Staff Selection Commission Combined Graduate Level Exam
Question : If $x+\frac{1}{x}=7$, the value of $x^6+\frac{1}{x^6}$ is:
Option 1: 113682
Option 2: 103682
Option 3: 103882
Option 4: 103862
Correct Answer: 103682
Solution : Given: $x+\frac{1}{x}=7$ Squaring both sides, we get: $(x+\frac{1}{x})^2=7^2$ ⇒ $x^2+\frac{1}{x^2}+2×x×\frac{1}{x}=49$ ⇒ $x^2+\frac{1}{x^2}=49-2$ ⇒ $x^2+\frac{1}{x^2}=47$ Now, cubing both sides, we get: ⇒ $x^6+\frac{1}{x^6}+3×x^2×\frac{1}{x^2}(x^2+\frac{1}{x^2})=47^3$ ⇒ $x^6+\frac{1}{x^6}+3×47=103823$ ⇒ $x^6+\frac{1}{x^6}=103823-141$ ⇒ $x^6+\frac{1}{x^6}=103682$ Hence, the correct answer is 103682.
Question : Which of the following is the correct Lewis structure of O3?
Option 1: c
Option 2: a
Option 3: b
Option 4: d
Correct Answer: d
Solution : The correct option is d.
The ozone molecule is represented by this Lewis structure, where the two outside oxygen atoms have partial positive charges, and the middle oxygen atom has a partial negative charge. The two outside oxygen atoms are forced closer together by
Question : Who among the following is said to have devised many ragas or melodies in Hindustani music?
Option 1: Tansen
Option 2: Raja Birbal
Option 3: Todar Mal
Option 4: Raja Man Singh
Correct Answer: Tansen
Solution : The correct answer is Tansen.
Among the options provided, Mian Tansen has devised many ragas or melodies in Hindustani music. Mian Tansen, whose full name was Ramtanu Pandey, was a prominent and highly influential musician in the court of Emperor Akbar during the Mughal
Question : Directions: The following bar diagram shows the total number of males and females in five different organisations. Study it carefully to answer the question.
What is the ratio of the number of females from Organisations B and C to the number of males from Organisations D and E?
Option 1: 12 : 11
Option 2: 12 : 15
Option 3: 11 : 15
Option 4: 15 : 11
Correct Answer: 15 : 11
Solution : As per the given graph, The number of females from organisations B and C = 3500 + 4000 = 7,500 The number of males from organisations D and E = 2250 + 3250 = 5,500 The required ratio = The number of females
Question : The value of $ \frac{(p-q)^3+(q-r)^3+(r-p)^3}{12(p-q)(q-r)(r-p)}$, where $p \neq q \neq r$, is equal to:
Option 1: $\frac{1}{9}$
Option 2: $\frac{1}{3}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{2}$
Correct Answer: $\frac{1}{4}$
Solution : $\frac{(p-q)^3+(q-r)^3+(r-p)^3}{12(p-q)(q-r)(r-p)}$ We know that $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ Let $a=p-q$, $b=q-r$ and $c=r-p$ We observe that $a+b+c=p-q+q-r+-p=0$ So, $a^3+b^3+c^3-3abc=0$ or, $a^3+b^3+c^3=3abc$ or, $(p-q)^3+(q-r)^3+(r-p)^3=3(p-q)(q-r)(r-p)$ So, $\frac{(p-q)^3+(q-r)^3+(r-p)^3}{12(p-q)(q-r)(r-p)}= \frac{3(p-q)(q-r)(r-p)}{12(p-q)(q-r)(r-p)}$ = $\frac{1}{4}$ Hence, the correct answer is $\frac{1}{4}$.
Question : Direction: In the following question, find out the wrong number in the series.
10, 13, 234, 681, 997
Option 1: 681
Option 2: 10
Option 3: 234
Option 4: 13
Correct Answer: 681
Solution : Given:
The pattern followed here is –
10 = 1 + 0 = 1 (Perfect square of 1)
13 = 1 + 3 = 4 (Perfect square of 2)
234 = 2 + 3 + 4 = 9 (Perfect square
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer. Due to heavy rains, the match was called____.
Option 1: of
Option 2: off
Option 3: down
Option 4: out
Correct Answer: off
Solution : The second option is the correct answer.
"Call off" means to cancel something, especially an event. This is the only phrasal verb that fits the sentence appropriately.
"Call down" means to request or order someone to come down from a higher place.
"Call out" means
Question : Select the correct active form of the given sentence.
Before she came all the work had been completed by me.
Option 1: I will complete all my work before she came.
Option 2: I had completed all my work before she came.
Option 3: I completed all my work before she came.
Option 4: I complete all my work before she came.
Correct Answer: I had completed all my work before she came.
Solution : The correct choice is the second option.
Active voice is the voice where the subject performs the action. When converting a sentence from the passive voice to the active voice, the agent of the action becomes
Question : If $a+b=1$, find the value of $a^{3}+b^{3} - ab-(a^{2}-b^{2})^{2}$.
Option 1: –1
Option 2: 1
Option 3: 0
Option 4: 2
Correct Answer: 0
Solution : Given: $a+b=1$ We know that $a^{3}+b^{3}=(a+b)^{3}-3ab(a+b)$ So, $a^{3}+b^{3}-ab-(a^{2}-b^{2})^{2}=(a+b)^{3}-3ab(a+b)-ab-(a+b)^{2}(a-b)^{2}$ Putting the value of $a+b=1$, we get, $a^{3}+b^{3}-ab-(a^{2}–b^{2})^{2}$ $=(1)^{3}-3ab(1)-ab-(1)^{2}[(1)^{2}-4ab]$ $= 1-3ab-ab-1+4ab$ $=0$ Hence, the correct answer is 0.
Question : Smooth muscles are likely to be found in:
Option 1: muscles of leg
Option 2: muscles of arms
Option 3: stomach
Option 4: heart
Correct Answer: stomach
Solution : The correct option is Stomach
Smooth muscles in the stomach serve an important function in digestion and food movement. These muscles facilitate mechanical digestion by mixing and churning the food with stomach secretions. They also aid in the movement of partly digested food from the
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