Explanation

Required capacity = HCF of 120 litres and 56 litres

= 8 litres = 8000 cc [∴ 1 litres = 1000 cc]

Explanation

The Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

In this series, the next number is found by adding the two numbers before it.

Hence, the next term in the series is 8 + 13 = 21.

Explanation

The diameter of a circle is considered to be the longest chord because it joins to points on the circumference of a circle.

Explanation

A sequence is arithmetic if the common difference of all terms of a sequence is the same.

A sequence is geometric if the common ratio of all terms of sequence is the same.

A common difference is the difference between consecutive numbers in an arithmetic sequence

Sh14-8-2023

Explanation

Let, a and b two given numbers.

Let,

$A_1,A_2,A_3.............A_n$ be Arithmetic means between a and b.

$a,A_1,A_2,A_3.............A_n,b$ are in A.P.

$a+A_1+A_2+A_3+......A_n+b=\left(\frac{n+2}{2}\right)\left(a+b\right)$      (first term is =a, last term=b, number of term=n+2)

  $A_1,A_2,A_3.............A_n=\frac{\left(n+2\right)\left(a+b\right)}{2}-(a+b)$

 $=\left(a+b\right)\left[\frac{n+2}{2}-1\right]$

 $=\left(a+b\right)\left[\frac{n+2-2}{2}\right]$

 $=n\left(\frac{a+b}{2}\right)$

$SH14-8-2023$

Explanation

To evaluate this logically:

(i) Passing the CSS examination gives happiness.

(ii) Happiness produces a smile.

From these, we can infer that passing the CSS examination results in happiness, and happiness leads to a smile. Thus, we can logically conclude that passing the CSS examination results in a smile (since happiness, which follows from passing CSS, leads to a smile).

Therefore, statement (iii) "Passing CSS examination gives smile" follows logically from (i) and (ii).

The correct answer is:

(a) True

Explanation

Total Cows= 10

Died Except 4 = 6

Left = 4

Explanation

To solve the series $(-3) times (-3) times (-3)$, let's break it down:

1. First multiplication:

   $$(-3)\times (-3)=9$$

   (Multiplying two negative numbers gives a positive result.)

2. Next, multiply the result by $-3$:

   $$9\times (-3)=-27$$

Explanation

The square root of -25 is 5i, where i is the imaginary unit (√-1). 

Since the square root of a negative number is not a real number, we use imaginary numbers to express it.  

So, √(-25) = 5i.

Explanation

We are given: (-2x)^3

To solve this, we need to cube both -2 and x separately:

(-2)^3 * x^3

Calculating the cube of -2:

(-2) * (-2) * (-2) = -8

So, the expression becomes:

-8 * x^3