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Question : If $\left(x^2 - \frac{1}{x^2}\right) = 4 \sqrt{6}$ and $x>1$, what is the value of $\left(x^3 - \frac{1}{x^3}\right)?$
Option 1: $20 \sqrt{2}$
Option 2: $24 \sqrt{2}$
Option 3: $18 \sqrt{2}$
Option 4: $22 \sqrt{2}$
Correct Answer: $22 \sqrt{2}$
Solution : Given: $x^2 -\frac{1}{x^2} = 4\sqrt6$ Squaring both sides we get, ⇒ $x^4 +\frac{1}{x^4} - 2 = 96$ ⇒ $x^4 +\frac{1}{x^4}+2 = 98+2$ ⇒ $ (x^2+\frac{1}{x^2})^2 =100$ ⇒ $x^2 +\frac{1}{x^2} = 10$ ---------------(1) ⇒ $x^2 +\frac{1}{x^2} -2= 10-2$ ⇒ $(x-\frac{1}{x})^2=8$ ⇒ $(x-\frac{1}{x}) = 2\sqrt2$ ----------------(2)
Question : Parts of the following sentence have been given as options. Select the option that contains an error.
There was a saying that they’re their own enemies with negligble reason to be shared.
Option 1: There
Option 2: negligble
Option 3: they’re
Option 4: their
Correct Answer: negligble
Solution : The error lies in the second option.
The correct spelling of the word is negligible. The word negligible means something that is so small or unimportant that it can be disregarded or considered insignificant.
The correct sentence is: There was a saying that they’re
Question : The given histogram shows the frequency distribution of the speed of cars passing though at a particular spot on a highway. Study the graph and answer the question that follows. What is the ratio of the number of cars with speeds less than 60 km/hr to the number of cars with speeds more than 80 km/hr?
Option 1: 8 : 7
Option 2: 4 : 5
Option 3: 5 : 4
Option 4: 7 : 8
Correct Answer: 8 : 7
Solution : As per the graph, The number of cars with speeds less than 60 km/hr = 50 + 70 = 120 The number of cars with speeds more than 80 km/hr = 60 + 45 = 105 The required ratio = 120 : 105
Question : Directions: In the following questions select the related figure from the given alternatives.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figure – All the elements in the given pair are rotating 180 degrees. So, following the same pattern the missing figure will be –
Therefore, the figure in the fourth option is the correct required missing image. Hence, the fourth option is
Question : Which article deals with the ‘power of parliament to amend the constitution and procedure therefore’?
Option 1: Article 352
Option 2: Article 249
Option 3: Article 368
Option 4: Article 356
Correct Answer: Article 368
Solution : The correct answer is Article 368.
Article 368 deals with the ‘power of parliament to amend the constitution.’ Under Article 368, parliament can amend the constitution by passing a bill with a special majority. It is taken directly from the South African Constitution.
Question : Which of the following archaeological sites has evidence of pit-dwellings?
Option 1: Rana Ghundai
Option 2: Mehrgarh
Option 3: Burzahom
Option 4: Palavoy
Correct Answer: Burzahom
Solution : The correct answer is Burzahom.
Burzahom archaeological sites have evidence of pit-dwellings. It is located in Srinagar district in Jammu and Kashmir. At Burzahom many pit houses have been found. Pit-dwelling refers to the houses which are dug into the ground. These dwelling pits
Question : A alone can do a work in 4 days, which B alone can do in 6 days. In how many days they together can do it?
Option 1: $\frac{7}{12}$
Option 2: $\frac{12}{7}$
Option 3: $\frac{12}{5}$
Option 4: $\frac{5}{12}$
Correct Answer: $\frac{12}{5}$
Solution : Given: A alone can do a work in 4 days. B alone can do it in 6 days. They together in 1 day can do ($\frac{1}{4}+\frac{1}{6}$) part of the work $=\frac{6+4}{24}=\frac{10}{24}=\frac{5}{12}$ part of the work So, they together can complete the work in $\frac{12}{5}$ days.
Question : What is the smallest perfect square number that is divisible by both 10 and 15?
Option 1: 1200
Option 2: 1800
Option 3: 360
Option 4: 900
Correct Answer: 900
Solution : Given: The number is divisible by both 10 and 15. Finding the lowest multiple of two or more numbers is done using the LCM method. LCM of 10 and 15 = 30 The prime factors of 30 = 2 × 3 × 5 Make it
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: AJDG
Option 2: KTNQ
Option 3: JMSP
Option 4: UDXA
Correct Answer: JMSP
Solution : Let's check the options – First option: AJDG; A + 9 = J; J – 6 = D; D + 3 = G Second option: KTNQ; K + 9 = T; T – 6 = N; N + 3 = Q Third option: JMSP; J
Question : The value of $\frac{\cot30^{\circ}-\cot75^{\circ}}{\tan15^{\circ}-\tan60^{\circ}}$ is equal to:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
Correct Answer: –1
Solution : We know that $\tan(90-\theta)=\cot \theta$ $\frac{\cot30^{\circ}-\cot75^{\circ}}{\tan15^{\circ}-\tan60^{\circ}}$ = $\frac{\tan(90^{\circ}-30^{\circ})-\tan(90^{\circ}-75^{\circ})}{\tan15^{\circ}-\tan60^{\circ}}$ = $\frac{\tan60^{\circ}-\tan15^{\circ}}{\tan15^{\circ}-\tan60^{\circ}}$ = $\frac{-1(\tan15^{\circ}-\tan60^{\circ})}{\tan15^{\circ}-\tan60^{\circ}}$ = $-1$ Hence, the correct answer is –1.
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