1. Volume of Cylinder:

   Vcylinder=πr2h=π(2x)2(2x)=8πx3Vcylinder​=πr2h=π(2x)2(2x)=8πx3

2. Volume of Sphere:

   Vsphere=4/3πr3=4/3πx3

3. Remaining Water Volume:

   Vwater=Vcylinder−Vsphere=8πx3−4/3πx3=20/3πx3Vwater​=Vcylinder​−Vsphere​=8πx3−34​πx3=320​πx3

1. Complement of $B$ (B′B′):

   B′=U−B={1,3,5}B′=U−B={1,3,5}

2. Intersection with $A$:

   A∩B′={1,2,3}∩{1,3,5}={1,3}A∩B′={1,2,3}∩{1,3,5}={1,3}

Osun State is home to many prestigious educational institutions, earning it the nickname "Centre of Learning."

Correct answer:
(d) addressing

Complete correct sentence:
"Instead of addressing the issue, the speaker digressed to unimportant matters."

This shows the speaker failed to deal directly with the issue and instead wandered off topic, making "addressing" the perfect opposite of the implied "digressing" in this context.

The correct answer is:

(c) lucrative

The complete sentence would be:
Because the new venture was lucrative, many businessmen and women went into it.

Explanation:

• Lucrative means "producing a great deal of profit," which explains why many businesspeople would be attracted to it.

• Rich (A) usually describes a person or entity with wealth, not a venture itself.

• Manageable (B) means "easy to control," which doesn't necessarily attract investors.

• Satisfying (D) refers to personal fulfillment, not financial gain.

Thus, lucrative is the best fit.

Pension eligibility under the Pension Reform Act requires a minimum of 10 years of service (Section 2(1)), regardless of age.

Civil service operations require professionalism and impartiality. Relationships must be official (based on rules/procedures) and non-personal (avoiding favoritism or bias) to ensure efficiency and fairness.

Latin America is often referred to as Hispanic America due to Spanish and Portuguese colonial influence.

1. Mean:

   1+2+3+4+5+7+8+9+109=499≈5.4491+2+3+4+5+7+8+9+10​=949​≈5.44

2. Median (5th term): 5

3. Difference:

   5.44−5=0.44≈495.44−5=0.44≈94​

Direct allocation (via Section 162(6) of the 1999 Constitution) ensures financial autonomy, preventing state governments from withholding LG funds.

Nigeria's first Prime Minister, Tafawa Balewa, is featured on the ₦20 note.

1. Interior Angle Formula:

   Interior Angle=(n−2)×180°/n=140°Interior Angle=n(n−2)×180°​=140°

2. Solve for $n$:

   (n−2)×180°/n=140°  ⟹  180n−360=140n  ⟹  40n=360  ⟹  n=9n(n−2)×180°​=140°⟹180n−360=140n⟹40n=360⟹n=9

3. Find $k$:

   $$2k+1=9⟹2k=8⟹k=4$$

Prof. Yemi Osinbajo served as Nigeria's 5th elected Vice President from 2015 to 2023.

Charles Chukwuma Soludo
- *Explanation:* Prof. Charles Soludo became the Governor of Anambra State in March 2022.

The correct answer is:

(a) meandered

The complete sentence would be:
The river meandered towards the sea.

Explanation:

• Meandered means to follow a winding or sinuous course, which is how rivers typically flow.

• Rolled (B) is more appropriate for waves or solid objects.

• Ran (C) is too general and doesn't capture the winding nature of a river's flow.

• Trickled (D) suggests a very slow, small flow, which doesn't necessarily apply to all rivers.

Thus, meandered is the most precise and natural choice to describe a river's movement

FAAN is the Federal Airports Authority of Nigeria, managing the country's airports.

Independence requires separation of powers. Members must avoid ties to the executive/legislature to prevent bias and uphold impartiality.

The numerator \(8 + 125x^3\) is a sum of cubes, which factors into \((2 + 5x)(4 - 10x + 25x^2)\). The denominator matches the second factor, simplifying the expression to \(2 + 5x\).

The Civil Service comprises employees of government ministries and departments, not statutory corporations (like NEPA, NNPC) or the armed forces.

Niger State is the largest by land area in Nigeria.

Gusau is the capital city of Zamfara State.

The modern Nigerian state was created in 1914 when the Northern and Southern Protectorates were amalgamated by Lord Lugard.

Sir Abubakar Tafawa Balewa was Nigeria's first Prime Minister at independence in 1960. Nnamdi Azikiwe was the ceremonial President.

The time difference is calculated based on the total longitudinal difference (26°), with each degree equivalent to 4 minutes, resulting in 104 minutes.

These three individuals served as Senate Presidents during that period.

King Charles III ascended to the throne in 2022 following the death of Queen Elizabeth II.

Niger State is the largest by land area in Nigeria.

1. Radius:

   r=3.6/2=1.8 cm

2. Arc Length:

   L=θ/360°×2πr=35°/360°×2×π×1.8≈1.1 cm

3. Perimeter (Arc + 2 Radii):

   $$P=L+2r=1.1+3.6=4.7\text{ cm}$$

Mass layoffs increase unemployment, poverty, and crime rates (e.g., robbery), while fueling social unrest and political instability.

Civil service structures follow a clear hierarchy (e.g., from permanent secretary to junior staff).

Plateau State is part of Nigeria's North-Central geopolitical zone.

1. Test possible roots:
   x = 1: 1 - 7 + 6 = 0 ⇒ (x - 1) is a factor

2. Polynomial division or synthetic division gives:
   x³ - 7x + 6 = (x - 1)(x² + x - 6) = (x - 1)(x + 3)(x - 2)

The correct answer is:

(b) corporal

The complete sentence would be:
Many educationists feel that corporal punishment should still be retained in schools.

Explanation:

• Corporal punishment refers to physical punishment, such as caning or spanking, administered in schools.

• Capital punishment (A) refers to the death penalty, which is unrelated to school discipline.

• Corporate (C) relates to businesses or corporations, making it irrelevant here.

• Physical (D) is close in meaning but not the standard term used in educational contexts (the fixed phrase is "corporal punishment").

Thus, the most accurate choice is (b) corporal.

1. Express $y$ in terms of $x$:

   $$y=10-x$$

2. Substitute into the second equation:

   x2+(10−x)2=58x2+(10−x)2=58x2+100−20x+x2=58x2+100−20x+x2=582x2−20x+42=02x2−20x+42=0x2−10x+21=0x2−10x+21=0

3. Solve the quadratic equation:

   x=10±100−842=10±42x=210±100−84​​=210±4​$$x=7\text{ or }x=3$$

4. Find corresponding $y$:

   • If $x=7$, $y=3$

   • If $x=3$, $y=7$

1. |x/5| = |x/2| ⇒ x/5 = x/2 or x/5 = -x/2

2. First case: x = 0

3. Second case: 2x = -5x ⇒ 7x = 0 ⇒ x = 0

Judicial review is the exclusive power of courts to invalidate laws (including bye-laws) that violate constitutional provisions.

Public corporations are state-owned entities created to deliver essential services (e.g., water, electricity) that may not be profit-driven but serve public welfare. Profit maximization is a goal of private enterprises.