Staff Selection Commission Combined Graduate Level Exam
Question : If $a^2+b^2+c^2=a b+b c+a c$, then the value of $\frac{11 a^4+13 b^4+17 c^4}{17 a^2 b^2+9 b^2 c^2+15 c^2 a^2}$ is:
Option 1: 1
Option 2: 2
Option 3: 11
Option 4: 4
Correct Answer: 1
Solution : Given: $a^2+b^2+c^2=a b+b c+a c$ Multiplying both sides with 2, we get: $2a^2+2b^2+2c^2=2ab+2bc+2ac$ ⇒ $a^2+b^2-2ab+b^2+c^2-2bc+c^2+a^2-2ac=0$ ⇒ $(a-b)^2+(b-c)^2+(c-a)^2=0$ So, $a-b=0$, $b-c=0$, $c-a=0$ ⇒ $a=b=c$ Now, $\frac{11 a^4+13 b^4+17 c^4}{17 a^2 b^2+9 b^2 c^2+15 c^2 a^2}$ $=\frac{11 a^4+13 a^4+17 a^4}{17 a^2 a^2+9 a^2 a^2+15 a^2 a^2}$ $=\frac{41
Question : Select the most appropriate one word substitution for the given words.
Profane talk
Option 1: Origami
Option 2: Alchemy
Option 3: Polygamy
Option 4: Blasphemy
Correct Answer: Blasphemy
Solution : The correct choice is the fourth option.
Blasphemy refers to speech or actions that show disrespect or contempt for sacred or divine things, making it the most appropriate substitution for profane talk.
The meanings of the other options are as follows:
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: All spoons are forks. All knives are forks. All forks are plates. Conclusions: I. All knives are plates. II. All plates are spoons. III. Some plates are knives.
Option 1: All conclusions follow
Option 2: Both conclusions II and III follow
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
Correct Answer: Both conclusions I and III follow
Solution : According to the given statements, the following Venn diagram can be drawn –
Conclusion I: All knives are plates – From the given statements, the circle of knives is completely inside the circle of plates. Therefore, this conclusion follows.
Question : Select the most appropriate meaning of the given idiom. Someone's heart is in the right place.
Option 1: Suddenly feel so excited or frightened that your heart beats faster.
Option 2: Change your opinion or the way you feel.
Option 3: Share secret worries with someone else.
Option 4: Someone is good even if they sometimes behave in a wrong manner.
Correct Answer: Someone is good even if they sometimes behave in a wrong manner.
Solution : The correct option is the fourth option.
Explanation: This idiom refers to the inherent goodness of a person despite occasional mistakes or wrong actions. It suggests that, despite any faults or errors, the person
Question : The question consists of two statements, namely, Assertion (A) and Reason (R). Use them to choose the correct alternative. Assertion (A): During British rule, India's exports exceeded the imports leading to a surplus of balance of trade. Reason (R): The surplus of the balance of trade was used for the growth and development of India.
Option 1: Both A and R are true, and R is the correct explanation of A
Option 2: Both A and R are true, but R is not the correct explanation of A
Option 3: A is false but R is true
Option 4: A is true and R is false
Correct Answer: A is true and R is false
Solution : The correct option is A is true, and R is false.
During British rule, India had periods where its exports exceeded imports, creating a trade surplus. However, this surplus was not primarily used for the growth and development of
Question : Red rot is a disease caused by which of the following plants?
Option 1: Paddy
Option 2: Sugarcane
Option 3: Mustard
Option 4: Wheat
Correct Answer: Sugarcane
Solution : The correct option is Sugarcane.
The sugar sector suffers huge financial losses as a result of the dangerous fungal disease known as red rot disease, which destroys sugarcane plants. The fungus Colletotrichum falcatum is responsible for the illness. It mostly impacts the sugarcane plant's
Question : In a division sum, the divisor is 13 times the quotient and 6 times the remainder. If the remainder is 39, the dividend is:
Option 1: 4240
Option 2: 4576
Option 3: 4251
Option 4: 4800
Correct Answer: 4251
Solution : Divisor = 13 × Quotient Divisor = 6 × Remainder Remainder = 39 ⇒ Divisor = 39 × 6 = 234 So, Quotient $=\frac{234}{13} = 18$ Dividend = Divisor $×$ Quotient + Remainder $\therefore$ Dividend = 234 × 18 + 39 = 4251 Hence, the
Question : If 10% of $x$ is 3 times of 15% of $y$, then find $x:y$.
Option 1: $7:2$
Option 2: $9:2$
Option 3: $8:3$
Option 4: $11:4$
Correct Answer: $9:2$
Solution : Given: $10$% of $x$ = $3×15$% of $y$ ⇒ $x×\frac{10}{100}=3×y×\frac{15}{100}$ ⇒ $10x=45y$ ⇒ $\frac{x}{y}=\frac{45}{10}=\frac{9}{2}$ ⇒ $x:y=9:2$ Hence, the correct answer is $9:2$.
Question : Directions: Arrange the following words as per their order in the dictionary. 1. Patriot 2. Pastor 3. Patron 4. Pattern 5. Pastern
Option 1: 5, 2, 3, 1, 4
Option 2: 5, 2, 1, 3, 4
Option 3: 5, 2, 4, 1, 3
Option 4: 5, 2, 4, 3, 1
Correct Answer: 5, 2, 1, 3, 4
Solution : Given: 1. Patriot 2. Pastor 3. Patron 4. Pattern 5. Pastern
Step 1: Since all the words start with the same letter P, so move on to the next letter. Step 2: The second letter of each word is the
Question : Which Mughal ruler contributed to the revolt of 1857?
Option 1: Shah Alam II
Option 2: Bahadur Shah I
Option 3: Alamgir II
Option 4: Bahadur Shah II
Correct Answer: Bahadur Shah II
Solution : The correct option is Bahadur Shah II.
The Mughal ruler associated with the Indian Rebellion of 1857, also known as the Sepoy Mutiny or the First War of Indian Independence, was Bahadur Shah II, commonly known as Bahadur Shah Zafar. Bahadur Shah II
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