Staff Selection Commission Combined Higher Secondary Level Exam
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Friendship is one of the most significant aspects (1)_____human life. It is a relationship based on mutual trust, respect and support. True friendship is not just about spending time (2)_____, but also about sharing each other's joys, sorrows and dreams. Good friends are those who stand by us in both good times and bad times, providing emotional and moral support. Having good friends can have a positive impact on one's mental health and well-being. Friends can be a source of happiness, laughter and comfort. They can also provide different perspectives and ideas that can help us grow as (3)_____ Moreover, friends can serve as a support system during challenging times, offering words of encouragement and helping us navigate through difficult situations. (4)_____building and maintaining friendships requires effort, patience and understanding. It is important to be there for each other, listen to one another and respect each other's boundaries. It is important to remember that friendships can evolve and change over time, and it is okay to let go of (5)_____friendships.
Select the most appropriate option to fill in the blank number 5.
Option 1: toxic
Option 2: unsafe
Option 3: happy
Option 4: safe
Correct Answer: toxic
Solution : The correct choice is the first option.
Toxic means something that is not good for someone. In this context, it is used to convey that it is okay to let go of friendships that are not good for the individual.
Question : The cost of 3 pieces of bread and 1 packet of juice at a certain store is Rs. 323.50. At the same store, the cost of 5 pieces of bread and 1 packet of juice is Rs. 433.50. What will be the cost of 2 pieces of bread and 2 packets of juice at this store?
Option 1: Rs. 427
Option 2: Rs. 350
Option 3: Rs. 433
Option 4: Rs. 403
Correct Answer: Rs. 427
Solution : Let the cost of one bread be b and the cost of one packet of juice be j. The cost of 3 breads and 1 packet of juice. ⇒ 3b + j = 323.50---(1) The cost of 5 breads and 1 packet of juice.
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".
Another baffling change (1) / that I noticed in him nowadays (2) / is that he avoids speaking to me. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
Explanation: The verb noticed will be replaced with notice, as it is not used in "-ing form" because words of feeling, thinking, possession, and sense are not normally used in the present continuous
Question : ${L}$ is the incentre of $\triangle ONP$. If $\angle {OLP}+\angle {ONP}=195^\circ$, then what will be the value of $\angle {OLP}$?
Option 1: $115^\circ$
Option 2: $140^\circ$
Option 3: $135^\circ$
Option 4: $125^\circ$
Correct Answer: $125^\circ$
Solution : Given: $\angle {OLP}+\angle {ONP}=195^\circ$ ⇒ $\angle {OLP}=195^\circ-\angle {ONP}$ L is the incentre So, $\angle OLP = 90^\circ+\frac{1}{2}\angle ONP$ ⇒ $195^\circ-\angle {ONP} = 90^\circ+\frac{1}{2}\angle ONP$ ⇒ $105^\circ= \frac{3}{2}\angle ONP$ ⇒ $\angle ONP=70^\circ$ $\therefore \angle OLP = 195^\circ-70^\circ= 125^\circ$ Hence, the correct answer is $125^\circ$.
Question : Directions: Pointing towards a girl, Shilpa said, “She is the daughter of my husband’s wife”. How is Shilpa’s son related to that girl?
Option 1: Son
Option 2: Paternal Uncle
Option 3: Brother
Option 4: Nephew
Correct Answer: Brother
Solution : As per the given information, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, Shilpa’s son is the brother of that girl. Hence, the third option is correct.
Question : If $x=(7+3 \sqrt{5})$, then find the value of $x^2+\frac{1}{x^2}$.
Option 1: $ \frac{580+315 \sqrt{5}}{8}$
Option 2: $\frac{799+328 \sqrt{5}}{8}$
Option 3: $\frac{799+315 \sqrt{5}}{12}$
Option 4: $\frac{799+315 \sqrt{5}}{8}$
Correct Answer: $\frac{799+315 \sqrt{5}}{8}$
Solution : Given, $x=(7+3 \sqrt{5})$ Squaring both sides, we get, $x^2=(7+3 \sqrt{5})^2$ ⇒ $x^2=49+9\times 5+2\times 7\times 3\sqrt5$ [As $(a+b)^2=a^2+b^2+2ab$] ⇒ $x^2=49+45+42\sqrt5$ ⇒ $x^2=94+42\sqrt5$ And, $\frac{1}{x^2}=\frac{1}{(7+3\sqrt5)^2}=\frac{1}{94+42\sqrt5}$ Rationalising the equation, ⇒ $\frac{1}{x^2}=\frac{1}{94+42\sqrt5}\times\frac{{94-42\sqrt5}}{{94-42\sqrt5}}$ ⇒ $\frac{1}{x^2}=\frac{{94-42\sqrt5}}{(94)^2-(42\sqrt5)^2}$ ⇒ $\frac{1}{x^2}=\frac{{94-42\sqrt5}}{8836-8820}$ ⇒ $\frac{1}{x^2}=\frac{{94-42\sqrt5}}{16}$ ⇒ $\frac{1}{x^2}=\frac{{47-21\sqrt5}}{8}$ Now, $x^2+\frac{1}{x^2}$ Putting the value of $x^2$ and
Question : The sex ratio refers to the number of women
Option 1: per sq. km. with males
Option 2: per 1000 males
Option 3: per states with males
Option 4: and the number of men in an area
Correct Answer: per 1000 males
Solution : The correct answer is per 1000 males.
The sex ratio is a demographic metric that measures the number of females present per thousand males. As per the 2011 census, the sex ratio in India is 943, which is an improvement over the 2001
Question : Directions: A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given folded paper is unfolded, it will look like –
Hence, the third option is correct.
Question : If $x - y = 8$ and $8xy = 8$, then what is the value of $2 x^3-2 y^3$?
Option 1: 536
Option 2: 1092
Option 3: 1072
Option 4: 1608
Correct Answer: 1072
Solution : $8xy = 8$ $⇒ xy = 1$ and $x - y = 8$ Cubing both sides, we get, $(x - y)^3 = 8^3$ ⇒ $x^3 - y^3 - 3xy(x - y) = 512$ Putting the given values, we get, ⇒ $x^3 - y^3 - 3
Question : The Graph shows the number of students (in thousands) admitted to five schools. The ratio between the total number of students admitted to schools B and D to the total number of students admitted to schools A, C, and E is:
Option 1: 11 : 10
Option 2: 10 : 11
Option 3: 12 : 11
Option 4: 11 : 12
Correct Answer: 11 : 12
Solution : Given: Total number of students admitted to schools B and D (in thousands) = (60 + 50) =110 Total number of students admitted to schools A, C and E = (40 + 35 + 45) = 120 Ratio of (B + D) and
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