Staff Selection Commission Combined Graduate Level Exam
Question : The value of $\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$ is:
Option 1: $2-2 \sqrt{2}$
Option 2: $4+2 \sqrt{2}$
Option 3: $4-2 \sqrt{2}$
Option 4: $2+2 \sqrt{2}$
Correct Answer: $4-2 \sqrt{2}$
Solution : This is a telescoping series, where each term cancels out a part of the next term. $\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$ Rationalising the denominator and use the formula $a^2 - b^2 = (a+b)(a-b)$, we get, $=\frac{\sqrt{15}+4}{1}-\frac{\sqrt{15}+\sqrt{14}}{1}+\frac{\sqrt{14}+\sqrt{13}}{1}-\frac{\sqrt{13}+\sqrt{12}}{1}+\frac{\sqrt{12}+\sqrt{11}}{1}-\frac{\sqrt{11}+\sqrt{10}}{1}+\frac{\sqrt{10}+3}{1}-\frac{3+\sqrt{8}}{1}$ $=\sqrt{15}+4-\sqrt{15}-\sqrt{14}+\sqrt{14}+\sqrt{13}-\sqrt{13}-\sqrt{12}+\sqrt{12}+\sqrt{11}-\sqrt{11}-\sqrt{10}+\sqrt{10}+3-3-\sqrt{8}$ $=4-\sqrt{8}$ $=4-2\sqrt{2}$ Hence, the correct answer is $4-2\sqrt{2}$.
Question : The following table shows the number of elected persons from various parties in a state assembly.
Find the difference between the number of seats won by party R and party Q in all the elections put together.
Option 1: 18
Option 2: 19
Option 3: 17
Option 4: 20
Correct Answer: 19
Solution : Total number of seats won by party R = 90 + 80 + 100 + 50 + 80 + 65 = 465 Total number of seats won by party Q = 80 + 90 + 60 + 70 + 76 + 70 = 446 $\therefore$
Question : Select the correct indirect form of the given sentence.
The little girl said, "This bicycle is mine."
Option 1: The little girl said that bicycle was her.
Option 2: The little girl said that this bicycle is mine.
Option 3: The little girl said that this bicycle is hers.
Option 4: The little girl said that that bicycle was hers.
Correct Answer: The little girl said that that bicycle was hers.
Solution : The correct choice is the fourth option.
When converting direct speech to indirect speech, pronouns need to be changed to reflect the perspective of the reporting speaker.
Narration Conversion:
Question : The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the sum of the cubes of the two given numbers.
Option 1: 576
Option 2: 250
Option 3: 640
Option 4: 512
Correct Answer: 576
Solution : Let the 2 numbers be $a$ and $b$. According to the question, $(a+b)^3 = 1728$ ⇒ $a+b = 12$ Also, $a\times b = 32$ We have to find, $a^3 + b^3$ $(a+b)^3 = 1728$ ⇒ $a^3 + b^3 + 3ab(a+b) = 1728$ ⇒ $a^3 +
Question : Comprehension:
Read the given passage and answer the questions that follow.
In the stress-ridden world, traditional pastimes that could prove therapeutic are dying for want of patronage. One such is the art of puppetry. The word “puppet” is derived from the Latin word pupa, meaning “doll” or “girl”. Puppets came into being in India in the third century A.D. Here it was honed into a theatrical art. It helped to propagate the works of saints and religious leaders, and also depict stories from epics. Later, it spread to South East Asia. The Cambodian puppeteers inspired the Thais. Java and Bali followed though it didn’t catch on in Sumatra. The Malays followed the Siamese and Japanese styles in the nineteenth century. Gradually, puppets became more sophisticated in appearance, as skilled craftsmen began to make the models. Puppeteers became trained as performers. In the eighteenth and nineteenth centuries, puppet theatres became extremely popular in artistic circles. Writers like George Sands and Goethe organised their own well-prepared puppet shows to entertain their friends. Puppet shows have been mentioned in the literature by Shakespeare, Ben Johnson, and many others.
