Basic Mathematics MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: March 16, 2025

Solution:

In the number 85,396, the digit 5 is in the thousands place.

The place value of a digit is determined by its position in the number.

Since 5 is in the thousands place, its value is:

5 × 1,000 = 5,000

Thus, the correct answer is 5,000.

Solution:

A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself.

Prime Number Table (1 to 10)

Solution:

Let the number be X.
Given that 20% of X = 50, we can set up the equation:

20/100 × X = 50

Solving for X:

X = (50 × 100) / 20
X = 250

Thus, the correct answer is 250.

Solution:

First, convert both values to the same unit (minutes):

• 2 hours = 120 minutes
• 30 minutes = 30 minutes

Now, express the ratio:

120 : 30

Simplifying by dividing both terms by 30:

(120 ÷ 30) : (30 ÷ 30) = 4:1

Thus, the correct answer is 4:1.

Solution:

The formula for profit percentage is:

Profit % = (Profit / Cost Price) × 100

First, calculate the profit:

Profit = Selling Price – Cost Price
Profit = 1,000 – 800 = 200

Now, calculate the profit percentage:

Profit % = (200 / 800) × 100 = 25%

Thus, the correct answer is 25%.

Solution:

The formula for the selling price after a discount is:

Selling Price = Marked Price – Discount

First, calculate the discount amount:

Discount = (10/100) × 2,000 = 200

Now, find the selling price:

Selling Price = 2,000 – 200 = 1,800

Thus, the correct answer is Rs. 1,800.

Solution:

The formula for simple interest (SI) is:

SI = (P × R × T) / 100

Where:
P = 5,000 (Principal)
R = 6% (Rate)
T = 3 years (Time)

Now, calculating the interest:

SI = (5,000 × 6 × 3) / 100
SI = (90,000) / 100
SI = 900

Thus, the correct answer is Rs. 900.

Solution:

The compound interest formula is:

A = P(1 + R/100)ⁿ

Where:
A = 9,680 (Final Amount)
P = 8,000 (Principal)
R = Rate of Interest
n = 2 years (Time)

Now, solving for R:

9,680 = 8,000(1 + R/100)²

Dividing both sides by 8,000:

(1 + R/100)² = 9,680 / 8,000
(1 + R/100)² = 1.21

Taking square root on both sides:

1 + R/100 = 1.1

R/100 = 0.1
R = 10%

Thus, the correct answer is 10%.

Solution:

Given the equation:

3x + 5 = 20

Step 1: Subtract 5 from both sides:

3x = 20 – 5
3x = 15

Step 2: Divide both sides by 3:

x = 15 / 3
x = 5

Thus, the correct answer is 5.

Solution:

Given the equation:

x² – 9 = 0

Step 1: Add 9 to both sides:

x² = 9

Step 2: Take the square root on both sides:

x = ±√9
x = ±3

Thus, the correct answer is ±3.

Solution:

The formula for the average is:

Average = (Sum of all numbers) / (Total count)

Step 1: Find the sum of numbers:

10 + 20 + 30 + 40 + 50 = 150

Step 2: Divide by the total count (5):

Average = 150 / 5 = 30

Thus, the correct answer is 30.

Solution:

Step 1: Find the total age of 5 students:
Total Age = Average × Number of students
Total Age = 18 × 5 = 90
Step 2: Add the new student’s age:
New Total Age = 90 + 24 = 114
Step 3: Find the new average:
New Average = 114 / 6 = 19
Thus, the correct answer is 19.

Solution:

The formula for speed is:

Speed = Distance / Time

Step 1: Given data:
Distance = 240 km
Time = 4 hours

Step 2: Calculate speed:

Speed = 240 / 4 = 60 km/h

Thus, the correct answer is 60 km/h.

Solution:

The formula for distance is:

Distance = Speed × Time

Step 1: Convert speed from km/h to m/s:

1 km/h = 5/18 m/s

So,
Speed = 72 × (5/18) = 20 m/s

Step 2: Multiply by time:

Distance = 20 × 10 = 200 meters

Thus, the correct answer is 200 m.

Solution:

Probability is calculated as:

Probability = (Favorable Outcomes) / (Total Outcomes)

Step 1: A fair coin has two sides: Head and Tail.

Step 2: The probability of getting a tail is:

P(Tail) = 1 / 2 = 0.5

Thus, the correct answer is 1/2.

