Explanation

Compare the probabilities:  

Getting odd on die = 0.33

Getting head on coin = 0.50

0.50 > 0.33, so getting a head is more likely.

Last verified on 14-04-2026

Explanation

t⁴ - 16 = (t²)² - 4² = (t² - 4)(t² + 4) = (t - 2)(t + 2)(t² + 4)

(t² + 4)(t + 2)(t - 2)

Last verified on 14-04-2026

Explanation

Area of flag = 3 m × 2 m = 6 m²  

Cost = 6 × Rs. 75 = Rs. 450  

Last verified on 14-04-2026

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

Three consecutive odd numbers: n-2, n, n+2  

Sum = 3n = 57 → n = 19  

Last verified on 14-04-2026