If $$4^{\log_2 x} - 4x + 9^{\log_3 y} - 16y + 68 = 0$$, then $$y - x$$ equals:
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If $$4^{\log_2 x} - 4x + 9^{\log_3 y} - 16y + 68 = 0$$, then $$y - x$$ equals:
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A fruit seller has oranges, apples, and bananas in the ratio 3 : 6 : 7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is:
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The number of real solutions of the equation $$(x^2 -15x + 55)^{x^2 - 5x + 6} = 1$$ is:
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The following table shows the number of employees and their median age in eight companies located in a district.
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H. The highest possible age of an employee of company A is:
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Person A borrows Rs. 4000 from another person B for a duration of 4 years. He borrows a portion of it at 3% simple interest per annum, while the rest at 4% simple interest per annum. If B gets Rs. 520 as total interest, then the amount A borrowed at 3% per annum in Rs. is:
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The number of triangles with integer sides and with perimeter 15 is:
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If $$A = \begin{bmatrix}x_1 & x_2 & 7 \\y_1 & y_2 & y_3 \\z_1 & 8 & 3 \end{bmatrix}$$ is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is:
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The number of factors of 1800 that are multiple of 6 is:
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The following table shows the number of employees and their median age in eight companies located in a district.
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
The median age of employees across the eight companies is:
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Let $$\triangle ABC$$ be a triangle right-angled at B with AB = BC = 18. The area of the largest rectangle that can be inscribed in this triangle and has B as one of the vertices is:
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The number of pairs (x, y) of integers satisfying the inequality $$\mid x - 5 \mid + \mid y - 5 \mid \leq 6$$ is:
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The following table shows the number of employees and their median age in eight companies located in a district.
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
In company F, the lowest possible sum of the ages of all employees is:
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In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like more than one drink is:
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The price of a chocolate is increased by x% and then reduced by x%. The new price is 96.76% of the original price. Then x is:
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Let f and g be two functions defined by $$f(x) = \mid x + \mid x \mid \mid$$ and $$g(x) = \frac{1}{x}$$ for $$x \neq 0$$. If $$f(a) + g(f(a)) = \frac{13}{6}$$ for some real a, then the maximum possible value of $$f(g(a))$$ is:
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The terms of a geometric progression are real and positive. If the p-th term of the progression is q and the q-th term is p, then the logarithm of the first term is
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If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is
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If $$\mid x + 1 \mid + (y + 2)^2 = 0$$ and $$ax - 3ay = 1$$, Then the value of a is
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The number of real solutions of the equation $$x^2 - 10 \mid x \mid - 56 = 0$$ is
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The greatest number among $$2^{300}, 3^{200}, 4^{100}, 2^{100} + 3^{100}$$ is
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The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of n for which the sum of its first n terms is closest to 100, is
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Let $$n$$ be the number of ways in which $$20$$ identical balloons can be distributed among $$5$$ girls and $$3$$ boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then
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Let $$a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_7 25(\log_7 8 - \log_7 4)}$$. Then the value of $$5^a$$ is
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The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is
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The side AB of a triangle ABC is c. The median BD is of length k. If $$\angle BDA = \theta$$ and $$\theta < 90^\circ$$, then the area of triangle ABC is
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Let $$\triangle ABC$$ be a triangle with $$AB = AC$$ and $$D$$ be a point on $$BC$$ such that $$\angle BAD = 30^\circ$$. If E is a point on $$AC$$ such that $$AD = AE$$, then $$\angle CDE$$ equals
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If $$\log_4 x = a$$ and $$\log_{25} x = b$$, then $$\log_x 10$$ is
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If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is
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A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of the apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was
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A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day it starts from point A, goes downstream for 1 hour, then upstream for 1 hour, and repeats this for four more times, that is, 5 upstream and 5 downstream journeys. Then the boat would be
