Staff Selection Commission Combined Higher Secondary Level Exam
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%.
Question : An amount of INR $P$ was put at simple interest at a certain rate for 4 years. If it had been put at a 6% higher rate for the same period, it would have fetched INR 600 more interest. What is the value of $2.5P$?
Option 1: INR 3,750
Option 2: INR 6,250
Option 3: INR 4,850
Option 4: INR 2,500
Correct Answer: INR 6,250
Solution : Let's denote the initial rate of interest as $r$, and the principal amount as $P$ [Given]. The time is given as 4 years. The interest earned at the initial rate $r$ is $I=\frac{P×r×T}{100}$, where T is the time in years. The interest earned at
Question : A grocer mixes two varieties of tea priced at INR 80 per kg and INR 85 per kg in a certain ratio to produce a new variety priced at INR 82 per kg. What is the ratio in which the two varieties were mixed to obtain the new variety?
Option 1: 1 : 3
Option 2: 2 : 5
Option 3: 4 : 4
Option 4: 3 : 2
Correct Answer: 3 : 2
Solution : By using the rule of alligation, we get the required ratio = (85 – 82) : (82 – 80) = 3 : 2 Hence, the correct answer is 3 : 2.
Question : Directions: Karthik travelled 3 km east, then took a right turn and travelled 4 km. How far is he from the starting point?
Option 1: 5 km
Option 2: 15 km
Option 3: 3 km
Option 4: 7 km
Correct Answer: 5 km
Solution : Firstly, we will draw the diagram as per the given instructions –
Here, AB = 3 km and BC = 4 km AC is the distance between the starting and the finishing point. By applying the Pythagoras theorem – ⇒ (AC)2 = (AB)
Question : Directions: In the following question, four number pairs are given. In each pair, the number on the left side of (–) is related to the number on the right side of (–) with some Logic/Rule /Relation. Three pairs are similar based on the same Logic/Rule/Relation. Select the odd one out from the given alternatives. (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: 14 – 2844
Option 2: 12 – 1728
Option 3: 20 – 8000
Option 4: 10 – 1000
Correct Answer: 14 – 2844
Solution : Let's check each option – First option: 14 – 2844; 143 = 2744 ≠ 2844 Second option: 12 – 1728; 123 = 1728 Third option: 20 – 8000; 203 = 8000 Fourth option: 10 – 1000; 103 = 1000
Question : In which House, is the presiding officer, not a member of that House?
Option 1: Lok Sabha
Option 2: Rajya Sabha
Option 3: Vidhan Sabha
Option 4: Vidhan Parishad
Correct Answer: Lok Sabha
Solution : The correct option is Lok Sabha.
In India, the presiding officer who is not a member of the house is the Speaker of the Lok Sabha. The Speaker of the Lok Sabha is elected by the members of the Lok Sabha, but once
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