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Question : $x$ varies inversely as the square of $y$. Given that $y=2$ for $x=1$, the value of $x$ for $y=6$ will be equal to:
Option 1: 3
Option 2: 9
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{9}$
Correct Answer: $\frac{1}{9}$
Solution : $x$ varies inversely as a square of $y$. $⇒x=\frac{a}{y^2}$, where $a$ is constant At $y=2, x=1$ $⇒1=\frac{a}{2^2}$ $⇒a=4$ If $y=6$, then, $\therefore x=\frac{4}{6^2}=\frac{4}{36}=\frac{1}{9}$ Hence, the correct answer is $\frac{1}{9}$.
Question : Who said that "India's soul lives in villages"?
Option 1: Vinoba Bhave
Option 2: Jayaprakash Narayan
Option 3: Jawaharlal Nehru
Option 4: Mahatma Gandhi
Correct Answer: Mahatma Gandhi
Solution : The correct answer is Mahatma Gandhi.
"The soul of India lives in its villages", was declared by Mahatma Gandhi. He always believed in India's traditional value framework. His attire, style of life and way of worship were all inspired by rural India. He consistently
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Daniel talks to people about the right to life. He says, “We have the right to live in freedom and safety!” but the people do not (1)_______ and they say that the War is a big deal and it is not up to us nor up to the government. The government knows what to do and only the government can decide (2)______ is best. And if the government says that there must be war, then it must be so. Daniel does not accept this and asks if there is a better solution. As all wars end with agreements, can’t we make the agreements without fighting? Can’t the government solve this (3)_________? Isn’t that the reason we have a government in the first place? He decides to (4)______ to people in his government. He decides to write to them and let them know what he thinks. He knows one opinion does not matter much, but he also knows that if everyone in his own country and on the other side would do this, there will (5)________ be no more wars.
Question:
Select the most appropriate option to fill in the blank number 1.
Option 1: grant
Option 2: agree
Option 3: consent
Option 4: announce
Correct Answer: agree
Solution : The correct choice is the second option.
"Agree" means to have the same opinion about something or to concur, and is the appropriate choice for the blank, which helps in conveying the intended meaning.
Question : If $x=a(\sin\theta+\cos\theta), y=b(\sin\theta-\cos\theta)$, then the value of $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –2
Correct Answer: 2
Solution : Given: $x=a(\sin\theta+\cos\theta), y=b(\sin\theta-\cos\theta)$ So, $\frac{x}{a}=(\sin\theta+\cos\theta), \frac{y}{a}=(\sin\theta-\cos\theta)$ Now, $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ = $(\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2$ = $\sin^2\theta+2×\sin\theta×\cos\theta+\cos^2\theta+\sin^2\theta-2×\sin\theta×\cos\theta+\cos^2\theta$ = $\sin^2\theta+\cos^2\theta+\sin^2\theta+\cos^2\theta$ = $1+1$ = $2$ Hence, the correct answer is $2$.
Question : Syed Ahmad Khan founded Muhammadan Anglo-Oriental College in _________ in 1875.
Option 1: Aligarh
Option 2: Calcutta
Option 3: Delhi
Option 4: Lahore
Correct Answer: Aligarh
Solution : The correct answer is Aligarh.
Sir Syed Ahmad Khan founded Muhammadan Anglo-Oriental College in Aligarh in 1875. It was started as a primary school in the initial stage. It was inspired by the Cambridge education system. It started operations on Queen Victoria's 56th birthday,
Question : From the peak of a hill 300 m high, the angle of depression of two sides of a bridge lying on the ground are $45°$ and $30°$ (both ends of the bridge are on the same side of the hill). Then the length of the bridge is:
Option 1: $300(\sqrt3 - 1)$ m
Option 2: $300(\sqrt3 + 1)$ m
Option 3: $300\sqrt3$ m
Option 4: $\frac{300}{\sqrt3}$ m
Correct Answer: $300(\sqrt3 - 1)$ m
Solution : $AB$ = height of peak = 300 m $CD$ = length of Bridge We are given the angle of depression, i.e., $\angle EAC = 45°$ and $\angle EAD = 30°$ ⇒ $\angle ACB = 45°$ and $\angle ADB = 30°$ Now, \(In
Question : Directions: Seeta and Geeta started walking from point A. Seeta walks 6 km towards North and then takes a right turn and walks 3 km. She then takes a right turn and walks for 6 km. She again takes a left turn, walks 3 km, and reaches a point B. Geeta walks for 3 km towards the west, takes a left turn, and walks for 6 km. She then takes a left turn, walks 9 km, and reaches point C. How far is point B from point C?
Option 1: 3 km
Option 2: 4 km
Option 3: 9 km
Option 4: 6 km
Correct Answer: 6 km
Solution : Firstly, we will draw the diagram as per the given instructions –
So, from the above, the distance between points B and C is 6 km. Hence, the fourth option is correct.
Question : A sum of Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will the same sum become in 3 years?
Option 1: Rs. 1025
Option 2: Rs. 1042
Option 3: Rs. 1052
Option 4: Rs. 1024
Correct Answer: Rs. 1052
Solution : Given: Principal = Rs. 800, Amount = Rs. 956, and Time = 3 years Rate of interest, $R$ = 4% for extra interest Use the formula below. Extra Simple Interest = $\frac{\text{Principle×Rate×Time}}{100}$ = $\frac{800×3×4}{100}$ = Rs. 96 So, the total amount received = 956
Question : Directions: Which two signs should be interchanged to make the given equation correct? 95 × 5 + 19 ÷ 2 − 21 = 36
Option 1: ÷ and ×
Option 2: + and −
Option 3: ÷ and −
Option 4: + and ×
Correct Answer: ÷ and ×
Solution : Given: 95 × 5 + 19 ÷ 2 − 21 = 36
Replace the given symbols in the options one by one with the original symbols in the given equation. First option: ÷ and × ⇒ 95 ÷ 5 + 19 × 2
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: Which of the following words is the ANTONYM of the word 'precedence' used in the passage?
Option 1: Orders
Option 2: Sequences
Option 3: Disruptions
Option 4: Successions
Correct Answer: Disruptions
Solution : The correct choice is the third option.
While precedence refers to the condition of being considered more important or having a higher priority, disruptions indicate the act of interrupting or causing a disturbance, suggesting a lack of order or priority.
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