Staff Selection Commission Combined Higher Secondary Level Exam
Question : Rearrange the parts of the sentence in the correct order.
Approaching her P. upon the impacts of county lines drug-running networks Q. 80th birthday in February next year, Hill’s R. relevance and urgency this time focusing S. writing has lost none of its immediate
Option 1: QSRP
Option 2: SQRP
Option 3: RPQS
Option 4: PQSR
Correct Answer: QSRP
Solution : The correct choice is the first option.
Explanation:
Part Q sets the context or the timeframe of the event. Part S describes the continued significance of the writing despite the passing time. Part R specifies the current focus or subject matter. Part P introduces the
Question : $\cos 2 \theta=$________.
Option 1: $1-2 \cos^2 \theta$
Option 2: $2 \cos^2 \theta-1$
Option 3: $2 \sin^2 \theta-1$
Option 4: $1-\sin^2 \theta$
Correct Answer: $2 \cos^2 \theta-1$
Solution : $\cos2\theta = \cos^2\theta-\sin^2\theta$ $= \cos^2\theta-(1-\cos^2\theta)$ $= 2\cos^2\theta-1$ Hence, the correct answer is $2\cos^2\theta-1$.
Question : Select the option that can be used as a one-word substitute for the given group of words. A life history of a person written by himself.
Option 1: Biography
Option 2: Epic
Option 3: Story
Option 4: Autobiography
Correct Answer: Autobiography
Solution : The fourth option is the correct choice.
"Autobiography" precisely represents the life history of a person written by that person.
The meanings of the other options are as follows:
Question : The diameter of a circle is 20 cm. The length of a chord AB is 10 cm. What will be the angle made by this chord at the centre of this circle?
Option 1: 75°
Option 2: 45°
Option 3: 60°
Option 4: 90°
Correct Answer: 60°
Solution : Radius = $\frac{\text{Diameter}}{2}$ In an equilateral triangle, since the three sides are equal the three angles opposite to the equal sides, are equal in measure. OA = OB = AB = 10 cm ⇒ $\triangle$OAB is an equilateral triangle. So, $\angle$OAB = $\angle$OBA = $\angle$AOB
Question : Bihu is a folk dance of which state?
Option 1: Assam
Option 2: Maharashtra
Option 3: Odisha
Option 4: Uttarakhand
Correct Answer: Assam
Solution : The correct option is Assam.
The Bihu dance is a dynamic traditional folk dance originating from the northeastern Indian state of Assam. It holds a place in the Bihu festival, with various agricultural and cultural events throughout the year. This dance form is characterised
Question : Direction: The pie chart shows how the school fund is spent under different heads in a certain school. Using the pie chart answer the question.
Which head had the most expense?
Option 1: Art and Craft
Option 2: Sports
Option 3: Library
Option 4: Science
Correct Answer: Sports
Solution : As per the chart, The sum of all the central angles in a pie chart is 360°. The Sports head has the maximum expenditure with a central angle of 120°. Hence, the correct answer is Sports.
Question : If $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^2=9$, then what is the value of $\mathrm{k}^3+\frac{1}{\mathrm{k}^3} ?$
Option 1: 27
Option 2: 18
Option 3: 15
Option 4: 21
Correct Answer: 18
Solution : $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^2=9$ $⇒\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right) = 3$ $⇒\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^3 = 3^3$ $⇒\mathrm{k}^3+ \frac{1}{\mathrm{k}^3}+3×\mathrm{k}×\frac{1}{\mathrm{k}}(\mathrm{k}+\frac{1}{\mathrm{k}})=27$ $⇒ \mathrm{k}^3 + \frac{1}{\mathrm{k}^3}=27- 3(\mathrm{k} + \frac{1}{\mathrm{k}} )$ $⇒\mathrm{k}^3 + \frac{1}{\mathrm{k}^3} = 27 - 3\times3$ $⇒\mathrm{k}^3 + \frac{1}{\mathrm{k}^3}=18$ Hence, the correct answer is 18.
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 solar system is made up of the sun, planets, moons, asteroids, and comets that 1.______ around it. Its mysteries and wonders have captured the imagination of people from all walks of life, and it continues to be an area of active research and exploration. The sun is at the centre of the solar system and is the largest object in it. The eight planets in the solar system, 2._________ Earth, orbit around the sun in nearly circular paths. While the sun is at the centre of the solar system and dominates its gravitational pull, each planet has its own unique set of characteristics that makes it a fascinating object to study. Each planet in the solar system has unique characteristics and features. 3._________ planets, such as Mercury and Venus, are small and rocky, while others, like Jupiter and Saturn, are much larger and made up mostly of gas. The outer planets, Uranus and Neptune, are 4._______ as 'ice giants' because they contain more water, ammonia, and methane than the gas giants. In addition to the planets, the solar system also has numerous moons, asteroids, and comets. These objects provide important 5.______ about the formation and evolution of the solar system. Question: Select the most appropriate option to fill in the blank 2.
Option 1: excluding
Option 2: diluting
Option 3: dissolving
Option 4: including
Correct Answer: including
Solution : The most appropriate option is the fourth option.
Explanation: Including means to contain as part of a whole. In this context, it implies that among the eight planets in the solar system, Earth is one of them. "The eight planets in the solar system, including
Question : Wood spirit is
Option 1: Methyl alcohol
Option 2: Ethyl alcohol
Option 3: Butyl alcohol
Option 4: Propyl alcohol
Correct Answer: Methyl alcohol
Solution : The correct option is - Methyl alcohol
Other names for methanol include methyl alcohol, wood alcohol, and wood spirits and its chemical formula is CH3OH. It got the name "wood alcohol" because, in the past, it was mostly produced as a byproduct
Question : If $\left(x-\frac{1}{x-2}\right)=7$, then the value of $(x-2)^3-\frac{1}{(x-2)^3}$ is:
Option 1: 130
Option 2: 115
Option 3: 140
Option 4: 125
Correct Answer: 140
Solution : Given: $\left(x-\frac{1}{x-2}\right)=7$ ⇒ $\left(x-2-\frac{1}{x-2}\right)=5$ ⇒ $\left(x-2-\frac{1}{x-2}\right)^3=5^3$ ⇒ $(x-2)^3 - (\frac{1}{x-2})^3-3×(x-2)×(\frac{1}{x-2})\left(x-2-\frac{1}{x-2}\right)=125$ ⇒ $(x-2)^3 - (\frac{1}{x-2})^3=125+(3×5)$ $\therefore (x-2)^3 - (\frac{1}{x-2})^3=140$ Hence, the correct answer is 140.
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