Explanation

We are given two equations:

Let:

• Cost of one apple = x

• Cost of one orange = y

From the problem:

1. $4x + 2y = 30$
   

2. $$x+3y=15

   
   Step 1: Solve the system of equations

Equation (1):
$4x + 2y = 30$
Divide the whole equation by 2:
→ $2x + y = 15$→ (3)

Equation (2):
$x + 3y = 15$ → (2)

Step 2: Solve equations (2) and (3)

From (3):
$y = 15 - 2x$ → (4)

Substitute (4) into (2):
$x + 3(15 - 2x) = 15$
$x + 45 - 6x = 15$
$-5x+45=15$
$-5x=15-45=-30$
$$x=−30−5=6

Explanation

 We are given:

• Red balls = 8

• Blue balls = 7

• Green balls = 6

Total balls = 8 + 7 + 6 = 21

We are asked to find the probability that the ball is neither red nor green.

That means we want the probability that the ball is blue.

Number of favorable outcomes = Number of blue balls = 7

Probability = (Favorable outcomes) / (Total outcomes)

= 7/31

=1/3
$$721=13frac{7}{21} = frac{1}{3}

Explanation

Given:

• 10 lb of meat at Rs 1.69 per lb

• 20 lemons at Rs 60 per dozen

Step 1: Cost of meat

$$10 text{ lb} times 1.69 = 16.90$$

Step 2: Cost of lemons

• 1 dozen = 12 lemons

• So, price per lemon = $frac{60}{12} = 5$ Rs per lemon

• 20 lemons =$20\times 5=100$ Rs

  Step 3: Total cost

$$16.90 + 100 = 116.90$$

 Correct answer: (D) None of these

Explanation

2x=32

Step 1: Express 32 as a power of 2

32=2^5

Step 2: Set the exponents equal

2^x=2^5⇒x=5

 Correct answer: 5

Explanation

We are given:

• Product of two numbers = 1320

• HCF (Highest Common Factor) = 6

We are asked to find the LCM (Least Common Multiple).

Key formula:

$$\text{Product of two numbers}=\text{HCF}\times \text{LCM}$$

Substitute values:

$$1320 = 6 times text{LCM}$$LCM=32061​=220

Explanation

The greatest source of religious knowledge, according to revealed religions, is revelation.

Revealed Religions:

Many major religions, including Judaism, Christianity, and Islam

Consider revelation to be a primary source of religious knowledge.

Explanation

 During the Islamic Golden Age, Baghdad was the primary center of learning and scholarship, particularly with the establishment of the "House of Wisdom" 

Explanation

Optical disk drives (like CD, DVD, and Blu-ray drives) use laser technology to read and write data on optical discs.

The laser beam detects the pits and lands on the disc surface to interpret data.

Explanation

Horses have a unique anatomy and a stay apparatus

That allows them to sleep standing up, but they lack the anatomical structure (a proper “down apparatus”) to sit like dogs or cats. 

Explanation

The four pillars of the state are traditionally considered to be:

1. Legislature

2. Executive

3. Judiciary

4. Media (also referred to as the Fourth Estate)

Media plays a crucial role in shaping public opinion and holding other pillars accountable.