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Question : If $\tan3\theta \tan7\theta = 1$, where $7\theta$ is an acute angle, then find the value of $\cot15\theta$.
Option 1: $1$
Option 2: $-1$
Option 3: $-\sqrt{3}$
Option 4: $\sqrt{3}$
Correct Answer: $-1$
Solution : $\tan3\theta \cdot \tan7\theta = 1$ ⇒ $\tan 7\theta = \frac{1}{\tan 3\theta}$ ⇒ $\tan7\theta = \cot3\theta$ ⇒ $\tan7\theta = \tan(90° - 3\theta)$ ⇒ $7\theta + 3\theta = 90°$ ⇒ $10\theta = 90°$ ⇒ $\theta = 9°$ $\therefore$ $\cot15\theta = \cot (15\times 9)°=\cot135° = \cot(90° + 45°)=-\tan45°
Question : Directions: In the given question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
I need to buy _______.
Option 1: a bread
Option 2: a loaf of bread
Option 3: a loaf bread
Option 4: breads
Correct Answer: a loaf of bread
Solution : The correct choice is the second option.
Loaf of bread means bread that has been shaped and baked into one piece. Thus, it is the appropriate choice to fill the blank with.
Therefore, the complete sentence is: I need to buy
Question : Which of the following government schemes provides subsidised food grains to poor households in India?
Option 1: Pradhan Mantri Kaushal Vikas Yojana
Option 2: Pradhan Mantri Garib Kalyan Anna Yojana
Option 3: Pradhan Mantri Jan Arogya Yojana
Option 4: Atal Pension Yojana
Correct Answer: Pradhan Mantri Garib Kalyan Anna Yojana
Solution : The correct option is Pradhan Mantri Garib Kalyan Anna Yojana.
The Pradhan Mantri Garib Kalyan Anna Yojana (PM-GKAY) is a government scheme that provides subsidized food grains to poor households in India. Under the PM-GKAY, the government provides 5
Question : Study the graph and answer the question. In which year, were the exports of type B cars exactly 20% more than the exports of type A cars in 2014?
Option 1: 2015
Option 2: 2016
Option 3: 2012
Option 4: 2013
Correct Answer: 2016
Solution : Exports of type A cars in 2014 = 225 120% of 225 = $225\times\frac{120}{100}$ = 270 In 2016 the exports of type B cars were exactly 20% more than the exports of type A cars in 2014. Hence, the correct answer is 2016.
Question : If $(y-\frac{1}{y})=8$, find the value of $(y^2+\frac{1}{y^2})$.
Option 1: 64
Option 2: 62
Option 3: 60
Option 4: 66
Correct Answer: 66
Solution : Given, $(y-\frac{1}{y})=8$ Squaring both sides, we get: $y^2+\frac{1}{y^2}-2(y)(\frac{1}{y})=64$ ⇒ $y^2+\frac{1}{y^2}=64+2$ ⇒ $y^2+\frac{1}{y^2}=66$ Hence, the correct answer is 66.
Question : Directions: In the following question a word is followed by four other words, one of which cannot be formed by using the letters of the given word. Find this word. PRONUNCIATION
Option 1: RATION
Option 2: PRONOUN
Option 3: PRINT
Option 4: NATURAL
Correct Answer: NATURAL
Solution : Given: PRONUNCIATION
First option: RATION; All the letters of RATION are present in the word PRONUNCIATION. Second option: PRONOUN; All the letters of PRONOUN are present in the word PRONUNCIATION. Third option: PRINT; All the letters of PRINT are present in the word PRONUNCIATION. Fourth
Question : Which country is the leading producer of jute?
Option 1: Brazil
Option 2: China
Option 3: India
Option 4: Columbia
Correct Answer: India
Solution : The correct option is India.
India is the world's largest producer of raw and jute goods, contributing over 50 and 40 per cent to global production. Jute is a significant agricultural product, and India has a long history of the cultivation and processing of
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.
As writers, we live life twice, like (1) _________ cow that eats its food once and then regurgitates it to chew and digest (2) __________ again. We have a second chance (3)_________ biting into our experience and examining it. This is our life and it's not going to last forever. There isn't time to talk about someday writing that short story, poem, or novel. Slow down now, touch what is (4) __________ you, and out of care and compassion for (5) __________ moment and detail, put pen to paper and begin to write.
Select the most appropriate option to fill in the blank number 5.
Option 1: each
Option 2: both
Option 3: few
Option 4: little
Correct Answer: each
Solution : The correct choice is the first option.
The word each is used to emphasise the importance of considering and valuing every individual moment and detail.
Each is a determiner, which in the context of a sentence signifies that care and compassion should be
Question : Which of the following areas or regions is most prone to earthquakes?
Option 1: Deccan Plateau
Option 2: Ganga-Brahmaputra Valley
Option 3: Plains of Northern India
Option 4: Western Ghats
Correct Answer: Ganga-Brahmaputra Valley
Solution : The correct answer is Ganga-Brahmaputra Valley.
Ganga-Brahmaputra Valley is the choice most likely to experience earthquakes out of all of the possibilities provided because of its proximity to the Himalayan foothills. According to the most recent version of India's seismic zone map (2002), the
Question : Direction: In the following question, select the one which is different from other three alternatives.
Option 1: DCFG
Option 2: FEHI
Option 3: JILM
Option 4: HGJL
Correct Answer: HGJL
Solution : Split the given letter clusters in the group of 2 and then swap the letters of the first group –
First option: DCFG
DCFG → DC FG → CD FG
Both the letter groups are consecutive alphabets.
Second option: FEHI
FEHI → FE HI →
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