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Question : Find the value of the given expression. $\sqrt{20-\sqrt{20-\sqrt{20-\sqrt{20-\cdots \infty}}}}$
Option 1: 4
Option 2: 6
Option 3: 5
Option 4: 2
Correct Answer: 4
Solution : Given expression, $\sqrt{20-\sqrt{20-\sqrt{20-\sqrt{20-\cdots \infty}}}}$ Let us equate this with $y$ ⇒ $y=\sqrt{20-\sqrt{20-\sqrt{20-\sqrt{20-\cdots \infty}}}}$ ⇒ $y=\sqrt{20-y}$ Squaring both sides, ⇒ $y^2=20-y$ ⇒ $y^2+y-20=0$ ⇒ $y^2+5y-4y-20=0$ ⇒ $y(y+5)-4(y+5)=0$ ⇒ $(y+5)(y-4)=0$ ⇒ $y=-5$ and $y=4$ Hence, the correct answer is 4.
Question : Directions: In a certain code language. MAPS is written as 49 and SOLD is written as 50. How will KIDS be written in that language?
Option 1: 45
Option 2: 44
Option 3: 42
Option 4: 43
Correct Answer: 43
Solution : Given: MAPS is written as 49 and SOLD is written as 50.
Add the positional value of letters to obtain the code – MAPS; M→13; A→1; P→16; S→19 13 + 1 + 16 + 19 = 49 Thus, MAPS is coded as 49. SOLD; S→19;
Question : Select the most appropriate meaning of the underlined idiom that can be substituted in the following sentence.
Right now, my hands are full.
Option 1: My hands are filled up
Option 2: My hands are swollen
Option 3: l'm very tired
Option 4: I'm very busy
Correct Answer: I'm very busy
Solution : The fourth option is correct.
When someone says my hands are full, it's an idiomatic expression used to convey that the person is occupied or busy with various tasks or responsibilities, to the extent that they have as much as they can
Question : The Constitution forbids the employment of children below the age of________ years for dangerous jobs like factories and mines.
Option 1: 15
Option 2: 14
Option 3: 16
Option 4: 18
Correct Answer: 14
Solution : The correct answer is 14.
The key legislation related to the employment of children in India is the "Child and Adolescent Labour (Prohibition and Regulation) Act, 1986" (often referred to as the Child Labour Act). This Act prohibits the employment of children below the age
Question : Direction: In each of the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
BR _ _ NB _ O _ NB
Option 1: OWOW
Option 2: RORO
Option 3: WNWN
Option 4: OWRW
Correct Answer: OWRW
Solution : Given:
We have to check the order of the letters in the given series.
To fill the series we have to divide the series, BR _ _ / NB _ O / _ NB.
So, the series
Question : ________is a process in which natural rubber is treated with sulphur to make it more durable and elastic.
Option 1: Saponification
Option 2: Fermentation
Option 3: Vulcanisation
Option 4: Carbonation
Correct Answer: Vulcanisation
Solution : The correct answer is Vulcanisation.
Vulcanisation is a process in which natural rubber is treated with sulphur to make it more durable and elastic. The vulcanisation process is done to enhance the properties of rubber, and it was discovered by Charles Goodyear.
Question :
Study the given graph and answer the question that follows.
What is the ratio of the total expenditure in 2015 and 2016 to the total revenue of the company in 2016 and 2018?
Option 1: 6 : 7
Option 2: 19 : 20
Option 3: 4 : 5
Option 4: 11 : 20
Correct Answer: 4 : 5
Solution : According to the question Total expenditure in 2015 and 2016 = 210 + 350 = 560 Total revenue in 2016 and 2018 = 320 + 380 = 700 Required ratio = $\frac{560}{700}$ = $\frac{4}{5}$ = 4 : 5 Hence, the correct answer is
Question : Directions: In the following question, the given sentence has four parts marked P, Q, R, and S. Choose the part of the sentence with the error and select it as your answer. If there is no error, select 'No Error (S)' as your answer.
Wherever you live, (P) / there is surely some countryside or coastline (Q) / not too far away that you are proud of. (R) / No Error (S)
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Solution : The correct answer is the fourth option.
Since the sentence is grammatically accurate and doesn't need any change. The sentence conveys the idea that regardless of where one resides, there is likely some coastal or rural area nearby that one can take pride in.
Question : If $\tan x = –\frac{12}{5}$, where $x$ lies in the second quadrant, what is the value of $\sin x-\cot x$?
Option 1: $\frac{209}{156}$
Option 2: $\frac{169}{156}$
Option 3: $\frac{156}{209}$
Option 4: $\frac{144}{169}$
Correct Answer: $\frac{209}{156}$
Solution : In the second quadrant, $\sin x$ and $\operatorname{cosec x}$ are positive. $\tan x = –\frac{12}{5}$ $⇒\cot x=\frac{1}{\tan x}=-\frac{5}{12}$ We know, $\sec^2x -\tan^2x=1$ $⇒\sec^2x=1+(–\frac{12}{5})^2$ $⇒\sec^2x=1+\frac{144}{25}$ $⇒\sec^2x=\frac{169}{25}$ $⇒ \sec x=\frac{13}{5}$ $⇒\cos x = \frac{5}{13}$ $\therefore\sin x = \sqrt{1-\cos^2x}=\sqrt{1-\frac{25}{169}}=\frac{144}{169}=\frac{12}{13}$ $\sin x - \cot x = \frac{12}{13} – (-\frac{5}{12})
Question : Select the most appropriate synonym of the given word.
Authentic
Option 1: Genuine
Option 2: False
Option 3: Doubtful
Option 4: Corrupt
Correct Answer: Genuine
Solution : The correct option is the first option.
In the context of the word authentic, genuine is the most appropriate synonym because it closely aligns with the meaning of authentic, which means genuine, real, or true. It refers to something that is not a
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