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Question : Simplify the expression $\frac{s^2+t^2+2 s t-u^2}{s^2-t^2-2 t u-u^2}$, provided $(s+t+u) \neq 0$.
Option 1: $\frac{s+t-u}{s-t-u}$
Option 2: $\frac{s+t+u}{s-t+u}$
Option 3: $\frac{s-t-u}{s+t-u}$
Option 4: $\frac{s-t+u}{s+t+u}$
Correct Answer: $\frac{s+t-u}{s-t-u}$
Solution : Given: $\frac{(s^2+t^2+2 s t)-u^2}{s^2-(t^2+2 t u+u^2)}$ We know $\small a^2+b^2 +2ab = (a+b)^2$ and $\small a^2+b^2-2ab = (a-b)^2$ So, $\frac{(s^2+t^2+2 s t)-u^2}{s^2-(t^2+2 t u+u^2)}=\frac{(s+t)^2 - u^2}{s^2 - (t+u)^2}$ $=\frac{(s+t+u)(s+t-u)}{(s+t+u)(s-t-u)}$ [using $\small a^2 - b^2 = (a+b)(a-b)$] $=\frac{s+t-u}{s-t-u}$ Hence, the correct answer is $\frac{s+t-u}{s-t-u}$.
Question : Who among the following is not a moderate?
Option 1: Pherozeshah Mehta
Option 2: Surendranath Banerjee
Option 3: Womesh Chandra Bonnerjee
Option 4: Bal Gangadhar Tilak
Correct Answer: Bal Gangadhar Tilak
Solution : The correct answer is Bal Gangadhar Tilak.
Bal Gangadhar Tilak disagreed with its moderate stance, particularly about the struggle for self-government. He started a large-scale movement for independence by focusing on religious and cultural renewal.
Question : A alone can do a work in 16 days and B alone can do the same work in 12 days. If they worked together on it for 4 days and A left. How long did B take to finish the remaining work?
Option 1: 7 days
Option 2: 5 days
Option 3: 6 days
Option 4: 8 days
Correct Answer: 5 days
Solution : Time taken by A to do the work = 16 days Part of work done by A in a day = $\frac{1}{16}$ Time taken by B to do the work = 12 days Part of work done by B in a day = $\frac{1}{12}$
Question : The joint sector industry is one of the classifications of industries based on ______.
Option 1: source of raw material
Option 2: capital investment
Option 3: bulk and weight of raw material
Option 4: ownership
Correct Answer: ownership
Solution : The correct answer is ownership.
Ownership Industries can be divided into four categories: joint, cooperative, state-owned, or public and private. Industries in the private sector are owned and run by a single person or a group of people.
Question : How many tax slabs are classified in the GST Bill?
Option 1: Seven
Option 2: Three
Option 3: Eight
Option 4: Four
Correct Answer: Four
Solution : The correct option is Four.
India's goods and services tax (GST) has four tax slabs.
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. DP, EY, FJ, ?
Option 1: GX
Option 2: GS
Option 3: GT
Option 4: GW
Correct Answer: GW
Solution : Given: DP, EY, FJ, ?
Add 1 and 9 to the positional value of the first and second letters respectively of the previous term to obtain the next term in the series – First letter of the series→D + 1 = E; E + 1
Question : Subsidiary alliance treaty was imposed on Awadh in ______.
Option 1: 1802
Option 2: 1803
Option 3: 1801
Option 4: 1804
Correct Answer: 1801
Solution : The correct answer is 1801.
The subsidiary alliance treaty was imposed on Awadh in 1801. This was one of the measures taken by the British East India Company to extend its control and influence over various Indian princely states during the period of British
Question : Directions: In the following question, select the related number from the given alternatives. 20 : 30 :: ? : 72
Option 1: 56
Option 2: 59
Option 3: 68
Option 4: 61
Correct Answer: 56
Solution : Given: 20 : 30 :: ? : 72
In the given number pairs, add squares of consecutive numbers to itself. Like, 20 : 30→(4)2 + 4 = 16 + 4 = 20; (5)2 + 5 = 25 + 5 = 30 Similarly, follow
Question : Directions: Rakesh is six ranks ahead of Tanvir in a class of 42 students. If Tanvir's rank is eighteenth from the last, then what is Rakesh's rank from the start?
Option 1: 14th
Option 2: 15th
Option 3: 19th
Option 4: 17th
Correct Answer: 19th
Solution : Given: Tanvir is 6 positions behind Rakesh in a class of 42 students. Tanvir is ranked 18th from the bottom.
Rakesh's position from last is (18 + 6) = 24 The rank of Rakesh from the start is 42 – 24 + 1 = 19
Question : What organic compounds are found in the cells of apples, and when these are exposed to oxygen in the air, for example, through slicing, the oxygen causes a reaction?
Option 1: Phenols
Option 2: Carboxylic acid
Option 3: Resorcinol
Option 4: Cyclohexanol
Correct Answer: Phenols
Solution : The correct answer is Phenols.
Phenols are found in the cells of apples, and when these are exposed to oxygen in the air, for example, through slicing, the oxygen causes a reaction. Phenols are the organic compounds which are sometimes known as phenolics.
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