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Question : Simplify the following expression. 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}]
Option 1: $\frac{120}{61}$
Option 2: $\frac{61}{120}$
Option 3: $3$
Option 4: $-3$
Correct Answer: $3$
Solution : 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}] = 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 + 3}] = 120 ÷ 15 of 4 + [11
Question : The sum of the three numbers is 540. The ratio of second to third is 9 : 13 and that of first to third is 2 : 7. The third number is:
Option 1: 273
Option 2: 280
Option 3: 250
Option 4: 286
Correct Answer: 273
Solution : The ratio of 2nd : 3rd = 9 : 13 And the ratio of 1st : 3rd = 2:7 3rd number is common in both ratios, so to make the value equal, we need to multiply by 7 in 9 : 13 and by 13
Question : Directions: Which sequence of mathematical symbols can replace * in the given equation? 8 * 5 * 9 * 31
Option 1: –, ×, =
Option 2: –, =, ×
Option 3: =, ×, –
Option 4: ×, –, =
Correct Answer: ×, –, =
Solution : Given: 8 * 5 * 9 * 31
Replace * with the mathematical signs and solve the equations one by one using BODMAS. Let's check the given options – First option: –, ×, = ⇒ 8 – 5 × 9 = 31 Solving
Question : The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be $\alpha$ and $\beta(\alpha>\beta)$. The height of the tower is $h$ units. A possible distance (in the same unit) between the points is:
Option 1: $\frac{h(\cot\beta–\cot\alpha)}{\cos(\alpha+\beta)}$
Option 2: $h(\cot\alpha–\cot\beta)$
Option 3: $\frac{h(\tan\beta–\tan\alpha)}{\tan\alpha\tan\beta}$
Option 4: $h(\cot\alpha+\cot\beta)$
Correct Answer: $h(\cot\alpha+\cot\beta)$
Solution : $AD=h$ unit In $\Delta ADB$, $\tan\alpha=\frac{AD}{BD}$ $⇒\tan\alpha=\frac{h}{BD}$ $⇒BD=h\cot\alpha$ --------------------------------------(1) In $\Delta ADC$, $\tan\beta=\frac{AD}{DC}$ $⇒\tan\beta=\frac{h}{DC}$ $⇒DC=h\cot\beta$ -------------------------------------(2) Now $BC=BD+DC$ $⇒BC=h\cot\alpha+h\cot\beta$ $\therefore BC=h(\cot\alpha+\cot\beta)$ Hence, the correct answer is $h(\cot\alpha+\cot\beta)$.
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. Posters are (1) _ to promote a brand or pass (2) _ important information. They can be used for (3) _ purposes ranging from telling people to be cautious as the floor is wet, to informing them about an upcoming sale or event. They usually include a picture (4) _ very few words. A suitable (5) _ makes a poster effective and memorable. Select the most appropriate option to fill in blank no.3.
Option 1: little
Option 2: varied
Option 3: much
Option 4: similar
Correct Answer: varied
Solution : The third option is the correct choice.
In the context of posters, the sentence discusses the different purposes or uses of posters, which can range from cautionary messages to advertising sales or events. Varied means diverse or having a wide range of different kinds, which
Question : Comprehension: Read the given passage carefully and answer the questions that follow.
As the world's population approaches 8 billion and resource use intensifies, pollution is becoming more extensive, pervasive, and persistent. It affects our health through the food we eat, the water we drink, and the air we breathe. By 2025, the world's cities will produce 2.2 billion metric tonnes of waste every year, more than three times the amount produced in 2009. That said, pollution is not a new phenomenon and is largely controllable and often avoidable, as shown in some countries and cities that have succeeded in decoupling economic growth from pollution and waste accumulation.
With the end goal of eradicating all forms of pollution by 2030, the UN Environment Programme was tasked by the UN Environment Assembly to coordinate the implementation of a global plan reiterating that pollution is not only an environmental priority, it's a priority for the achievement of the Sustainable Development Goals.
Question: Which is the best description of the tone of the passage?
Option 1: Technical
Option 2: Sarcastic
Option 3: Dogmatic
Option 4: Humanistic
Correct Answer: Humanistic
Solution : The correct answer is the fourth option.
The best description of the tone of the passage is likely "humanistic". The passage discusses the challenges of pollution and its impact on health and the environment and emphasises the goal of eradicating all forms of pollution by
Question : How many oxygen atoms are there in an acetone molecule?
Option 1: 3
Option 2: 1
Option 3: 2
Option 4: 4
Correct Answer: 1
Solution : The correct option is 1.
Acetone has the molecular formula C3H6O.
Therefore, in 1 molecule of
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
It was only when they met that (1)/ they found he has a childish simplicity (2)/ in him. (3)/ No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
The sentence contains an error in verb tense consistency. The verb form has should be changed to had to maintain the past tense consistency since the sentence is referring to a past event. Moreover, childish
Question : Which of the following is correct?
Option 1: $\frac{2}{3}< \frac{3}{5}< \frac{11}{15}$
Option 2: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$
Option 3: $\frac{11}{15}< \frac{3}{5}< \frac{2}{3}$
Option 4: $\frac{3}{5}< \frac{11}{15}< \frac{2}{3}$
Correct Answer: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$
Solution : Given: The numbers are $\frac{2}{3}, \frac{3}{5}, \frac{11}{15}$. To find the greatest fraction, we have to find the LCM of denominators. LCM of denominators $=$ LCM $(3, 5, 15) = {(3×5)} = 15$ We have to make all denominators the same for comparison, $
Question : Directions: Rajiv is the brother of Arun. Sonia is the sister of Sunil. Arun is the son of Sonia. How is Rajiv related to Sunil?
Option 1: Nephew
Option 2: Son
Option 3: Brother
Option 4: Father
Correct Answer: Nephew
Solution : As per the given information, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, from the above family tree, Rajiv is the nephew of Sunil. Hence, the first option
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