Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\sin A=\frac{2}{5}$, where $A$ is an acute angle, what is the value of $\frac{5 \sin A+2 \operatorname{cosec} A}{\sqrt{21} \sec A}$?
Option 1: $\frac{5}{4}$
Option 2: $\frac{7}{5}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{5}{7}$
Correct Answer: $\frac{7}{5}$
Solution : $\sin A=\frac{2}{5}$ $⇒\cos A = \sqrt{1-\sin^2 A}$ $⇒\cos A = \sqrt{1-(\frac{2}{5})^2}$ $⇒\cos A = \sqrt{1-(\frac{4}{25})}$ $⇒\cos A = \sqrt{(\frac{21}{25})}$ $⇒\cos A = \frac{\sqrt{21}}{5}$ So, $\sec A = \frac{5}{\sqrt{21}}$ And, $\operatorname{cosec} A = \frac{5}{2}$ $\frac{5 \sin A+2 \operatorname{cosec} A}{\sqrt{21} \sec A}$ $=\frac{5 \times \frac{2}{5} +2 \times
Question : Directions: In the following question, select the one which is different from the other three alternatives.
Option 1: 4367
Option 2: 3245
Option 3: 6578
Option 4: 7689
Correct Answer: 4367
Solution : Let's check the options – The first option: 4367; The first and second halves are 43 and 67. ⇒ 67 – 43 = 24 ≠ 13 Second option: 3245; The first and second halves are 32 and 45. ⇒ 45 – 32 = 13 Third
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
Entrance exams for the (1) / posts of associate professors (2) / will begin from Tuesday. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The correct choice is the second option.
''Posts'' should be replaced with ''post'' to convey the intended meaning of recruitment for the post of assistant professor.
''Post'' should be used instead of ''posts'' because it refers to the position of an associate professor, which refers
Question : Directions: In the given question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
With his political_____, the party president deftly handled the rebellion.
Option 1: temperament
Option 2: sagacity
Option 3: attitude
Option 4: inexperience
Correct Answer: sagacity
"Sagacity" directly implies political wisdom or shrewdness, which fits in the context of the sentence where the party president effectively handled the rebellion.
The meanings of the other options are as follows:
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No substitution required’. If I was you, I would not have appeared for the entrance exam.
Option 1: would
Option 2: would have been
Option 3: No substitution required
Option 4: were
Correct Answer: were
Solution : The right choice is the fourth option.
The sentence "if I were you, I would not have appeared for the entrance exam" uses the subjunctive mood to express a hypothetical situation. In English, the subjunctive mood often uses "were" instead of "was" when talking
Question : Who was appointed as the new chairman of the Central Board of Direct Taxes (CBDT) in June 2022?
Option 1: Atulesh Jindal
Option 2: Rani Singh Nair
Option 3: Sudha Sharma
Option 4: Nitin Gupta
Correct Answer: Nitin Gupta
Solution : The correct option is Nitin Gupta.
Nitin Gupta has been appointed as the new chairman of the Central Board of Direct Taxes (CBDT). CBDT is a statutory body that functions under the Department of Revenue in the Ministry of Finance, Government of India. The
Question : If $\cot 3 \mathrm{~A}=\tan \left(\mathrm{A}-36^{\circ}\right)$, then what is the value of $\mathrm{A}$?
Option 1: 33.5 degrees
Option 2: 25 degrees
Option 3: 30 degrees
Option 4: 31.5 degrees
Correct Answer: 31.5 degrees
Solution : $\cot 3 \mathrm{~A}=\tan \left(\mathrm{A}-36^{\circ}\right)$ $⇒ \tan (90-3 \mathrm{~A})=\tan \left(\mathrm{A}-36^{\circ}\right)$ $⇒ 90^{\circ}-3 \mathrm{~A} = \mathrm{~A}-36^{\circ}$ $⇒ 4 \mathrm{~A} = 126^{\circ}$ $\therefore \mathrm{~A} = 31.5^{\circ}$ Hence, the correct answer is 31.5 degrees.
Question : Directions: The position of how many letters will remain unchanged if each letter in the word HEARDVG is arranged in alphabetical order.
Option 1: Three
Option 2: One
Option 3: Two
Option 4: None
Correct Answer: None
Solution : Given: HEARDVG When the letters of HEARDVG are arranged in alphabetical order, the letter cluster formed is ADEGHRV.
So, no letter has the same position as before. Hence, the fourth option is correct.
Question : A man sold his watch at a loss of 5%. Had he sold it for Rs 56.25 more, he would have gained 10% what is the cost price of the watch in Rs?
Option 1: 370
Option 2: 365
Option 3: 375
Option 4: 390
Correct Answer: 375
Solution : Let the cost price of the watch be Rs. $x$. Given that, Had he sold it for Rs. 56.25 more, he would have gained 10%. At a loss of 5%, Selling price = $\frac{(100-5)}{100}\times x=\frac{95x}{100}$ At a gain of 10%, Selling price = $\frac{(100+10)}{100}\times x=\frac{110x}{100}$
Question : Which of the following is not a component of investment?
Option 1: In addition to residential construction
Option 2: Money spent on purchasing shares of a company
Option 3: Machinery and equipment employed by a firm
Option 4: Inventories of raw materials stocked by a firm
Correct Answer: Money spent on purchasing shares of a company
Solution : The correct option is Money spent on purchasing shares of a company.
Money spent on purchasing shares of a company is not considered a component of investment in the traditional sense. While buying shares is a financial transaction,
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
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The Question is not relevant to User
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