Staff Selection Commission Combined Higher Secondary Level Exam
Question : Iodine can be separated from a mixture of Iodine and potassium chloride by
Option 1: sedimentation
Option 2: Filtration
Option 3: sublimation
Option 4: distillation
Correct Answer: sublimation
Solution : The correct option is sublimation.
Iodine can be separated from a mixture of iodine and potassium chloride through a process called sublimation. Sublimation is a physical process in which a solid substance transitions directly into a gas without passing through the liquid phase. The steps
Question : If $a-b = 5$ and $ab = 24$, find the value of $a^3-b^3$.
Option 1: 455
Option 2: 485
Option 3: 385
Option 4: 360
Correct Answer: 485
Solution : Given: $a-b = 5$ and $ab = 24$ $(a-b)^3=5^3$ $⇒a^3 - b^3 - 3ab(a-b) = 125$ $⇒a^3 - b^3 = 125 + (3×24×5) = 125 + 360 = 485$ Hence, the correct answer is 485.
Question : When were the Fundamental Duties of the Indian citizens incorporated in the constitution
Option 1: 1952
Option 2: 1976
Option 3: 1979
Option 4: 1981
Correct Answer: 1976
Solution : The correct option is 1976.
The Fundamental Duties of Indian citizens were added to the Constitution in 1976 through the 42nd Amendment Act. These duties, listed in Article 51A, serve as a moral and civic code for citizens. They aim to encourage a sense of
Question : Directions: Select the pair from the below options that have the same analogy as the following given pairs. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 5 : 26 9 : 82
Option 1: 4 : 24
Option 2: 3 : 12
Option 3: 2 : 5
Option 4: 6 : 55
Correct Answer: 2 : 5
Solution : Given: 5 : 26; 9 : 82
Here, 5 : 26→(5)2 + 1 = 25 + 1 = 26 9 : 82→(9)2 + 1 = 81 + 1 = 82
Now, let's check the given options – First option: 4 :
Question : The point $Q(a,b)$ is first reflected in the y-axis to $Q_1$ and $Q_1$ is reflected in the x-axis to $(-5,3)$. The coordinates of point $Q$ are:
Option 1: $(–5,–3)$
Option 2: $(5,3)$
Option 3: $(–5,3)$
Option 4: $(5,–3)$
Correct Answer: $(5,–3)$
Solution : Given: $Q1$ is reflected over the x-axis to $(–5,3)$. $Q1$ = image of $Q(a,b)$ over Y-axis = $(–5,3)$ Image of $Q(a,b)$ over Y-axis = $(–(–5),–(3))$ Image of $Q(a,b)$ over Y-axis = $(5,–3)$ Hence, the correct answer is $(5,–3)$.
Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:
Option 1: $\frac{2 \sqrt{6}-6}{5}$
Option 2: $\frac{4 \sqrt{6}-6}{5}$
Option 3: $\frac{4 \sqrt{6}-6}{3}$
Option 4: $\frac{4 \sqrt{3}-6}{5}$
Correct Answer: $\frac{4 \sqrt{6}-6}{5}$
Solution : Given: $x=(\sqrt{6}-1)^{\frac{1}{3}}$ Cubing both sides, we get, $x^3=\sqrt6-1$ $\therefore \frac{1}{x^3}=\frac{1}{\sqrt6-1}=\frac{\sqrt6+1}{5}$ Now, $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ $=x^3-\frac{1}{x^3}-3×x×\frac{1}{x^3}(x-\frac{1}{x})-3(x-\frac{1}{x})$ $=x^3-\frac{1}{x^3}$ Putting values, we get, $=(\sqrt6-1)-\frac{\sqrt6+1}{5}$ $=\frac{4 \sqrt{6}-6}{5}$ Hence, the correct answer is $\frac{4 \sqrt{6}-6}{5}$.
Question : Find the $n$th term of the following sequence: 5 + 55 + 555 + ........+$T_n$
Option 1: $5(10^n-1)$
Option 2: $5^n(10^n-1)$
Option 3: $\frac{5}{9}(10^{n} - 1)$
Option 4: $(\frac{5}{9})^{n} (10^{n} -1)$
Correct Answer: $\frac{5}{9}(10^{n} - 1)$
Solution : Given: 5 + 55 + 555 + ........ $n$th term = 5 (1 + 11 + 111 + ... to $n$ terms) Multiplying and divide by 9 in series, $n$th term = $\frac{5}{9}$(9 + 99 + 999 +... to $n$ terms) ⇒ $n$th
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
Only me can solve the problem.
(1) Only me can
(2) Only I can
(3) I can only
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The sentence can be improved using the second option.
The pronoun "I" should be used in place of "me" in the sentence. "Me" is used as an object, whereas "I" is used as a subject in a sentence. As the sentence
Question : In Microsoft Word, under character formatting, ______ is used to underline some particular text.
Option 1: font style
Option 2: underline
Option 3: effects
Option 4: size
Correct Answer: underline
Solution : The correct option is underline.
The underline, known by various names such as understrike or underbar, originally appeared on typewriter keyboards. Its primary purpose was to emphasise words or numbers by placing a line beneath them. In Word's wavy underline system, red signifies spelling
Question : The line chart given below shows the population of two states P and Q in 5 years. What is the difference between the total population of P and Q in all the years?
Option 1: 150
Option 2: 75
Option 3: 275
Option 4: 125
Correct Answer: 125
Solution : Total population of Q = 300 + 200 + 125 + 75 + 150 = 850 Total population of P = 150 + 250 + 175 + 100 + 50 = 725 Difference = 850 – 725 = 125 Hence, the correct answer is 125.
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