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Question : If the angle of elevation of the top of a pillar from the ground level is raised from 30° to 60°, the length of the shadow of a pillar of height $50\sqrt{3}$ metres will be decreased by:
Option 1: 60 metres
Option 2: 75 metres
Option 3: 100 metres
Option 4: 50 metres
Correct Answer: 100 metres
Solution : Height of the pillar, $AB$ = $50\sqrt{3}$ metres For the length of the shadow at an angle of elevation of 30°, $\frac{50\sqrt{3}}{BC} = \tan 30°$ ⇒ $\frac{50\sqrt{3}}{BC} = \frac{1}{\sqrt{3}}$ ⇒ $BC = 150$ metres For the length of the shadow at an angle of
Question : $\triangle ABC$ is a triangle. PQ is a line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and the length of PQ is 18 cm. The length of BC is:
Option 1: 28 cm
Option 2: 48 cm
Option 3: 84 cm
Option 4: 42 cm
Correct Answer: 48 cm
Solution : Given: AP : BP = 3 : 5 And PQ = 18 cm Let BC = $x$ cm In $\triangle$APQ and $\triangle$ABC, $\frac{AP}{AB}=\frac{PQ}{BC}$ (since PQ is parallel to base BC) Putting the values, we get: $\frac{3}{8}=\frac{18}{x}$ $\therefore x=\frac{18×8}{3}$ = 48 Hence, the correct answer
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.
Words convey meaning because they are used in human activities in different forms. Different words may (1) ______ the same thing in different languages, and this is what is referred to as 'family resemblance'. In other words, languages help us (2) ______ reality and then communicate it to others. There are tens and thousands of languages in the world, and all of them help us (3) ______ express ourselves, which in turn gives meaning to our lives. One's mother tongue is (4) ______ for one's literary growth, but if you want to communicate to a wider audience, then you will (5) ______ to reach out to the target audience in a language they understand.
Select the most appropriate option to fill in the blank number 1.
Option 1: meaningful
Option 2: meaning
Option 3: mean
Option 4: meant
Correct Answer: mean
Solution : The third option is the correct answer.
The sentence structure suggests that different words may refer to the same thing in different languages, emphasising the idea that words convey meaning.
The appropriate term to use in this context is mean, which completes the sentence to
Question : Who among the following was the slave-general of Alauddin Khalji, who led his army in the battle against Ramachandra of Devagiri?
Option 1: Nusrat Khan
Option 2: Malik Kafur
Option 3: Ulugh Khan
Option 4: Zafar Khan
Correct Answer: Malik Kafur
Solution : The correct option is Malik Kafur.
Malik Kafur was Alauddin Khalji's renowned slave general. Alauddin Khalji grabbed him while he was occupying Gujarat. He overcame the King of Devagiri, the Kakatiyas of Warangal, the Hoysalas of Halebidu, and other powerful opponents while leading
Question : Select the most appropriate idiom from the following options that can substitute the underlined part of the given sentence. He is a disgrace to his family
Option 1: A fish out of water
Option 2: A white elephant
Option 3: A lone wolf
Option 4: A black sheep
Correct Answer: A black sheep
Solution : The correct option is the fourth option.
Explanation:
A black sheep refers to a person who is seen as different or disgraceful compared to the rest of their family or group due to their behaviour or actions. It implies someone who stands out
Question : Study the bar graph and answer the question. Percentage decrease in the number of trees planted in 2016 in state A as compared to that in 2015 in the same state was:
Option 1: $15 \frac{5}{13}$%
Option 2: $15 \frac{2}{3}$%
Option 3: $13 \frac{1}{3}$%
Option 4: $13 \frac{2}{3}$%
Correct Answer: $13 \frac{1}{3}$%
Solution : The total number of trees planted in 2016 in state A = 78 The total number of trees planted in 2015 in state A = 90 The required percentage $=\frac{90–78}{90}\times 100=\frac{12}{90}\times 100=13 \frac{1}{3}$% Hence, the correct answer is $13 \frac{1}{3}$%.
Question : 40 men can complete a work in 30 days. However, if 10 men leave the group, how many days will the group take to complete the work?
Option 1: 40
Option 2: 35
Option 3: 45
Option 4: 50
Correct Answer: 40
Solution : Given: 40 men can complete a work in 30 days. But 10 men left. Let (40 – 10) = 30 men complete the work in $x$ days. Now, M1 × D1 = M2 × D2 where M1 and M2
Question : Directions: From the given options, which word will appear fourth in the dictionary?
Option 1: Degrade
Option 2: Density
Option 3: Deterioration
Option 4: Determination
Correct Answer: Determination
Solution : Given: 1. Degrade 2. Density 3. Deterioration 4. Determination
Step 1: Compare the first letter of each word. Since all the words start with the same letter D, then move on to the next letter. Step 2: Compare the second letter of each word.
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.
The massive ransomware attack that has crippled the e-hospital services of AIIMS, Delhi, highlights the (1)______ vulnerability of the country's healthcare infrastructure, and possibly other critical IT systems, to cyber criminals. The premier public healthcare institute (2)______ to around 15 lakh outpatients and 80,000 inpatients every year. Consequently, there are fears that the attackers could sell the now force-encrypted AIIMS databases that contain (3)______ information of patients-including political leaders, senior administrators, and judges, and their healthcare records on the Dark Web. Of course, what has happened to AlIMS is hardly a local phenomenon. A (4)_____ increase in cyberattacks on healthcare institutes worldwide (5)_____ during the Covid pandemic. The Indian healthcare sector was the second-most targeted globally. It is clear that Indian hospitals are vulnerable to cybersecurity. Government and hospitals need to use best practices to ward off future crises.
Question:
Select the most appropriate option to fill in the blank 5.
Option 1: has witnessed
Option 2: is witnessed
Option 3: was witness
Option 4: has been witnessed
Correct Answer: has been witnessed
Solution : The most appropriate choice is the fourth option.
The context in the passage discusses a trend or occurrence that has been ongoing, and it's implied that the increase in cyberattacks on healthcare institutes worldwide is a continuing situation. The present perfect tense i.e.,
Question : Which country shares a sea-line border with India?
Option 1: Maldives
Option 2: Philippines
Option 3: Fiji
Option 4: Pakistan
Correct Answer: Maldives
Solution : The correct answer is Maldives.
The Maldives and India are neighbours that share a sea boundary. A bilateral agreement was signed on December 28, 1976, and went into effect on June 8, 1978, establishing the maritime border between India and the Maldives. The line,
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