Solution:

Step 1: Find the number of boys:

Total students = 50
Girls = 20
Boys = 50 – 20 = 30

Step 2: Calculate the percentage of boys:

Percentage = (Number of Boys / Total Students) × 100
Percentage = (30 / 50) × 100 = 60%

Thus, the correct answer is 60%.

Solution:

Step 1: Find the factors of 24 and 36.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 2: Identify the common factors:
Common factors: 1, 2, 3, 4, 6, 12

Step 3: The highest common factor (HCF) is 12.

Thus, the correct answer is 12.

Solution:

Step 1: Convert 0.75 into a fraction

0.75 can be written as:
75/100

Step 2: Simplify the fraction

To simplify 75/100, divide both the numerator and denominator by their HCF (Highest Common Factor), which is 25:

75 ÷ 25 = 3
100 ÷ 25 = 4

So, 75/100 simplifies to **3/4**.

Step 3: Verify the answer

Since 0.75 is equal to 3/4, the correct answer is **B) 3/4**.

Solution:

Step 1: Convert decimal numbers into fractions

1.5 = 15/10
2.5 = 25/10

Step 2: Multiply the fractions

(15/10) × (25/10) = (15 × 25) / (10 × 10)
= 375 / 100

Step 3: Convert to decimal

375 ÷ 100 = 3.75

Thus, the correct answer is **D) 3.75**.

Solution:

A triangle always has three angles, and their sum is calculated as:
(Sum of interior angles) = (n – 2) × 180°
= (3 – 2) × 180° = 180°
Thus, the correct answer is **C) 180°**.

Solution:

Perimeter of a square = 4 × side
= 4 × 5 = 20 cm
Thus, the correct answer is **C) 20 cm**.

Solution:

Area of a circle = π × r²
= (22/7) × (7 × 7)
= (22/7) × 49 = 154 cm²
Thus, the correct answer is **C) 154 cm²**.

Solution:

Volume of a cube = side³
= 3³ = 3 × 3 × 3 = 27 cm³
Thus, the correct answer is **C) 27 cm³**.

Solution:

Work done by A in 1 day = 1/10
Work done by B in 1 day = 1/15
Total work done in 1 day = (1/10) + (1/15)
= (3/30) + (2/30) = 5/30 = 1/6
So, they will complete the work in **6 days**.
Thus, the correct answer is **C) 6 days**.

Solution:

Filling rate of first pipe = 1/5 per hour
Emptying rate of second pipe = 1/10 per hour
Net filling rate = (1/5) – (1/10)
= (2/10) – (1/10) = 1/10
So, the tank will be filled in **10 hours**.
Thus, the correct answer is **B) 10 hours**.

Solution:

This is a geometric sequence where each term is multiplied by **2**:
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = **32**
Thus, the correct answer is **B) 32**.

Solution:

The sum of the first **n** natural numbers is given by the formula:
Sum = (n × (n + 1)) / 2
For n = 5:
Sum = (5 × 6) / 2 = 30 / 2 = 15
Thus, the correct answer is **B) 15**.

Solution:

Let the number be **x**.
Equation:
6x – 4 = 32
Solving for x:
6x = 32 + 4
6x = 36
x = 36 / 6 = **6**
Thus, the correct answer is **D) 6**.

Solution:

Since a week has **7 days**, we divide 45 by 7:
45 ÷ 7 = 6 full weeks + **3 extra days**
If today is **Monday**, after **3 extra days**, it will be:
Monday → Tuesday → Wednesday → **Thursday**
Thus, the correct answer is **B) Thursday**.

Solution:

Logarithm definition: log_b(a) = c means **b^c = a**
Here, log₁₀(1000) = x
Since **10³ = 1000**,
x = **3**
Thus, the correct answer is **B) 3**.

Solution:

By logarithm rule: log_b(1) = 0 for any base **b**
Because any number raised to the power **0** equals **1**
b⁰ = 1
Thus, the correct answer is **A) 0**.

Solution:

Number of ways to arrange **n** objects = **n!**
For **4 people**, we calculate:
4! = 4 × 3 × 2 × 1 = **24**
Thus, the correct answer is **C) 24**.

