Explanation

Let's find the unknown value x using the proportion x : 5 :: 6 : 15.

We can set up the proportion as x/5 = 6/15.

Step 1: Cross-multiply

15x = 6 * 5

Step 2: Simplify

15x = 30

Step 3: Solve for x

x = 30 / 15

x = 2

Explanation

The complement of set A (written as A′ or U – A) includes all elements in the universal set U that are not in A.

Hence, it's the difference between U and A.

Explanation

Gram seed has an embryo located near the center of the seed, not at one side.

Endosperm is absent in gram seed, and it has two cotyledons.

Explanation

Neon (Ne) has an atomic number of 10, which places it in the 2nd period of the periodic table.

Periods indicate the number of electron shells; Neon has 2 shells.

Explanation

Any number raised to a power means multiplying that number by itself repeatedly.

Since 1 × 1 = 1, even when repeated, 1 raised to any power is always 1.

Explanation

The least common multiple (LCM) of 4, 8, and 16 is 16.

The 4th common multiple is: 16 × 4 = 64.

Explanation

2⅔ can be written as 2^(2/3), which equals ∛(2²) = ∛4 = ³√4.

Explanation

Given the roots are 1 + √5 and 1 - √5, we can find the quadratic equation using the sum and product of roots.

Step 1: Calculate the sum of roots

Sum of roots = (1 + √5) + (1 - √5) = 2

Step 2: Calculate the product of roots

Product of roots = (1 + √5)(1 - √5) = 1 - 5 = -4

Step 3: Form the quadratic equation

x² - (sum of roots)x + (product of roots) = 0

x² - 2x - 4 = 0

Explanation

The adjectives follow the correct order: opinion → size → age → color → material → noun.

"Charming" (opinion), "little" (size), "old" (age), "white" (color), "stone" (material), followed by "house" (noun).

Explanation

"Ox" is an irregular noun because its plural form is "oxen", not "oxes."

The dish → dishes, chocolate → chocolates, plant → plants follow regular plural rules.