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The number of solutions of the equation $$x_1 + x_2 + x_3 + x_4 = 50$$, where $$x_1 , x_2 , x_3 , x_4$$ are integers with $$x_1 \geq1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0$$ is
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The numbers $$2^{2024}$$ and $$5^{2024}$$ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is
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If $$\theta$$ is the angle between the pair of tangents drawn from the point $$\left(0, \frac{7}{2}\right)$$ to the circle $$x^2 + y^2 - 14x + 16y + 88 = 0$$, then $$\tan \theta$$ equals
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The difference between the maximum real root and the minimum real root of the equation $$(x^2 - 5)^4 + (x^2 - 7)^4 = 16$$ is
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The angle of elevation of the top of a pole from a point A on the ground is $$30^\circ$$. The angle of elevation changes to $$45^\circ$$, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, is
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The number of values of x for which $$C\left(\begin{array}{c}17-x\\ 3x + 1\end{array}\right)$$ is defined as an integer is
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Let ABC be an equilateral triangle, with each side of length k. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is
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Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is
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In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2- wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4- wheeler nor a 2-wheeler. Then the number of people who owned both is
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For some non-zero real values of $$a, b$$ and $$c$$, it is given that $$\mid \frac{c}{a} \mid = 4, \mid \frac{a}{b} \mid = \frac{1}{3}$$ and $$\frac{b}{c} = -\frac{3}{4}$$. If $$ac > 0$$, then $$\left(\frac{b + c}{a}\right)$$
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In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner.
The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively. - S2 and S3 were won by C while A won only S1. - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
The constituency in which B got lower number of votes compared to A and C is
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The number of votes obtained by B in S2 is
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The number of votes obtained by A in S5 is
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Comparing the number votes obtained by A across different constituencies, the lowest number of votes were in constituency
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Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
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Recently, India was in the news again as a world leader - but this time for the wrong reason. According to the Swiss firm IQAirʼs assessment of the air quality of world cities 2023, New Delhi is back to being the worldʼs most polluted capital. New Delhiʼs annual air quality rating is 19 times the World Health Organizationʼs annual limit recommended in 2021 for its pollutant level. The picture is no better as far as the larger Union Territory of Delhi is considered - its annual record of pollutant levels makes it the third most polluted region globally.
Delhi may have hogged the headlines on air pollution, but the problem is far from unique to metropolises. IQAirʼs findings reveal that even lower-tier cities and towns in India are choking because of very poor air quality. Indeed, Begusarai in Bihar is the worldʼs most polluted city. Partly industrialized, housing among others an oil refinery, Begusarai is primarily agrarian. And Begusarai is not an outlier: Mullanpur in Punjab, which is
transitioning to an urban settlement, and Siwan in Bihar are among the 42 Indian cities/towns that are among the 50 most polluted globally.
Many judicial pronouncements have upheld “the right to clean airˮ as a corollary to the fundamental right to life and pushed governments to act. But Delhiʼs bad air is despite the introduction of CNG in public transport and the building of a metro network in the early years of this decade, and in spite of the presence of a Graded Response Action Plan (GRAP) that kicks in when the air quality turns bad and becomes more stringent as the air quality worsens.
Improving air quality across Indian cities requires three fundamental changes. One, governments must turn to science to understand, measure, and monitor the problem. Two, they have to understand that the response will have to include behavioural changes and use a combination of incentives and penalties to achieve this. And three, clean air has to be seen as a common public good. To be sure, it is not just the responsibility of the Centre or a battle for courts to wage, but a fight that states and municipal governments have to be a part of. This is the battle for our future.
The first sentence in the passage mentions that India was in the news again as a world leader. What is the writerʼs intention in pointing this out?
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Based on the information in the passage, who has endorsed the right to clean air?
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In the last sentence of the passage, 'This is the battle for our future', the writer is
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The phrase 'that kicks in' (para 3) means
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Which of the following points is not made by the writer?
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Based on the information in the passage, which one of the following statements is correct?
