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Question : If $3 \tan \theta=4$, then what is the value of $7 \sin \theta-2 \cos \theta$?
Option 1: $\frac{12}{5}$
Option 2: $4$
Option 3: $\frac{22}{5}$
Option 4: $\frac{17}{5}$
Correct Answer: $\frac{22}{5}$
Solution : Given, $3 \tan \theta=4$ ⇒ $\tan\theta=\frac43=\frac{\text{Perpendicular}}{\text{Base}}$ Using the Pythagoras theorem, $\small\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2$ ⇒ $h^2=4^2+3^2$ ⇒ $h^2=16+9$ ⇒ $h^2=25$ ⇒ $h=5$ We know, $\sin\theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}$ and $\cos\theta=\frac{\text{Base}}{\text{Hypotenuse}}$ ⇒ $\sin\theta=\frac{4}{5}$ and $\cos\theta=\frac35$ So, $7 \sin \theta-2 \cos \theta=7\times\frac{4}{5}-2\times\frac{3}{5}=\frac{28}{5}-\frac{6}{5}=\frac{22}{5}$ Hence, the correct answer is $\frac{22}{5}$.
Question : If the sewage is fully oxidized, the nitrogen is in the form of
Option 1: Nitrites
Option 2: Ammonia
Option 3: Nitramines
Option 4: Nitrates
Correct Answer: Nitrates
Solution : The correct option is Nitrates.
The presence of Nitrates in waste indicates complete decomposition of organic matter. By converting nitrogen to nitrate and then potentially removing it through denitrification, sewage treatment facilities aim to minimise the environmental impact of nitrogen discharge.
Question : If $5A=12B=13C$, then find $A: B: C$.
Option 1: $60:65:156$
Option 2: $65:156:60$
Option 3: $156:65:60$
Option 4: $3:12:5$
Correct Answer: $156:65:60$
Solution : Given: $5A=12B=13C$ Let $5A=12B=13C=k$ $⇒A=\frac{k}{5},B=\frac{k}{12},C=\frac{k}{13}$ Ratio of $A:B:C=\frac{k}{5}:\frac{k}{12}:\frac{k}{13}$ $⇒A:B:C=\frac{1}{5}:\frac{1}{12}:\frac{1}{13}$ LCM of $(5, 12, 13) = 780$ Multiplying with it, we get, $⇒A:B:C=\frac{780}{5}:\frac{780}{12}:\frac{780}{13}$ $\therefore A : B : C = 156:65:60$ Hence, the correct answer is $156:65:60$.
Question : Parts of the following sentence are given as options. Identify the segment that contains a grammatical error. He won’t come to school tomorrow, won’t he?
Option 1: He won’t come
Option 2: tomorrow
Option 3: to school
Option 4: won’t he
Correct Answer: won’t he
Solution : The correct choice is the fourth option.
Explanation: The error lies in the structure of the tag question. When the main part of the sentence contains a modal verb (like won't, can't, shouldn't, etc.), the tag question should use the opposite polarity. So,
Question : Which bill passed in the Lok Sabha in 2022 seeks to converge the National Rail and Transportation Institute, Vadodara (a deemed university) to the Gati Shakti Vishwavidyalaya?
Option 1: The Appropriation Bill
Option 2: The Competition (Amendment) Bill
Option 3: Central Universities (Amendment) Bill
Option 4: University Laws (Amendment) Bill
Correct Answer: Central Universities (Amendment) Bill
Solution : The correct option is the Central Universities (Amendment) Bill.
The Lok Sabha approved the Central Universities (Amendment) Bill 2022, facilitating the transformation of the National Rail and Transportation Institute (NRTI), previously deemed a university under the University Grants Commission Act, 1956,
Question : Which states are involved in the joint venture of the Chambal Project?
Option 1: Rajasthan and Haryana
Option 2: Rajasthan and Uttar Pradesh
Option 3: Uttar Pradesh and Madhya Pradesh
Option 4: Rajasthan and Madhya Pradesh
Correct Answer: Rajasthan and Madhya Pradesh
Solution : The correct option is Rajasthan and Madhya Pradesh.
