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Question : If $2\left (\cos^{2}\theta-\sin ^{2}\theta \right)=1$; ($\theta$ is a positive acute angle), then $\cot\theta$ is equal to:
Option 1: $-\sqrt3$
Option 2: $1\frac{1}{\sqrt3}$
Option 3: $1$
Option 4: $\sqrt3$
Correct Answer: $\sqrt3$
Solution : Given: $2\left (\cos^{2}\theta-\sin ^{2}\theta \right)=1$ ⇒ $2\cos^{2}\theta-2\sin ^{2}\theta=\cos^{2}\theta+\sin ^{2}\theta$ ⇒ $\cos^2\theta = 3\sin^2\theta$ ⇒ $\frac{\cos^2\theta}{\sin^2\theta} = 3$ ⇒ $\cot^2\theta=3$ ⇒ $\cot\theta = \pm\sqrt3$ As $\theta$ is a positive acute angle, So, $\cot\theta = \sqrt3$ Hence, the correct answer is $\sqrt3$.
Question : Select the option that can be used as a one-word substitute for the given group of words. A person who believes that all events are predetermined or subject to fate
Option 1: Fatalist
Option 2: Credulous
Option 3: Egotist
Option 4: Aristocrat
Correct Answer: Fatalist
Solution : The correct choice is the first option.
A fatalist is a person who believes that all events are predetermined or subject to fate. This term succinctly describes someone who accepts that events are unavoidable and predetermined.
The meanings of the other words are as follows:
Question : The famous mathematician Srinivasa Ramanujan was born in:
Option 1: Madras (now Chennai)
Option 2: Kumbakonam
Option 3: Namakkal
Option 4: Erode
Correct Answer: Erode
Solution : The correct answer is Erode.
Srinivasa Ramanujan was a brilliant mathematician born in 1887 in Erode, India. Every year, on his birth date of December 22nd, National Mathematics Day is celebrated in India. Ramanujan made significant contributions to mathematical analysis, number theory and infinite
Question : Comprehension:
Read the given passage and answer the questions that follow.
Although pollution of land, sea, and air has been well documented, the latest and the least recognised version is the swelling tide of noise which is engulfing urban as well as rural areas. This has long-term implications for the ecology, health and productivity of a fast-developing country like India.
Unlike other pollutants, noise lacks visibility, seldom registering on the consciousness, except as a trifling irritant to be dismissed at will and therefore less likely to be perceived as a threat. Available data indicates that noise does pose a threat to health and is known to have caused a number of complications. Declining productivity among workers in certain industries has been directly correlated with noise levels, particularly those under constant exposure to the menace.
The first-ever survey of the impact of noise on health, conducted by All India Institute of Medical Sciences (AlIMS), has established that noise not only impairs the physical and psychological functioning of the human organism but also causes nausea, vomiting, pain, hypertension and a lot of other complications, including cardio-vascular complaints. A study by the Post Graduate School of Basic Medical Sciences, Chennai, confirms such conclusions. In 50 per cent of industries, it was found that workmen exposed to higher intensities of noise in occupational capacities were often irritated, short-tempered, impatient and more likely to resort to agitation and disrupt production. This was true of units in heavy industrial pockets in and around the four metropolitan centres.
Recreational noise, another ugly facet, is becoming more widespread in cities and towns. Loudspeakers are turned at full volume during marriages, festivals, jaguars, and musical programmes, particularly at night, without the least consideration for others. Even at 50 dB, sound can awaken a person from a deep slumber. As experiments have shown, loudspeakers with output from 60 to 80 dB cause the pupils of a slumbering person to dilate, with increasing intake of oxygen, resulting in palpitation. The effect is more pronounced in narrow lanes. TV sets are played at full volume at prime time, invariably disturbing neighbours. Noise-making seems to have become the latest status symbol, be it an election campaign, slogan shouting, or advertising ownership of a TV set.
Question:
Noise can be differentiated from other pollutants because:
Option 1: it does not impact the productivity of the workers in industries
Option 2: it is regarded as a small irritant which may be easily dismissed
Option 3: it is not detrimental to our health in any way
Option 4: it is prevalent only in the urban areas of the country
Correct Answer: it is regarded as a small irritant which may be easily dismissed
Solution : The correct choice is the second option.
The passage in the second paragraph highlights that noise is differentiated from other pollutants primarily because it is regarded as a small irritant that may be easily
Question : Which of the following committees recommended the inclusion of fundamental duties in the Constitution of India?