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The passage below is accompanied by a few questions. Based on the passage, choose the best answer for each question.
Anxiety is an emotion that all people experience from time to time, and we do that for good reasons. It has been built into us; we have inherited it from our evolutionary past because, in general, anxiety has a survival function. It kicks in whenever we sense danger - we freeze, we devote all of our attention to the danger, and our bodies react with a big release of adrenaline, an increase in blood flow to the muscles, getting us ready to run as fast as we can or fight as fiercely as we might.
Anxiety also helps us to focus on things when we have deadlines, and if someone is driving too fast when we cross the road, it helps us to jump out of the way quickly. So, there is nothing wrong with anxiety in general, and in fact, we would have difficulties if we did not experience it to some extent. However, it can get problematic if the danger is imagined rather than real, or is something that is exaggerated. In those cases, particularly if the perceived danger is out of proportion to the real danger, and it is persistent and disabling, then there is a danger of an anxiety disorder.
Scientists are looking at what role genes play in the development of these disorders and are also investigating the effects of environmental factors such as pollution, physical and psychological stress, and diet. Several parts of the brain are key actors in the production of fear and anxiety. Using brain imaging technology and neurochemical techniques, scientists have discovered that the amygdala plays a significant role in most anxiety disorders. By learning more about how the brain creates fear and anxiety, scientists may be able to devise better treatments for these disorders.
The first psychotherapy treatment that was shown to be effective was ‘exposure therapyʼ, which essentially encourages people in a graded way to go into their feared situations and stay in them for as long as they can and build their confidence that way. Another is ‘group cognitive behaviour therapyʼ, a talking therapy that helps people to understand the link between negative thoughts and mood and how altering their behaviour can enable them to manage anxiety and feel in control. There are, of course, drugs that can help people with anxiety, but medication will not cure an anxiety disorder, it can only help to keep it under control while the person receives psychotherapy.
There is plenty of evidence that exercise can help with anxiety problems. When stress affects the brain, with its many nerve connections, the rest of the body feels the impact as well. Exercise and other physical activity produce endorphins, which are chemicals in the brain that act as natural painkillers. Additionally, getting physically tired can help people fall asleep faster and have deeper, more relaxing sleep. As many people suffering from anxiety often have problems with insomnia, just the ability to get a good nightʼs rest can change their perspectives.
Anxiety is a normal but highly subjective human emotion. While normal anxiety serves a beneficial and adaptive purpose, it can also become the cause of tremendous suffering for millions of people. It is important that people recognise excessive anxiety in themselves at the earliest, as treatment can be very successful. Leaving it untreated can be a misery.
Based on the information in the passage, which of the following statements best describes the potential danger associated with anxiety disorder?
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The passage is chiefly concerned with
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In what way might the relationship between exercise or physical activity and anxiety relief suggest a potential solution for individuals with anxiety disorders?
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Which of the following best indicates the relationship between anxiety and survival?
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In the passage, the information about anxiety treatments is organized in which of the following ways?
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Based on the information in the passage, which one of the following statements is correct?
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The studentsʼ picnic plans __________ when it started raining heavily in the morning.
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In a circus where performers share dressing rooms, training spaces and work in a fast-paced environment, the success of a show __________ fostering team-work and
collaboration.
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Sheila keeps interrupting Manohar when he is playing with his friends, but he __________ because she is his younger sister.
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In his address to the candidates contesting the student council elections the Principal said, “If you want others to take you seriously then you must __________ on issues like gender bias and inclusivity.ˮ
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Anil could not go to his friendʼs party, as he had fever and was __________.
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My supervisor seemed to be in a bad mood because he __________ when I asked if I could leave an hour early.
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All the employees agreed that the new regulations had __________ positive changes in the workplace.
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The negotiations are unsuccessful, and the Boardsʼ hopes to continuing talks on a future deal seems to be increasingly improbable.
