Staff Selection Commission Combined Graduate Level Exam
Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:
Option 1: 6
Option 2: 9
Option 3: 0
Option 4: 1
Correct Answer: 0
Solution : Given: $x+y+z=9$ Solution: Let $(x–4) = a, (y−2) = b, (z−3) = c$ So, this equation stands to $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ = $a^3+b^3+c^3–3abc$ Also, We know that $a^3+b^3+c^3–3abc$ = $(a+b+c)(a^2+b^2+c^2–bc–ab–ac) $. So, $a+b+c = x−4+y−2+z−3$ ⇒ $a+b+c = x+y+z−9$ ⇒ $a+b+c = 9−9$ ⇒ $a+b+c = 0$
Question : Ethanol containing 5% water is known as :
Option 1: Dilute alcohol
Option 2: Power alcohol
Option 3: Rectified spirit
Option 4: Absolute alcohol
Correct Answer: Rectified spirit
Solution : The correct option is Rectified spirit.
Rectified spirit is a highly concentrated and pure type of alcohol that is often produced from grains or sugarcane. Because of its high alcohol concentration, which typically exceeds 95% alcohol by volume (ABV), it is frequently employed in
Question : Chola inscriptions mention several categories of land, which of the following land was known as gifted to temples?
Option 1: Devadana
Option 2: Shalabhoga
Option 3: Pallichchandam
Option 4: Brahmadeya
Correct Answer: Devadana
Solution : The correct answer is Devadana.
Inscriptions from the Chola dynasty in ancient South India mention several categories of land, and the land that was known as gifted to temples was called Devadana land. Devadana land refers to land that was donated or gifted to temples
Question : Which sportsperson was named by homegrown pharma major Lupin Ltd as a brand ambassador for its Shakti campaign in 2022?
Option 1: Rahul Dravid
Option 2: Mithali Raj
Option 3: Mary Kom
Option 4: PV Sindhu
Correct Answer: Mary Kom
Solution : The correct option is Mary Kom
Lupin Pharmaceuticals is a pharmaceutical company based in India. It is one of the largest manufacturers of generic drugs globally. Lupin specializes in the production of a wide range of pharmaceutical products.
The "Shakti" campaign is a term
Question : Directions: In a certain code language, CHILDREN is written as FKLOGUHQ, and SCHOOL is written as VFKRRO, how will CLASSROOM be written in that language?
Option 1: EMCTTTQQO
Option 2: EMCTTURRP
Option 3: FOEWWURRP
Option 4: FODVVURRP
Correct Answer: FODVVURRP
Solution : Given: The code for CHILDREN is FKLOGUHQ, and the code for SCHOOL is VFKRRO.
As for, CHILDREN is written as FKLOGUHQ – C + 3 = F; H + 3 = K; I + 3 = L; L + 3 = O; D + 3
Question : If $\tan ^2 \theta+\tan ^4 \theta=1$, then:
Option 1: $\cot ^2 \theta+\cot ^4 \theta=1$
Option 2: $\cos ^2 \theta+\cos ^4 \theta=1$
Option 3: $\sin ^2 \theta+\sin ^4 \theta=1$
Option 4: $\operatorname{cosec}^2 \theta+\sec ^4 \theta=1$
Correct Answer: $\cos ^2 \theta+\cos ^4 \theta=1$
Solution : $\tan ^2 \theta+\tan ^4 \theta=1$ ⇒ $\tan^2\theta(1+\tan^2\theta) = 1$ ⇒ $\tan^2\theta(1+\frac{\sin^2\theta}{\cos^2\theta}) = 1$ ⇒ $\frac{\sin^2\theta}{\cos^2\theta}(\frac{cos^2\theta + \sin^2\theta}{\cos^2\theta}) = 1$ ⇒ $\frac{\sin^2\theta}{\cos^2\theta}(\frac{1}{\cos^2\theta}) = 1$ ⇒ $\sin^2\theta = \cos^4\theta$ ⇒ $1-\cos^2\theta = \cos^4\theta$ ⇒ $\cos^4\theta + \cos^2\theta = 1$ Hence, the correct answer
Question : Who among the following belonged to the ancient chiefly family of the Cholas from Uraiyur, who captured the Kaveri delta from the Muttaraiyar in the middle of the ninth century?
Option 1: Gandaraditya
Option 2: Vijayalaya
Option 3: Parantaka I
Option 4: Aditya I
Correct Answer: Vijayalaya
Solution : The correct answer is Vijayalaya.
A minor ruling family called the Muttaraiyar had control over the Kaveri delta, and they were under the authority of the Pallava kings of Kanchipuram. In the middle of the ninth century, a leader named Vijayalaya, hailing from the
Question : The table given below shows the foreign trade by two countries in 5 different years.
What is the value of average foreign trade by country P in all 5 years?
Option 1: 155
Option 2: 745
Option 3: 149
Option 4: 135
Correct Answer: 149
Solution : Average foreign trade by country P in all 5 years = $\frac{220+200+125+115+85}{5}$ = $\frac{745}{5}$ = 149 Hence, the correct answer is 149.
Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: I. All cancers are diseases. II. All tuberculosis is a disease. III. All diseases are curable. Conclusions: I. All tuberculosis is curable. II. Some cancers are tuberculosis. III. All cancers are curable.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and III follow
Option 3: All conclusions follow
Option 4: Only conclusions I and II follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All tuberculosis is curable – From the Venn diagram, it is evident that the circle representing tuberculosis lies inside the
Question : Direction: Anjali says, "He is the only son of the father of my sister's brother." How is that person related to Anjali?
Option 1: Uncle
Option 2: Cousin
Option 3: Brother
Option 4: Father
Correct Answer: Brother
Solution : According to the given information, the family tree is shown below.
According to the above family tree, the person is the brother of Anjali.
Hence, third option is correct.
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