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Question : If $x(x-5)=-1$, then the value of $x^3\left(x^3-110\right)=$?
Option 1: 0
Option 2: –1
Option 3: 1
Option 4: 2
Correct Answer: –1
Solution : Given: $x(x-5)=-1$ ⇒ $x-5=-\frac{1}{x}$ ⇒ $x+\frac{1}{x}=5$ Cubing both sides, we get: ⇒ $(x+\frac{1}{x})^3=5^3$ ⇒ $x^3+\frac{1}{x^3}+3(x\times\frac{1}{x})(x+\frac{1}{x})=125$ ⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=125$ ⇒ $x^3+\frac{1}{x^3}+3\times5=125$ ⇒ $x^3+\frac{1}{x^3}=110$ ⇒ $x^3-110=-\frac{1}{x^3}$ $\therefore x^3(x^3-110)=-1$ Hence, the correct answer is –1.
Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given question figures – 1. The number of triangles in each figure is a prime number in continuous increasing order. 2. In the first figure we have 2 triangles so in the next figure number of triangles is 3, 5, 7, and 11.
Question : Select the most appropriate synonym of the underlined word in the given sentence. The efforts of the doctors came to a futile end with the death of the patient.
Option 1: Fruitless
Option 2: Enriching
Option 3: Startling
Option 4: Terrifying
Correct Answer: Fruitless
Solution : The correct choice is the first option.
Explanation: Fruitless and futile both convey the idea of being unsuccessful or producing no result. In this context, the efforts of the doctors led to a futile end, meaning that despite their hard work, it was unsuccessful
Question : The breadth of a rectangle is $\frac{4}{5}$th of the radius of a circle. The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of the rectangle is 20 cm?
Option 1: 150 cm2
Option 2: 600 cm2
Option 3: 100 cm2
Option 4: 80 cm2
Correct Answer: 80 cm2
Solution : The breadth of a rectangle is $\frac{4}{5}$ of the radius of a circle The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm$^2$ The length of the rectangle is = 20 cm Formula Used: The
Question : Select the most appropriate ANTONYM to replace the italicised word.
He greeted Charles with a languid wave of his hand.
Option 1: Supine
Option 2: Sluggish
Option 3: Energetic
Option 4: Lackadaisical
Correct Answer: Energetic
Solution : The correct choice is the third option.
Languid describes a state of being lacking in energy, weak, or sluggish.
Energetic implies a lively, vigorous, and spirited action. Thus, it is the correct antonym.
The meanings of the other options are as follows:
Question : Fill in the blank with an appropriate option.
How can seawater from the oceans be _______ fresh water that is suitable for people to drink?
Option 1: change about
Option 2: surrender in
Option 3: minced on
Option 4: turned into
Correct Answer: turned into
Solution : The correct choice is the fourth option.
Explanation:
The phrase turned into is a phrasal verb that accurately expresses the process of transforming one thing into another. In this context, the sentence discusses the conversion of seawater into freshwater suitable for drinking. The
Question : Comprehension:
Read the following passage and answer the questions that follow.
Rajasthan's farmers have been banging plates and lighting fires these days. It is their desperate attempt to scare away the swarms of migratory locusts invading their fields and eating away crops. The pest attack has come as a double blow for farmers already reeling under the impact of the COVID lockdown.
Millions of locusts, covering 1-4 sq km of the skyline, have reached 10 of the state's 33 districts within three weeks of being first spotted on April 30. Last year, yellow locusts entered India from Pakistan in the second half of May. The attack had originated in Yemen, coming all the way to West Asia, Pakistan, and then India, creating havoc in 17 countries en route.
With the harvest nearly over in Rajasthan, the invading population of grasshoppers this May is feeding mainly on sprouting cotton crops sown last month, vegetables, and fodder. State officials, though, fear damage to the young millet and moong dal crops due in July and August if the locusts breed.
Flying in through the Pakistan border near Jaisalmer, the locust swarms have infiltrated as deep as Kishangarh in Ajmer district. Locusts can cover 200–250 km in a day if they get wind support. Presently, the dust storms sweeping parts of Rajasthan are aiding their flight. Officials said the Union Agriculture Ministry's Locusts Warning Organisation (LWO) is in the process of acquiring 60 vehicles with mounted insecticide sprayers from abroad by July. Ten such vehicles were purchased this January.