Basically, there are three kinds of puppets. Shadow puppets are made of translucent leather and coloured vegetable dyes. Buffalo, goat, or sheep skin is treated to become translucent. Limbs are loosely jointed so that they can be made to move separately. A stick is attached vertically in the middle. The movement of the stick causes general movements. But for special movements, single strings attached to the limbs are used. These leather puppets are projected on a screen, which is illuminated by a light source placed behind the puppets. The puppeteer manipulates the puppets to form moving shadows on the screen. He also speaks the parts, sings, or is accompanied by music. String puppets involve puppets that are manipulated by six strings. The performance is on a stage but the puppeteers are never seen. They wear anklets which produce the illusion that the puppets themselves are dancing. The main storyteller recites the storyline, while the puppets perform, and the dialogue and music are provided by the puppeteers. Rod or stick puppets are constructed around the main central rod. A short horizontal bar serves as the shoulders, from which the upper limbs dangle. The arms, made of cloth and stuffed with straw or paper, are jointed or manipulated with other thinner rods. These puppets can be the size of a human being. The puppeteer hides behind the puppet and manipulates it. The coordination of the limbs comes only through practice.
Puppetry is a good communication medium. Messages can be propagated in a realistic way. Puppet making and performing is good occupational therapy for convalescents and physically disabled people. Muscular coordination and manual dexterity improve with effort. However, the best use of this art is that it can provide delightful hours of fun to young and old alike.
Question:
The above passage is:
Option 1: literary
Option 2: narrative
Option 3: factual
Option 4: didactic
Correct Answer: factual
Solution : The correct choice is the third option.
The passage provides information about the history, types, and techniques of puppetry. It doesn't present a story or a fictional narrative (literary), nor is it specifically focused on teaching a moral lesson or instruction (didactic). Instead, it
Question : Select the option that can be used as a one-word substitute for the underlined group of words. My uncle is someone who loves good food and knows a lot about it.
Option 1: connoisseur
Option 2: gourmet
Option 3: chauffeur
Option 4: culinary
Correct Answer: gourmet
Solution : The second option is the correct choice.
A gourmet is someone who is knowledgeable and has refined tastes, especially in food and drink. They appreciate and enjoy high-quality food and often seek out unique or exquisite culinary experiences.
The meanings of the other options are
Question : Select the correct active form of the given sentence.
Let the guests be served some soup.
Option 1: Serve some soup to the guests.
Option 2: Let some soup serve the guests.
Option 3: Have you served some soup to the guests?
Option 4: You should have served some soup to the guests.
Correct Answer: Serve some soup to the guests.
Solution : The correct choice is the first option.
The active form of a sentence is a sentence in which the subject performs the action expressed by the verb. In an active sentence, the subject is the doer of the action.
The
Question : Direction: Arrange the following words as per order in the dictionary.
I. Euphrasy
ll. Eupepsy
lll. Euphonic
lV. Eugenic
V. Euphony
Option 1: IV, III, II, I, V
Option 2: III, IV, I, II, V
Option 3: IV, II, III, V, I
Option 4: III, V, II, IV, I
Correct Answer: IV, II, III, V, I
Solution : Given:
Start from Eugenic because g comes before p
Eugenic
Now, write Eupepsy because e comes before h
Eupepsy
Now, write Euphonic because i comes before
Question : The average of 100 items was found to be 30. If, at the time of calculation, two items were wrongly taken as 32 and 12 instead of 23 and 11, then the correct average is:
Option 1: 29.8
Option 2: 29
Option 3: 29.9
Option 4: 29.5
Correct Answer: 29.9
Solution : Given: The average of 100 items is 30. Sum of all items = 100 × 30 = 3000 A wrong entry of 32 and 12 instead of 23 and 11 is also included. The difference made by the wrong entry of 32 and 12 instead
Question : Select the option that expresses the given sentence in passive voice.
Rover would not swallow the pill.
Option 1: The pill would not be swallowing by Rover.
Option 2: The pill would not swallowed by Rover.
Option 3: The pill would not be swallowed by Rover.
Option 4: The pill would not be swallow by Rover.
Correct Answer: The pill would not be swallowed by Rover.
Solution : The correct option will be the third option.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject
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