Explanation

For x² - 4x + m to be a complete square, it must match (x - a)² = x² - 2ax + a²  

Compare: -2a = -4 → a = 2  

So m = a² = 2² = 4  

Check: x² - 4x + 4 = (x - 2)²  

Last verified on 14-04-2026

Explanation

Rate = distance / time  

Distance = 500 m = 0.5 km  

Time = 50 min = 50/60 hr = 5/6 hr  

Speed = 0.5 ÷ (5/6) = 0.5 × 6/5 = 3/5 = 0.6 km/hr  

Last verified on 14-04-2026

Explanation

• The most frequently occurring value in a dataset is called mode.
• It represents the most common data point.
• It can be one mode, more than one, or no mode.
• Mean = average value
• Median = middle value

Last verified on 14-04-2026

Explanation

• The set of all possible outcomes in a random experiment is called a sample space.
• It represents the total, exhaustive set of every possible result of a random trial, typically denoted by the letter 'S'.
• Each individual element within this set is called an outcome or sample point.

Last verified on 14-04-2026

Explanation

• The space occupied by a 3-dimensional object is called volume.
• It measures how much space an object contains inside.
• It is a fundamental concept in Geometry.
• It is always measured in cubic units.

Last verified on 14-04-2026

Explanation

• A Geometric Sequence is a sequence where each term is obtained by multiplying the previous term by a constant.
• This constant is called the common ratio (r).
• The value of r ≠ 0.
• Sequence grows or decreases depending on r.

Last verified on 14-04-2026

Explanation

Step 1: Let the numbers be

Three consecutive odd numbers:

$$x-2,x,x+2$$

Step 2: Form an equation

$$(x-2)+x+(x+2)=57$$$$3x = 57$$

Step 3: Solve

$$x=19$$

$$Last\; updated\; by\; NA\; on\; 24-April-2026$$

Explanation

Let original = x  

x + 20% of x = 540  

1.2x = 540  

x = 540 / 1.2 = 450  

Last verified on 14-04-2026

Explanation

LCM of 16, 24, 30:  

16 = 2⁴  

24 = 2³ × 3  

30 = 2 × 3 × 5  

LCM = 2⁴ × 3 × 5 = 240  

240 is three-digit, so that’s it.  

Last verified on 14-04-2026

Explanation

• A heat engine works between a hot source and a cold sink.
• Efficiency depends on the temperature difference between them.
• Greater the difference, higher the efficiency.
• Maximum efficiency is given by Carnot engine.

Last verified on 14-04-2026