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Question : The sum of twice a fraction and its reciprocal is $\frac{17}{6}$. What is the fraction?
Option 1: $\frac{4}{3}$
Option 2: $\frac{5}{4}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{5}$
Correct Answer: $\frac{3}{4}$
Solution : Let's assume the fraction is $x$. $⇒2x+\frac{1}{x}=\frac{17}{6}$ Multiplying both sides by $x$, we get, $⇒2x^2+1=\frac{17x}{6}$ $⇒2x^2-\frac{17x}{6}+1=0$ Multiplying both sides by 6, we get, $\Rightarrow 12x^2-17x +6=0$ $\Rightarrow (3x-2)(4x-3)=0$ $\Rightarrow (3x-2)$ or $(4x-3)=0$ $\Rightarrow x=\frac{2}{3}$ or $x=\frac{3}{4}$ After checking the options we get, $x=\frac{3}{4}$ Hence, the
Question : Given below are four sentences, three of which, are jumbled. Pick the option that gives the correct order. A. In less than ten minutes, the two young men found the way that led to the cliff top. B. Half way up, a large rock blocked their way. C. But their troubles were not over. D. They started shouting, hoping that someone might hear them.
Option 1: ABCD
Option 2: ACBD
Option 3: ADCB
Option 4: ADBC
Correct Answer: ABCD
Solution : The correct choice is the first option.
Explanation: The sequence begins with the two young men swiftly finding the path to the cliff top in less than ten minutes (A). However, their progress is hindered when they encountered a large rock halfway up (B). The
Question : Identify the segment that contains a grammatical error. If there is no error, select 'No error.' An appeasements policies / were all but a sham to misdirect / the local groups.
Option 1: the local groups.
Option 2: were all but a sham to misdirect
Option 3: An appeasements policies
Option 4: No error
Correct Answer: An appeasements policies
Solution : The error lies in the third option.
Explanation: The term "appeasements" is incorrect because "appeasement" is a word that doesn't require a plural form when used in this context to modify "policies". The correct form is "appeasement policy," as "appeasement" describes
Question : If $x-y=7$ and $xy=32$, then the value of $x^{2}+y^{2}$ is:
Option 1: 49
Option 2: 64
Option 3: 113
Option 4: 15
Correct Answer: 113
Solution : Given: $x-y=7$ and $xy=32$. We know that $(x-y)^{2}=x^{2}+y^{2}-2xy$. ⇒ $x^{2}+y^{2}=(x-y)^{2}+2xy$ By putting the value of $x-y=7$ and $xy=32$ in above expression, we get: ⇒ $x^{2}+y^{2}=7^{2}+2×32$ ⇒ $x^{2}+y^{2}=49+64$ ⇒ $x^{2}+y^{2}=113$ Hence, the correct answer is 113.
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative in case no improvement is needed your answer is (4).
Hitler was an absolute potentate.
(1) Dictator
(2) Militant
(3) Ruler
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option.
Dictator means a ruler who has total power over a country that is typically controlled by force, and it fits correctly in the context of the sentence.
The meanings of the other options are as follows:
Question : The basis of determining dearness allowance to employees in India is
Option 1: national income
Option 2: consumer price index
Option 3: standard of living
Option 4: inflation rate
Correct Answer: consumer price index
Solution : The correct answer is the consumer price index.
The consumer price index is used in India to calculate the Dearness Allowance (DA) for government employees. A benefit known as a Dearness Allowance (DA) is provided to employees to offset the impact of inflation
Question : Directions: Find the missing number from the given responses.
Option 1: 53
Option 2: 48
Option 3: 32
Option 4: 40
Correct Answer: 40
Solution : In a column, find the square of the first number to get the second number and then multiply the first number by consecutive natural numbers(starting from 3) to get the third number.
In the first column: 62 = 36 and 6 × 3 =
Question : The ratio of the area of two isosceles triangles having the same vertical angle (i.e. the angle between equal sides) is 1 : 4. The ratio of their heights is:
Option 1: 1 : 4
Option 2: 2 : 5
Option 3: 1 : 2
Option 4: 3 : 4
Correct Answer: 1 : 2
Solution : $\angle$ BAC = $\angle$ QPR $\angle$ ABC = $\angle$ ACB and $\angle$ PQR = $\angle$ PRQ $\angle$ ABC = $\angle$ ACB = $\angle$ PQR = $\angle$ PRQ $\triangle$ BAC ~ $\triangle$ QPR $\frac{area(\triangle BAC)}{area(\triangle PQR)}$ = $\frac{h^2}{H^2}$ ⇒ $\frac{1}{4}$ = $\frac{h^2}{H^2}$ ⇒ $\frac{h}{H}$
Question : Citric acid is present in free form in
Option 1: tamarind
Option 2: milk
Option 3: apple
Option 4: lemon
Correct Answer: lemon
Solution : The correct option is lemon.
Lemon contains citric acid in its free form. Lemons' sour flavour is caused by a natural organic acid. Lemon juice contains 5% to 6% citric acid. Other citrus fruits, such as oranges, limes, and grapefruits, contain citric acid. Other
Question : Directions: Which two numbers should be interchanged to make the given equation correct? 81 + 31 ÷ 9 – 7 = 33
Option 1: 9 and 7
Option 2: 31 and 9
Option 3: 31 and 81
Option 4: 81 and 7
Correct Answer: 31 and 81
Solution : Given: 81 + 31 ÷ 9 – 7 = 33
Let's check the options – First options: 9 and 7 81 + 31 ÷ 7 – 9 = 33 On solving the L.H.S. of the given equation – = 81 + 31 ÷
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