Explanation:

3x – 5y = 15 is a single linear equation in two variables, representing a straight line in the xy-plane.

A line has infinitely many points, hence infinitely many solutions over the real numbers. Equivalently, letting x = t (any real), we get y = (3t − 15)/5, yielding infinitely many (x, y) pairs. A unique solution would require another independent equation; none is given.

Explanation:

In a rhombus (a parallelogram), adjacent angles are supplementary and opposite angles are equal.

Let ∠A = 4x and ∠B = 5x. Then 4x + 5x = 180°, so x = 20°. Hence ∠A = 80° and ∠B = 100°. Since ∠C is opposite ∠A, ∠C = ∠A = 80°.

The ‘non-square’ condition just ensures the angles aren’t 90° and doesn’t affect the calculation.

Explanation:

Identify the pattern: reverse letters within fixed-size blocks from left to right—use 2-letter blocks; if the word ends with 3 letters (odd length), reverse that 3-letter block.
– SIMPLE (6): SI|MP|LE -> IS|PM|EL = ISPMEL
– CHAPTER (7): CH|AP|TER -> HC|PA|RET = HCPARET
To decode LFWORE (even length), swap each pair: LF|WO|RE -> FL|OW|ER = FLOWER.
Therefore, the word is FLOWER.

Explanation:

Three days after Sunday is Wednesday, so the 8th is a Wednesday.

The 17th is 9 days after the 8th. Since 9 ≡ 2 (mod 7), move 2 days ahead from Wednesday: Wednesday → Thursday → Friday.

Therefore, the 17th is a Friday.

Explanation:

Unnecessary use of “Reply All” should be avoided in group e-mails. It clutters recipients’ inboxes, wastes time, and may reveal information to people who don’t need it. Best practice is to reply only to the sender or the relevant subset unless your response benefits everyone.

The other options are good practices, not to be avoided:
– Using a signature helps identify the sender and provides contact details.
– Spell-checking ensures professionalism and clarity.
– Filling in a clear subject line aids in threading, search, and context.

Hence, Option 3 is correct.

Explanation:

Options 1, 3, and 4 are four consecutive letters arranged in strict reverse alphabetical order:
– NMLK = reverse of K L M N
– RQPO = reverse of O P Q R
– UTSR = reverse of R S T U
Option 2 (WXUV) is not a single continuous reverse (or forward) sequence. It forms two ascending pairs (W->X and U->V) with a break between X and U. The reverse of U V W X would be X W V U, not W X U V. Hence, Option 2 is different.

Explanation:

Let present ages be: Ravish = 3x, Shikha = 8x.

After 6 years, (3x + 6)/(8x + 6) = 4/9.

Cross-multiplying: 9(3x + 6) = 4(8x + 6) => 27x + 54 = 32x + 24 => 30 = 5x => x = 6.

Hence Ravish’s present age = 3x = 18 years. Check: After 6 years, ages are 24 and 54, ratio 24:54 = 4:9. Therefore, option 1.

Explanation:

A number divisible by 3, 4, 5, 6, and 8 must be a multiple of their LCM. LCM(3,4,5,6,8) = 2^3 * 3 * 5 = 120.

For the least perfect square multiple of 120, make all prime exponents even: 120 = 2^3 * 3^1 * 5^1 → multiply by 2 * 3 * 5 to get 2^4 * 3^2 * 5^2 = (60)^2 = 3600.

Thus, 3600 is the smallest perfect square divisible by all the given numbers.

Explanation:

Perimeter (circumference) of a circle = 2πr; Area of a circle = πr^2.

If they are numerically equal: 2πr = πr^2.

Dividing both sides by π gives 2r = r^2. Rearranging: r^2 − 2r = 0 ⇒ r(r − 2) = 0. Thus r = 0 or r = 2.

Radius cannot be zero for a non-degenerate circle, so r = 2 units.

Therefore, option 2 is correct.

Explanation:

Recognize the pattern: the nth term is n^3 − n^2 = n^2(n − 1).
Check:
– n=1: 1^3 − 1^2 = 0
– n=2: 8 − 4 = 4
– n=3: 27 − 9 = 18
– n=4: 64 − 16 = 48
– n=5: 125 − 25 = 100
Thus, next term (n=6): 6^3 − 6^2 = 216 − 36 = 180.