Staff Selection Commission Combined Higher Secondary Level Exam
Question : What is the value of $(a^2+b^2+4c^2-ab-2bc-2ca)(a+b+2c)$?
Option 1: $a^3 + b^3 + 8c^3 – 8abc$
Option 2: $a^3 + b^3 + 6c^3 – 4abc$
Option 3: $4a^3 + b^3 + 8c^3 – 9abc$
Option 4: $a^3 + b^3 + 8c^3 – 6abc$
Correct Answer: $a^3 + b^3 + 8c^3 – 6abc$
Solution : $(a^2+b^2+4c^2-ab-2bc-2ca)(a+b+2c)$ $= a^3+b^2a+4c^2a-a^2b-2abc-2ca^2 + a^2b+b^3+4c^2b-ab^2-2b^2c-2abc + 2a^2c+2b^2c+8c^3-2abc-4bc^2-4c^2a$ $= a^3+b^3+8c^3-2abc-2abc-2abc+b^2a-ab^2+4c^2a-4c^2a-a^2b+ a^2b-2ca^2 + 2a^2c-2b^2c+2b^2c-4bc^2+4c^2b$ $= a^3+b^3+8c^3-6abc$ Hence, the correct answer is $ a^3+b^3+8c^3-6abc$.
Question : If a + b + c = 0, then the value of (a + b – c)2 + ( b + c – a)2 + ( c + a – b)2 is:
Option 1: 0
Option 2: 8abc
Option 3: 4(a2 + b2 + c2)
Option 4: 4(ab + bc + ca)
Correct Answer: 4(a2 + b2 + c2)
Solution : a + b + c=0 ⇒ a + b = –c --------------(i) ⇒ b + c = –a --------------(ii) ⇒ c + a = –b --------------(iii) Substituting (i), (ii) and (iii) in (a + b – c)
Question : Which of the following was the host of ICC U19 Cricket World Cup 2022?
Option 1: Bangladesh
Option 2: Australia
Option 3: West Indies
Option 4: India
Correct Answer: West Indies
Solution : The correct answer is West Indies.
The 2022 ICC Under-19 Cricket World Cup took place in the West Indies in January and February 2022, featuring sixteen participating teams. This marked the fourteenth edition of the tournament and the first time it was hosted in
Question : The state electricity board gives a 15% discount on electric bills if it is paid before the due date. One person gets INR 54 as a discount. The amount of the actual bill was:
Option 1: INR 362
Option 2: INR 359
Option 3: INR 360
Option 4: INR 361
Correct Answer: INR 360
Solution : Let $x$ be the actual bill amount Discount = 15% of $x$ Discount% = $\frac{\text{Discount}}{\text{Actual Price}}$ × 100% ⇒ INR 54 = 15% of $x$ ⇒ $x$ = $\frac{5400}{15}$ = INR 360 Hence, the correct answer is INR 360.
Question : Comprehension:
In the following passage, some of the words have been deleted. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
Swollen joints (1)_______ when there is fluid in the tissues around the joints. It can be very (2)_______ and can make it difficult to move the affected joints. In some cases, swelling may cause affected joints to increase in size or appear to be in odd (3)_______. Joint pain and swelling can affect more than one (4)______ at a time. The most common joints to be (5)______ by pain and swelling are elbows, wrists, shoulders, the base of the spine, knuckles, hips, knees, or ankles. Question: Select the most appropriate option to fill in the blank number (5).
Option 1: blended
Option 2: affected
Option 3: balmed
Option 4: reacted
Correct Answer: affected
Solution : The correct choice is the second option.
The sentence discusses how pain and swelling affect joints. The term affected fits well in this context, implying that pain and swelling influence or alter the joints. When joints are affected, it means that they are experiencing these
Question : The average of 30 numbers is 40 and that of the other 40 numbers is 30. The average of all the numbers is:
Option 1: $34\frac{2}{7}$
Option 2: $35$
Option 3: $34$
Option 4: $34.5$
Correct Answer: $34\frac{2}{7}$
Solution : The sum of 30 numbers = 30 × 40 = 1200 The sum of 40 numbers = 30 × 40 = 1200 An average of 70 numbers is $=\frac{1200+1200}{30+40}=\frac{2400}{70}=34\frac{2}{7}$ Hence, the correct answer is $34\frac{2}{7}$.
Question : In which State of India is Sher Shah's Tomb located?
Option 1: Bihar
Option 2: Uttar Pradesh
Option 3: Punjab
Option 4: Bengal
Correct Answer: Bihar
Solution : The correct option is Bihar.
Sher Shah's Tomb is located in Sasaram in Bihar state. The tomb is an excellent example of Indo-Islamic architecture. It features a blend of Afghan and Indian architectural styles. The tomb is surrounded by beautiful Mughal-style gardens. The tomb
Question : What is the percentage horizontal reservation for women in the government jobs bill of Uttarakhand, approved by Governor Gurmit Singh?
Option 1: 30%
Option 2: 40%
Option 3: 20%
Option 4: 50%
Correct Answer: 30%
Solution : The correct answer is 30%.
Raj Bhavan received fourteen bills for approval. Twelve of these, including the one about women's reservations, have been approved. Women in Uttarakhand now have the legal right to 30% horizontal reservation in government employment, with the governor's approval. All women
Question : Who won the men's singles title at the Australian Open 2022?
Option 1: Rafael Nadal
Option 2: Casper Ruud
Option 3: Daniil Medvedev
Option 4: Novak Djokovic
Correct Answer: Rafael Nadal
Solution : The correct option is Rafael Nadal.
At the Australian Open 2022, Rafael Nadal from Spain emerged triumphant by defeating Daniil Medvedev from Russia in the men's singles final. This remarkable win marked Nadal's 21st major title. Nadal has won 22 Grand Slam men's singles
Question : Select the option that can be used as a one-word substitute for the given group of words. A particular form of a language which is peculiar to a specific region or social group.
Option 1: Singular
Option 2: Slang
Option 3: Dialect
Option 4: Referendum
Correct Answer: Dialect
The correct one-word substitute for the given group of words is dialect. A dialect refers to a particular form of language that is specific to a particular region, social group, or community. It involves variations in vocabulary, grammar,
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