Explanation

• The idiom “once in a blue moon” means something that happens very infrequently.
• It refers to an event that is rare or almost never happens.

Last verified on 04-05-2026

Explanation

• The words like on, over, at, under, by etc. are called Prepositions.
• "Under" is a preposition showing the relationship between the cat and the table.
• Prepositions indicate position, direction, or time in a sentence.

Last verified on 23-05-2026

Explanation

• A noun is a word that names a person, place, thing, or idea.
• Example: Patience, Virtue, Honesty, Kindness, Bravery, Wisdom

Last verified on 23-05-2026

Explanation

• Barely is an adverb because it modifies the verb “passed”.
• It shows the degree or extent of passing (very little margin).
• Adverbs usually tell us how, when, where, or to what extent something happens.

Last verified on 23-05-2026

Explanation

Given:  

a/b = 9/10  

b/c = 5/6  

Multiply both equations:  

(a/b) × (b/c) = (9/10) × (5/6)  

a/c = 45/60  

a/c = 3/4  

So a:c = 3:4.

Last verified on 23-05-2026

Explanation

Mean = (Sum of numbers) / (Total numbers)  

= (10 + 12 + 14) / 3  

= 36 / 3  

= 12  

Last verified on 23-05-2026

Explanation

• A secant is a line that cuts a circle and intersects it at exactly 2 distinct points.
• If it touches at 1 point, it’s a tangent.

Last verified on 23-05-2026

Explanation

cotθ = 1/tanθ  

So:  

cotθ × tanθ = (1/tanθ) × tanθ = 1  

Last verified on 23-05-2026

Explanation

Given:  

cos θ = 9/41  

Use the formula:  

sin²θ + cos²θ = 1  

Step 1: Put cos θ value  

sin²θ + (9/41)² = 1  

sin²θ + 81/1681 = 1  

Step 2: Find sin²θ  

sin²θ = 1 - 81/1681  

sin²θ = 1681/1681 - 81/1681  

sin²θ = 1600/1681  

Step 3: Take square root  

sin θ = ±√(1600/1681)  

sin θ = ±40/41  

Last verified on 23-05-2026

Explanation

Area = base × height  

Let original base = b, height = h  

Original area = b × h  

New base = b + 50% of b = b + 0.5b = 1.5b  

Height stays same = h  

New area = 1.5b × h = 1.5 × (b × h)  

So the area becomes 1.5 times the original, or increases by 50%.

Last verified on 23-05-2026