Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Four triads of numbers have been given out of which three are alike in some manner and one is different. Select a different one. 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.)
Option 1: 19 – 37 – 73
Option 2: 14 – 29 – 59
Option 3: 23 – 47 – 95
Option 4: 3 – 7 – 15
Correct Answer: 19 – 37 – 73
Solution : Let's check the options –
First option: (19 – 37 – 73)→(19 × 2) + 37 + 2 = 38 + 37 + 2 = 77 ≠ 73 Second option: (14 – 29 – 59)→(14 × 2) + 29 + 2
Question : The value of 32 + 12 × 36 ÷ 4 + 4 – 22 ÷ 11 × 3 is:
Option 1: 142
Option 2: 138
Option 3: 150
Option 4: 130
Correct Answer: 138
Solution : 32 + 12 × 36 ÷ 4 + 4 – 22 ÷ 11 × 3 Applying BODMAS, we get: = 32 + 12 × 9 + 4 - 2 × 3 = 32 + 108 + 4 - 6 = 138 Hence, the correct answer
Question : Study the given table and answer the question that follows. The table indicates the number of students studying in three disciplines in four different colleges.
Which college has the minimum number of students in Commerce?
Option 1: A
Option 2: B
Option 3: C
Option 4: D
Correct Answer: C
Solution : From the given data, the minimum number of students in commerce = 515 Hence, the correct answer is C.
Question : If $x^2-11x+1=0$, what is the value of $x^8-14159x^4+11$?
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 11
Correct Answer: 10
Solution : Given: $x^2-11x+1=0$ Divide both sides by $x$, we get $x-11+\frac{1}{x}=0$ ⇒ $x+\frac{1}{x}=11$ Squaring both sides we get ⇒ $x^2+\frac{1}{x^2}+2×x×\frac{1}{x}=11^2$ ⇒ $x^2+\frac{1}{x^2}=121-2$ ⇒ $x^2+\frac{1}{x^2}=119$ Again squaring both sides we get, ⇒ $x^4+\frac{1}{x^4}+2×x^2×\frac{1}{x^2}=119^2$ ⇒ $x^4+\frac{1}{x^4}=14161-2$ ⇒ $x^4+\frac{1}{x^4}-14159=0$ Multiplying with $x^4$ we get ⇒ $x^8-14159x^4+1=0$ $\therefore x^8-14159x^4+11=10$ Hence,
Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: I. Some buses are motorbikes. II. All motorbikes are vans. III. All buses are cars. Conclusions: I. Some cars are vans. II. Some vans are buses. III. Some vans are motorbikes.
Option 1: Only conclusion II follows
Option 2: All conclusions I, II and III follow
Option 3: Only conclusion I follows
Option 4: Both conclusions I and II follow
Correct Answer: All conclusions I, II and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some cars are vans – From the Venn diagram, we can see that the two circles representing cars and
Question : If $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$ and $\theta$ is acute, then the value of $\theta$ is:
Option 1: $60^{\circ}$
Option 2: $15^{\circ}$
Option 3: $45^{\circ}$
Option 4: $30^{\circ}$
Correct Answer: $60^{\circ}$
Solution : $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$ Multiplying the two fractions by $(1+\sin \theta)(1-\sin \theta)=\cos^2 \theta$. $⇒ \cos \theta (1-\sin \theta) + \cos \theta (1+\sin \theta) = 4 \cos^2 \theta$ $⇒ 2 \cos \theta = 4 \cos^2 \theta$ $⇒ 1 = 2 \cos \theta$ $⇒ \cos \theta
Question : Ramnad V. Raghavan is associated with which of the following musical instruments?
Option 1: Mridangam
Option 2: Flute
Option 3: Sitar
Option 4: Sarod
Correct Answer: Mridangam
Solution : The correct answer is the Mridangam.
Ramnad V. Raghavan was indeed associated with the musical instrument "Mridangam". He was a renowned Indian percussionist and mridangam player. The mridangam is a traditional double-headed drum that is widely used in the Carnatic music of South India.
Question : Directions: Looking at a woman sitting next to him, Gaurav said, "She is the sister of the husband of my wife." How is the woman related to Gaurav?
Option 1: Daughter
Option 2: Mother
Option 3: Wife's sister
Option 4: Sister
Correct Answer: Sister
Solution : Following the instructions of the question, the family tree will be –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, the woman is the sister of Gaurav. Hence, the fourth option is correct.
Question : Select the most appropriate option to fill in the blank.
The _________ of the new legislation has sparked a heated debate among lawmakers.
Option 1: affectation
Option 2: effection
Option 3: effect
Option 4: affect
Correct Answer: effect
Solution : The correct choice is the third option.
Effect refers to a change that something has brought about. It is a noun that is used to indicate the result of a change. Thus, effect is the correct choice, as the sentence requires a noun.
The
Question : The following bar graph shows the amount (in lakh Rs.) invested by a company in purchasing raw materials over the years 2015 to 2019. By how much percent did the company increase its investment in raw materials in 2019, as compared to 2015?
Option 1: 20%
Option 2: 33.33%
Option 3: 66.66%
Option 4: 11.66%
Correct Answer: 66.66%
Solution : Raw materials in 2015 = 330 Raw materials in 2019 = 550 Percentage increase $=\frac{\text{Raw materials in 2019 – Raw materials in 2015}}{\text{Raw materials in 2015}}\times100$ $=\frac{550-330}{330}\times100$ $=\frac{220}{330}\times100=66.66\%$ Hence, the correct answer is 66.66%.
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