"Immature pink locusts are very active, which is why they have reached the interiors of Rajasthan [from Pakistan] so quickly," says K.L. Gurjar, deputy director, of LWO. Their metabolism slows down during winters, but in summers, they can fly from 4 am to 8 pm, covering long distances and consuming more crops along the way than mature locusts would. The LWO has put 10 insecticide-spraying vehicles on the job in Rajasthan. The Rajasthan government has provided rented tractors, on which insecticide sprayers are mounted, and also the manpower to man them. The centre-state joint operation has so far cleared a few hundred sq km of fields of the locusts. Preliminary estimates put the loss to crops at a few crore rupees.
State officials say there is an urgent need to contain the pink locusts before they start breeding in the next few weeks. Indiscriminate aerial spraying of insecticides is ill-advised, as this can damage crops as well as affect human settlements.
One of the strategies being considered now is to use fixed-wing aircraft for ultra-low volume spraying of chemicals. The state government may request such aerial sorties from the air force. Drones have limited capabilities as they can carry only about 20 litres of insecticide at a time, making them effective only over small areas.
Question: If the locusts breed, which crops will they damage?
Option 1: Cotton crop
Option 2: Millet and moong
Option 3: Fodder
Option 4: Vegetables
Correct Answer: Millet and moong
Solution : The correct choice is the second option.
As stated in the third passage, if the locusts breed, they are feared to damage the young millet and moong dal crops due in July and August.
Therefore, the correct answer is millet and moong.
Read the given passage and answer the questions that follow.
You go up a dark, rickety stairwell of a building on a crowded street in Calcutta. You enter a small room. The centre of the room is empty but the corners are stacked with bedrolls, utensils and water bottles. Musical instruments, drums, cymbals and gongs are piled in a corner. Today, the room is filled with the laughter of men and women in colourful attire. Among the happy chorus of congratulations and laughter, the bride Chumki Pal and the groom Sandeep can be seen smiling. They are both blind, as are most of the people surrounding them. Pal is wearing a bright turquoise blue sari. “I know it’s blue because people have told me but I can’t imagine how it looks. But believe me, when I dream, I dream only in colours,” she says. Their romance blossomed when they met as members of Blind Opera, the only one of its kind in the country as well as in Asia.
The 36 spirited members of Blind Opera demonstrate that physical disability is not an obstacle. They enact plays by Rabindranath Tagore, considered challenging even by veteran theatre groups. Blind Opera was launched in 1996 by four theatre aficionados, who took it as a challenge to get together the talents of these visually impaired people. The challenge to present the cast on stage is immense since space management is a problem. To solve this, the directors use ropes to separate the stage and the wings. When the actors step on the rope they know that it is the entrance to the stage. The members cannot see, but they can smell, hear and touch – three elements inherent to any theatre. At Blind Opera, they “believe that the blind can see. That is, they see in their own way, if not in our way, with the help of these abilities.”
For the visually impaired, theatre is the medium for the expression of their creative urges. They respond instinctively; they cannot copy anyone else because they cannot see. Their body language tells the story and hence it is very spontaneous. The members have earned kudos from Calcutta audiences. For the members of the troupe, discovering the language of the body is in a way also a journey of the persona. Coming from diverse backgrounds but bound together by the same disability, they have found an outlet for their creativity through the plays. They do not feel isolated anymore because they can relate to their fellow performers. There is also a greater purpose behind it: to use theatre to build a community and mainstream the huge number of disabled living in isolation. Together they can be a force to demand better facilities in public life. Blind children should enter the mainstream from the beginning. The big dream of the group is to establish a drama school following the ideal of Tagore’s Shantiniketan, offering a platform for creative expression to all those who are economically and socially forced to stay in the periphery. Like Chumki Pal, they all dream in colour.
Question:
What is the biggest problem in presenting the troupe on stage?
Option 1: Space management
Option 2: Time management
Option 3: Communication
Option 4: Spontaneity
Correct Answer: Space management
In the second paragraph of the comprehension, it is stated that the challenge of presenting the cast on stage is immense since space management is a problem.
Therefore, the correct answer is space management.
Question : Select the sentence with the appropriate use of preposition.
Option 1: Are you interested along with modern art?
Option 2: Are you interested into modern art?
Option 3: Are you interested with modern art?
Option 4: Are you interested in modern art?
Correct Answer: Are you interested in modern art?
Explanation: The verb "interested" is commonly followed by the preposition "in" when expressing interest in a particular subject or topic. In this case, the correct preposition to use with "interested" is "in".
Question : What is the maximum strength prescribed for State Legislative Assemblies?
Option 1: 350
Option 2: 600
Option 3: 500
Option 4: 750
Correct Answer: 500
Solution : The correct answer is 500.
The Legislative Assembly has a maximum strength of 500 members and a minimum strength of 60. Its strength ranges from 60 to 500 depending on the size of the state's population. This is specified in Article 170 of the Indian
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