Correct Answer: 7 : 32

Solution : Let's check the options –
First option: 5 : 23; 5 × 4 = 20; 20 + 3 = 23
Second option: 4 : 19; 4 × 4 = 16; 16 + 3 = 19
Third option: 2 : 11; 2 × 4 = 8; 8 + 3 = 11
Fourth option: 7 : 32; 7 × 4 = 28; 28 + 4 = 32

So, the fourth option is different from the other three options as here, the number being added is 4 instead of 3. Hence, the fourth option is correct.

Correct Answer: 37

Solution : The teacher wants to arrange the students in a square formation, where the number of rows equals the number of columns.
The number of students, 1369, is a perfect square (since 37² = 1369).
Therefore, the teacher can arrange the students in 37 rows with 37 students in each row.
Hence, the correct answer is 37.

Correct Answer: it is raining cats and dogs

Solution : The correct choice is the second option.

Explanation: The correct idiom for heavy rainfall is "raining cats and dogs". This idiom is well-established and widely understood to convey the idea of a very heavy downpour.

So, the correct sentence would be: "As it is a rainy season, it is raining cats and dogs."

Correct Answer: Damage

Solution : The correct answer is Damage.

The primary goal of planning for disaster is to reduce the damage. In the planning process of disasters, the estimate of the range of risks and abilities should be prepared so that the minimum damage to life and property will occur during disasters. Planning is done to provide relief measures after the disaster and Rehabilitation programs and to protect the environment.

Correct Answer: 74th Amendment Act 1992

Solution : The correct option is the 74th Amendment Act 1992.

The provisions related to Municipalities in the Indian Constitution were added by the 74th Amendment Act of 1992. This amendment aimed at promoting local self-governance, and empowering urban local bodies. Some key features include the establishment of Municipalities in urban areas, the creation of three types of Municipalities (Municipal Corporation, Municipal Council, and Nagar Panchayat), and the provision for reservation of seats for Scheduled Castes, Scheduled Tribes, and women in these local bodies.

Correct Answer: 4

Solution : Given:
1. TRIM ⇒ 6794
2. MINT ⇒ 3679

By comparing the coded words, we find that –
In words 1 and 2, the common letters are M, I, and T and the common codes are 7, 9, and 6.
The remaining letters and codes in word 1 are R and 4, and in word 2, are N and 3.
Finally, M/I/T→7/9/6; R→4; N→3

So, the code for R is 4 in the code language. Hence, the second option is correct.

Correct Answer: 100

Solution : The correct answer is 100.

The Mahatma Gandhi National Rural Employment Guarantee Act was passed by the Indian government in 2005. According to this act, there is a legal guarantee for 100 days of wage employment in a financial year for every adult member of a rural household who demands employment and is willing to do unskilled manual work.

Correct Answer: Neither I nor II

Solution : The correct option is Neither I nor II.

Neither of the options is correct. In basketball, a team typically consists of 5 players, not 11. Volleyball teams also usually have six players on the court at a time, not 11.

Correct Answer: Delhi-Kolkata-Mumbai-Chennai

Solution : The correct option is Delhi-Kolkata-Mumbai-Chennai.

The Golden Quadrilateral is a network of four major cities in India, forming a quadrilateral shape. It connects the cities of Delhi in the north, Mumbai in the west, Chennai in the south and Kolkata in the east. This extensive highway system is a vital transportation route, linking these urban centres, and promoting economic development, and connectivity across the country.

Correct Answer: $\frac{h^2-x^2}{2h}$ metre

Solution :
Given:
AB = Height of tree = $h$ metre
Let the height at which the tree is broken, AC = $y$ metre
BC = CD = Broken part of tree = $(h – y)$ metre
∴ In ∆ ACD,
AC² + AD² = CD²
⇒ $y^2 + x^2 = (h – y)^2$
⇒ $y^2 + x^2 = h^2 + y^2 – 2hy$
⇒ $x^2 = h^2 – 2hy$
⇒ $2hy = h^2 – x^2$
$\therefore y =\frac{h^2-x^2}{2h}$ metre
Hence, the correct answer is $\frac{h^2-x^2}{2h}$ metre.