impartial, free and independent judiciary.

(iii) Enactment of laws that protect the rights of individuals.

(iv) The existence of a free and independent media.

(v) Citizens must be educated to be able to defend their rights.

(vi) Public opinion must be effectively used to protect any violation of the rights of the citizens.

(vii) Existence of institutions such as the Ombudsman and the Public Complains Commission.

(viii) Respect for the rule of law.

(ix) Respect for international laws and conventions.

(ix) Provision of free legal aid.

(xi) Adherence to the doctrine of Separation of Powers and Checks and Balances.

Correct Answer: D. a geo

Correct Answer: A. incubator

Correct Answer: B. 3000m

Explanation

t = 4s ; v = 150ms^-1

depth = X ; but 2X = vt

X = \(\frac {vt}{2}\) = \(\frac {1500 \times 4}{2}\)

X = 3000m