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While the bustling city streets were filled with the cacophony of honking horns and chatter of pedestrians, the serene countryside, where time seemed to move at a slower pace, provide a welcome retreat for their seeking solace amidst the chaos of urban living.
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I had been having a headache, so I will not attend the meeting.
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He is very careless and has loosed his keys all the time.
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In my opinion, the psychological thrillers of Alfred Hitchcock, who is a master of suspense and horror, have more lasting impact than any other filmmaker in history.
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The pursuit of a career in sports offers individuals opportunities for personal fulfilment and professional success. ______________________________. Athletes must therefore undergo rigorous training regimens to maintain peak physical condition and hone their skills. Additionally, competition in the sports industry is fierce, requiring dedication, perseverance, and mental resilience to succeed. Despite the challenges, successful athletes can enjoy lucrative contracts, endorsements, and global recognition for their achievements.
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______________________________. This happened after a lorry laden with tomatoes worth 21 lakh rupees went missing. One of the three traders who had sent his tomatoes on the lorry said that they had lost contact with the driver in Nashik and that his GPS had been switched off. The traders were not sure if the truck had been hijacked or if the driver had stolen the tomatoes. This is the third time tomatoes have been stolen following the rise of tomato prices to Rs.150 per kg.
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Most artificial intelligence (AI) applications in the fields of healthcare, industry, finance, transportation, and writing rely heavily on deep learning and natural language processing. However, while AI systems can mimic existing styles and patterns, there is an ongoing debate about whether AI can truly possess creativity in the same sense as humans. ______________________________.
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In an era where privacy and individualism are often prized above all else, Japanese architect Riken Yamamoto blurs the boundary between public and private. ______________________________. His work is a testament to the power of architecture to break down barriers and to foster a sense of community. Through his innovative designs, he challenges traditional notions of public and private spaces, seamlessly blending the two realms.
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Conspiracy theorists suggest that if climate change is slowly turning the planet into an oven, then this must have been the outcome of our enemiesʼ intentional ______________. If there are no coincidences in the world, then everything, including ______________ events, can be controlled. It is only a matter of power and ______________.
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In today's fast-paced world, individuals are inundated with information, necessitating the cultivation of critical thinking skills in order to navigate the influx of data ______________. Additionally, the prevalence of fake news and misinformation presents a ______________ challenge, undermining peopleʼs trust in media and institutions. Promoting media literacy and cultivating a culture of scepticism are vital for ______________ informed citizenship and democratic values.
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The outbreak of COVID-19 resulted in a health crisis and a drop in economic activity that were without ______________ in history. While containing and ______________ the spread of the virus was the first priority of public authorities, reducing the ______________ of the disease and limiting the pressure on healthcare systems were also considered equally important.
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It is widely argued that social media can benefit aspiring ______________. Populists in particular latch on to social media today as a way to connect directly with people, ______________ restraints on their behaviour that political parties would have provided in the pre-internet age. They can also profit from echo chambers, which reinforce the sense that a whole people ______________ supports a populist leader.
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An ______________ found that one of the marathon runners had ______________ slowed down in the last two kilometres and after ______________ to the one behind him had let him cross the finish line just one second before he did.
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In an era of globalization, cultural diversity is celebrated and valued across societies. However, the rise of xenophobia and intolerance poses a ______________ challenge to social cohesion and harmony. Building inclusive communities and promoting intercultural dialogue are essential for ______________ mutual understanding and respect among diverse populations. Additionally, educating individuals about the benefits of cultural diversity and challenging ______________ are crucial steps toward creating inclusive societies and encouraging peaceful coexistence.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided.
1. Farmers, however, especially during the peak farming season, ignore the warnings of the weather forecast.
2. People from some states of India have demanded that families of those who have been killed by lightning strikes should receive compensation.
3. The Minister for Disaster Management announced that over 2800 people have died after being struck by a lightning last year.
4. The Minister responded that pamphlets on the dangers of lightning and precautions to be taken are being distributed in villages.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided.
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