Solution:

Using Combination formula:
nCr = n! / (r!(n-r)!)
5C3 = 5! / (3!(5-3)!)
= (5 × 4 × 3!) / (3! × 2 × 1)
= (5 × 4) / (2 × 1) = **10**
Thus, the correct answer is **B) 10**.

Solution:

A ∩ B (Intersection) means **common elements** in both sets.
A = {1,2,3,4}
B = {3,4,5,6}
Common elements = **{3,4}**
Thus, the correct answer is **B) {3,4}**.

Solution:

A ∪ B (Union) means **all unique elements from both sets**.
Maximum possible elements = A + B (if no elements are common).
= 7 + 5 = **12**
Thus, the correct answer is **C) 12**.

Solution:

A **square matrix** has **equal rows and columns**.
For example, a 3×3 matrix:
⎡ a b c ⎤
⎢ d e f ⎥
⎣ g h i ⎦
Since it has **equal rows and columns**, it’s called a **square matrix**.
Thus, the correct answer is **B) Square Matrix**.

Solution:

An **identity matrix** of order 3 is:
⎡ 1 0 0 ⎤
⎢ 0 1 0 ⎥
⎣ 0 0 1 ⎦
The determinant of an **identity matrix** is always **1**.
Thus, the correct answer is **B) 1**.

Solution:

From trigonometric ratios:
sin 30° = **1/2**
Thus, the correct answer is **B) 1/2**.

Solution:

tan 45° = sin 45° / cos 45° = **1**
Thus, the correct answer is **B) 1**.

Solution:

Using the identity: **sin²θ + cos²θ = 1**
sin²θ + (3/5)² = 1
sin²θ + 9/25 = 1
sin²θ = 1 – 9/25 = 16/25
sin θ = **4/5**
Thus, the correct answer is **B) 4/5**.

Solution:

Total balls = 4 (red) + 6 (blue) = **10**
Probability of red ball = **4/10** = **2/5**
Thus, the correct answer is **A) 2/5**.

Solution:

Possible outcomes on a fair die = **1, 2, 3, 4, 5, 6**
Even numbers = **2, 4, 6** (3 outcomes)
Probability = 3/6 = **1/2**
Thus, the correct answer is **C) 1/2**.

Solution:

Let son’s age = **15 years**
Father’s age = **3 × 15 = 45 years**
Thus, the correct answer is **D) 45 years**.

Solution:

Using **Simple Interest (SI) formula**:
SI = (P × R × T) / 100
Since the sum doubles, SI = P, and T = 8 years:
P = (P × R × 8) / 100
100 = R × 8
R = **12.5%**
Thus, the correct answer is **B) 12.5%**.

Solution:

√144 = **12**
Thus, the correct answer is **B) 12**.

Solution:

Using exponent rule **aᵐ × aⁿ = aᵐ⁺ⁿ**:
2³ × 2² = 2^(3+2) = **2⁵**
Thus, the correct answer is **B) 2⁵**.

Solution:

5^x = 125
Since 125 = 5³, we get **x = 3**
Thus, the correct answer is **B) 3**.

√81 = 9, √9 = 3

9 ÷ 3 = 3

Since 3³ = 27, cube root of 27 is 3.

The origin is the point where the X-axis and Y-axis intersect at (0,0).

The general equation of a straight line in slope-intercept form is y = mx + c, where:

• m = slope of the line
• c = y-intercept

Minute hand:

At 15 minutes, the minute hand is exactly on the 3.

Each minute represents 6 degrees (360 degrees/60 minutes).

Thus, at 15 minutes, the minute hand is at
15 × 6 = 90 degrees.

Hour hand:

The hour hand moves 30 degrees per hour (360 degrees/12 hours).

At 3 o’clock, the hour hand is at
3 × 30 = 90 degrees.

By 15 minutes past 3, the hour hand has moved a bit further.

Each minute, the hour hand moves
30 / 60 = 0.5 degrees.

Thus, in 15 minutes, the hour hand moves
15 × 0.5 = 7.5 degrees.

So, the hour hand is at
90 + 7.5 = 97.5 degrees.

Finding the angle between the hour and minute hands:

The angle between them is
97.5 – 90 = 7.5 degrees.

Let the son’s age be x.

Father’s current age = 3x

After 5 years: (3x + 5) = 2(x + 5)

Solving: 3x + 5 = 2x + 10 → x = 10

Downstream speed = Boat speed + Current speed

= 12 + 3 = 15 km/h