Step by Step Solution
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.Q2: The smallest prime number is:
A) 0
B) 1
C) 2
D) 3
Answer: C) 2
Step by Step Solution
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)
| Number | Divisors | Prime or Not? |
|---|---|---|
| 1 | 1 | ❌ Not Prime |
| 2 | 1, 2 | ✅ Prime |
| 3 | 1, 3 | ✅ Prime |
| 4 | 1, 2, 4 | ❌ Not Prime |
| 5 | 1, 5 | ✅ Prime |
| 6 | 1, 2, 3, 6 | ❌ Not Prime |
| 7 | 1, 7 | ✅ Prime |
| 8 | 1, 2, 4, 8 | ❌ Not Prime |
| 9 | 1, 3, 9 | ❌ Not Prime |
| 10 | 1, 2, 5, 10 | ❌ Not Prime |
Step by Step Solution
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.Step by Step Solution
Solution:
First, convert both values to the same unit (minutes):- 2 hours = 120 minutes
- 30 minutes = 30 minutes
Step by Step Solution
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%.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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%.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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.Step by Step Solution
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%.Step by Step Solution
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.Step by Step Solution
Solution:
Step 1: Convert 0.75 into a fraction
0.75 can be written as: 75/100Step 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**.Step by Step Solution
Solution:
Step 1: Convert decimal numbers into fractions
1.5 = 15/10 2.5 = 25/10Step 2: Multiply the fractions
(15/10) × (25/10) = (15 × 25) / (10 × 10) = 375 / 100Step 3: Convert to decimal
375 ÷ 100 = 3.75 Thus, the correct answer is **D) 3.75**.Step by Step Solution
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°**.Step by Step Solution
Solution:
Perimeter of a square = 4 × side = 4 × 5 = 20 cm Thus, the correct answer is **C) 20 cm**.Step by Step Solution
Solution:
Area of a circle = π × r² = (22/7) × (7 × 7) = (22/7) × 49 = 154 cm² Thus, the correct answer is **C) 154 cm²**.Step by Step Solution
Solution:
Volume of a cube = side³ = 3³ = 3 × 3 × 3 = 27 cm³ Thus, the correct answer is **C) 27 cm³**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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}**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
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**.Step by Step Solution
Solution:
From trigonometric ratios: sin 30° = **1/2** Thus, the correct answer is **B) 1/2**.Step by Step Solution
Solution:
tan 45° = sin 45° / cos 45° = **1** Thus, the correct answer is **B) 1**.Step by Step Solution
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**.Step by Step Solution
Solution:
Total balls = 4 (red) + 6 (blue) = **10** Probability of red ball = **4/10** = **2/5** Thus, the correct answer is **A) 2/5**.Step by Step Solution
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**.Step by Step Solution
Solution:
Let son’s age = **15 years** Father’s age = **3 × 15 = 45 years** Thus, the correct answer is **D) 45 years**.Step by Step Solution
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%**.Step by Step Solution
Solution:
√144 = **12** Thus, the correct answer is **B) 12**.Step by Step Solution
Solution:
Using exponent rule **aᵐ × aⁿ = aᵐ⁺ⁿ**: 2³ × 2² = 2^(3+2) = **2⁵** Thus, the correct answer is **B) 2⁵**.Step by Step Solution
Solution:
5^x = 125 Since 125 = 5³, we get **x = 3** Thus, the correct answer is **B) 3**.Step by Step Solution
√81 = 9, √9 = 3 9 ÷ 3 = 3Step by Step Solution
Since 3³ = 27, cube root of 27 is 3.Step by Step Solution
The origin is the point where the X-axis and Y-axis intersect at (0,0).Step by Step Solution
The general equation of a straight line in slope-intercept form is y = mx + c, where:- m = slope of the line
- c = y-intercept