Option 1: Swaran Singh Committee
Option 2: Sarkaria Commission
Option 3: Rajamannar Committee
Option 4: Balwant Rai Mehta Committee
Correct Answer: Swaran Singh Committee
Solution : The correct answer is the Swaran Singh Committee.
The inclusion of fundamental duties in the Constitution of India was recommended by the "Swaran Singh Committee," or the Committee on Fundamental Duties. This committee was constituted by the Government of India in 1976,
Question : Direction: In the following question a word is followed by four other words, one of which can not be formed by using the letters of the given word. Find this word.
COMMERCIALISM
Option 1: CROME
Option 2: LANCER
Option 3: MISER
Option 4: OSCAR
Correct Answer: LANCER
Solution : Given:
First option: CROME;
All the letters of the above word are present in the given word COMMERCIALISM.
Second option: LANCER;
Letter N of the above word is not present in the given word COMMERCIALISM. So, LANCER can not be formed by using the
Question : A can do work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?
Option 1: 12 days
Option 2: 20 days
Option 3: 15 days
Option 4: 8 days
Correct Answer: 8 days
Solution : Given: A can do work in 12 days and B in 24 days. Total work = LCM of (12, 24) = 24 units Efficiency of A = $\frac{24}{12}$ = 2 units/day Efficiency of B = $\frac{24}{24}$ = 1 units/day Total efficiency of A and
Question : If p : q = 4 : 5, q : r = 3 : 4 and r : s = 2 : 5, then p : s is:
Option 1: 2 : 5
Option 2: 6 : 25
Option 3: 5 : 2
Option 4: 25 : 6
Correct Answer: 6 : 25
Solution : Here, we have, $\frac{p}{q} =\frac{4}{5}, \frac{q}{r} =\frac{3}{4}, \frac{r}{s} = \frac{2}{5}$ Now first, take $\frac{p}{q} =\frac{4}{5}$ and $\frac{q}{r} =\frac{3}{4}$ As q is common in both. So, it should be equal for both Multiply $\frac{p}{q}$ by 3 and $\frac{q}{r}$ by 5 $So,\frac{p}{q} =\frac{4×3}{5×3}$ and $\frac{q}{r}=\frac{3×5}{4×5}$
Question : Choose the sentence with no spelling errors.
Option 1: Take it up, and write your own storry.
Option 2: Take it up, and writte your on story.
Option 3: Take it up, and write your own story.
Option 4: Take it up, and wrrite your own story.
Correct Answer: Take it up, and write your own story.
Solution : The correct choice is the third option.
Question : Comprehension: An endangered species is a type of organism that is threatened by extinction. Species become endangered for two main reasons: loss of habitat and loss of genetic variation. A loss of habitat can happen naturally. Dinosaurs, for instance, lost their habitat about 65 million years ago. The hot, dry climate of the Cretaceous period changed very quickly, most likely because of an asteroid striking the Earth. The impact of the asteroid forced debris into the atmosphere, reducing the amount of heat and light that reached Earth's surface. The dinosaurs were unable to adapt to this new, cooler habitat. Dinosaurs became endangered, then extinct. Human activity can also contribute to a loss of habitat. Development for housing, industry, and agriculture reduces the habitat of native organisms. This can happen in several different ways.
Development can directly eliminate habitat and native species. In the Amazon rainforest of South America, developers have cleared hundreds of thousands of acres. To "clear" a piece of land is to remove all trees and vegetation from it. The Amazon rainforest is cleared for cattle ranches, logging, and urban use. Development can also endanger species indirectly. Some species, such as fig trees in the rainforest, may provide habitat for other species. As trees are destroyed, species that depend on that tree habitat may also become endangered. Tree crowns provide habitat in the canopy, or top layer, of a rainforest. Plants such as vines, fungi such as mushrooms, and insects such as butterflies live in the rainforest canopy. So do hundreds of species of tropical birds and mammals, such as monkeys. As trees are cut down, this habitat is lost. Species have less room to live and reproduce.
Based on the passage above, choose the correct option for the following question.
Question
Which of the following do not live in the canopy of the Amazon rain forests?
Option 1: Monkey
Option 2: Crocodiles
Option 3: Vines
Option 4: Butterflies
Correct Answer: Crocodiles
Solution : The correct choice is the second option (refer to the second paragraph).
Crocodiles are not typically found in the canopy of the Amazon rainforest; they are more associated with aquatic habitats. The other options—monkeys, vines, and butterflies—are mentioned in the passage as species that
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