Founded in 1954, the Chambal Valley project is a joint venture on the Chambal River between Rajasthan and Madhya Pradesh. In 1953–1954, Rajasthan and Madhya Pradesh launched a joint venture to begin the
Question : Direction: In the following question, select the related word from the given alternatives.
Hot : Cold :: ?
Option 1: Summer : Sun
Option 2: Germs : Diease
Option 3: Light : Dark
Option 4: Thin : Big
Correct Answer: Light : Dark
Solution : Given:
The relationship is that hot is the opposite of cold. They are antonyms representing opposite temperature conditions.
Now, let's apply the same logic to all the options of the analogy:
Option first: Summer : Sun
The
Question : The least number to be subtracted from 36798 to get a number which is exactly divisible by 78 is:
Option 1: 18
Option 2: 60
Option 3: 38
Option 4: 68
Correct Answer: 60
Solution : The given number is 36798. The divisor is 78. Divide 36798 by 78 and get the remainder. Remainder = $\frac{36798}{78}$ → 60 So, the least number to be subtracted from 36798 to get a number exactly divisible by 78 is 60. Hence, the correct answer
Question : Comprehension: Read the following passage and answer the question.
In the years leading up to the Russian Revolution of 1917, the country had a succession of wars. These were the Crimean War, the Russo-Turkish War, the Russo-Japanese War, and World War I. All of these required a lot from the state, including tax dollars and manpower. Russia suffered defeats in all, except against Turkey. This series of wars caused great discontent among the people and caused suffering in the country's economy and government.
Along with these wars, there were three major parties that contributed to the cause of the revolution. First, there were the peasants, who maintained the majority of the population in Russia. They were excessively poor and could barely escape famine from harvest to harvest. The population boom in Russia from 1867 to 1896 was felt most drastically by the peasants. The increase of 30 million people in less than 30 years was so great that the land for the peasants' disposal did not increase sufficiently. The government tried to help, but the war took precedence. Second, there was a rise in the industrial working class. These workers were employed in the mines, factories, and workshops of the major cities. They suffered low wages, poor housing, and many accidents. Again, the government tried to help by passing factory acts to restrict the number of hours one could work. However, their efforts were on too small a scale to have any real effect. As a result, there were many strikes and constant conflicts between the workers and the police. Lastly, the tsar of Russia was the cause of much disapproval. Tsar Nicholas II was much more interested in his family life than matters of the state. He had an obsession with retaining all his privileges and the belief that he was chosen by God to rule. Also, he didn't understand the forces of industrialization and nationalism that were growing throughout Russia. His disregard for the struggles of the people led them to lose faith in him and the longstanding tradition of autocracy. The people were not content and were ready to revolt. They just needed a good reason and a strong leader.
Question: On the basis of the information given in the passage, which of the following statements is NOT correct?
Option 1: Tsar Nicholas II was much more interested in matters of the state than his family life.
Option 2: Peasants maintained the majority of the population in Russia.
Option 3: There was a population boom in Russia from 1867-1896.
Option 4: The series of war caused great discontent among the people and caused suffering in the Russia's economy and government.
Correct Answer: Tsar Nicholas II was much more interested in matters of the state than his family life.
Solution : The correct choice is the first option.
The passage states the opposite: "Tsar Nicholas II is much more interested in his family life than matters of state." The passage
Question : In November 2022, the Supreme Court upheld the validity of the 103 constitutional amendment providing _______ per cent reservation to people belonging to economically weaker sections (EWS).
Option 1: 5
Option 2: 15
Option 3: 10
Option 4: 20
Correct Answer: 10
Solution : The correct answer is 10.
On November 7, 2022, the Supreme Court affirmed the constitutionality of the 103rd Constitution Amendment 2019, which allows 10% of the forward castes' share to go to the EWS, by a vote of 3-2.
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