Explanation

The LCM of 6, 8, and 12 is 24.

Let's denote the number as 24k + x, where x is the remainder.

Given the remainders:

24k + x ≡ 5 (mod 6)

24k + x ≡ 7 (mod 8)

24k + x ≡ 11 (mod 12)

From the given remainders, we can observe that:

6 - 5 = 1

8 - 7 = 1

12 - 11 = 1

The number is of the form 24k - 1.

Now, we need to find the least multiple of 13 in the form 24k - 1.

Let's check the options:

221 = 24 × 9 + 5 (not in the form 24k - 1)

143 = 24 × 6 - 1

143 = 13 × 11

Explanation

Let's denote the number of rabbits as R and the number of peacocks as P.

Given:

R + P = 60 (total heads)

4R + 2P = 192 (total legs)

Multiplying the first equation by 2:

2R + 2P = 120

Subtracting this from the second equation:

2R = 72

R = 36

Explanation

The first 10 even numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

Average = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10

= 110 / 10

= 11

Explanation

Explanation

Let Ali's present age be x.

Hyder's present age = x + 12

Ten years ago:

Ali's age = x - 10

Hyder's age = x + 12 - 10 = x + 2

Given that Ali's age was 1/3 of Hyder's age:

x - 10 = 1/3(x + 2)

3(x - 10) = x + 2

3x - 30 = x + 2

2x = 32

x = 16

Explanation

Explanation

Step 1: Let's denote the two numbers as x and y.
We have two equations:

1. x + y = 28

2. x - y = 4

Step 2: Solve the system of equations.
Adding the two equations eliminates y:
(x + y) + (x - y) = 28 + 4
2x = 32
Step 3: Solve for x.
x = 32 / 2
x = 16
Step 4: Solve for y.
Substitute x into one of the original equations:
16 + y = 28
y = 28 - 16
y = 12
Step 5: Identify the correct pair of numbers.
The numbers are 16 and 12.

Explanation

Laser technology is used in compact disc

Compact Disc is an example of Optical Storage

James T. Russell invented C.D. (Compact Disc).

 co-developed by Philips and Sony to store and play digital audio recordings.

history

 In August 1982, the first compact disc was manufactured.

It was then released in October 1982 in Japan and branded as Digital Audio Compact Disc.

It was released on March 2, 1983, in North America and Europe.

Explanation

The decimal system is base 10, using digits 0–9.

Base 8 → Octal number system (digits 0–7).

Base 16 → Hexadecimal number system (digits 0–9, A–F).

Base 4 → Quaternary number system (digits 0–3).

Explanation

Carbon is a non-metal, found in forms like graphite and diamond.

Copper, iron, and chromium are all metals.