Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given set. (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.) (101, 10201, 10302) (95, 9025, 9120)
Option 1: (103, 10069, 10172)
Option 2: (105, 11025, 11230)
Option 3: (104, 10816, 10820)
Option 4: (102, 10404, 10506)
Correct Answer: (102, 10404, 10506)
Solution : Given: (101, 10201, 10302) (95, 9025, 9120)
Here, the pattern followed is as follows – (101, 10201, 10302)→(101)2 = 10201; (101 × 102) = 10302 (95, 9025, 9120)→(95)2 = 9025; (95 × 96) = 9120
Let's check the options – First
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on line MN). So, the left side of the reflected image will appear
Question : Which of the following is a correct expression?
Option 1: Depreciation = Net investment - Gross investment
Option 2: Gross investment = Net investment - Depreciation
Option 3: Net investment = Gross investment - Depreciation
Option 4: Net investment = Gross investment + Depreciation
Correct Answer: Net investment = Gross investment - Depreciation
Solution : The correct option is Net investment = Gross investment - Depreciation.
Depreciation is subtracted from Gross investment to determine net investment. Depreciation is the term used to describe how capital assets lose value over time as a result
Question : If $\tan \theta -\cot \theta =0$, find the value of $\sin \theta +\cos \theta$.
Option 1: $0$
Option 2: $1$
Option 3: $\sqrt{2}$
Option 4: $2$
Correct Answer: $\sqrt{2}$
Solution : Given: $\tan\theta -\cot\theta =0$ $⇒\tan\theta=\cot\theta$ $\therefore\theta = 45^{\circ}$ $\therefore \sin\theta +\cos\theta = \sin45^{\circ} + \cos45^{\circ}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2}{\sqrt2}=\sqrt2$ Hence, the correct answer is $\sqrt2$.
Question : In a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?
Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)
Option 2: 2(AD + BE + CF) > (AB + BC + AC)
Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)
Option 4: AB + BC + AC > AD + BE + CF
Correct Answer: AB + BC + AC > AD + BE + CF
Solution : AB + AC > 2AD -------------(i) AB + BC > 2BE -------------(ii) AC + BC > 2CF -------------(iii) Adding (i), (ii), and (iii) ⇒ 2(AB + BC + AC) > 2 (AD + BE +
Question : Simplify the following expression: $\frac{\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2}{b^2-c^2}$
Option 1: $3a^2$
Option 2: $4a^2$
Option 3: $5a^2$
Option 4: $2a^2$
Correct Answer: $4a^2$
Solution : Given: $\frac{(a^2+b^2-c^2)^2-(a^2-b^2+c^2)^2}{b^2-c^2}$ $= \frac{(a^2+b^2-c^2+a^2-b^2+c^2)(a^2+b^2-c^2-a^2+b^2-c^2)}{b^2-c^2}$ $= \frac{(2a^2)(2b^2-2c^2)}{b^2-c^2}$ $= \frac{4a^2(b^2-c^2)}{b^2-c^2}$ $= 4a^2$ Hence, the correct answer is $4a^2$.
Question : Directions: If the age of Rahul is 5 years more than his friend Ajay's age, the age of Rahul's wife is 6 years less than Rahul's, and Ajay's wife is 1 year older than Rahul's wife, then which of the following statements is true?
Option 1: Rahul's age and Ajay's wife's age are the same
Option 2: Ajay's wife's age and Ajay's age are the same
Option 3: Rahul and Ajay are of the same age
Option 4: Rahul's and Ajay's age difference is 3 years
Correct Answer: Ajay's wife's age and Ajay's age are the same
Solution : Given: Let Ajay's age be x years. Rahul's age = x + 5 years Rahul's wife's age = x + 5 – 6 = x – 1 years Ajay's wife's age = x – 1 + 1
Question : __________ was the first governor-general of Bengal.
Option 1: Warren Hastings
Option 2: William Bentinck
Option 3: Charles Metcalfe
Option 4: John Shore
Correct Answer: Warren Hastings
Solution : The correct answer is Warren Hastings.
Warren Hastings was the first governor-general of Bengal from 1773 to 1785. He became the governor-general of Bengal by the Regulating Act of 1773, which brought the presidencies of Madras and Bombay under Bengal’s control.
Question : Which state has become the first to launch a dedicated Semiconductor Policy in July 2022?
Option 1: Haryana
Option 2: Madhya Pradesh
Option 3: Kerala
Option 4: Gujarat
Correct Answer: Gujarat
Solution : The correct option is Gujarat.
Gujarat has established a dedicated semiconductor policy, making it the first state in the nation to do so. The state government has agreed to offer significant electricity, land, and water tariff subsidies to entrepreneurs who wish to engage in
Question : Directions: Select the Venn diagram that best represents the relationship between the following classes. Language, Punjabi, Hindi, Malayalam
Solution : Based on the general information, Hindi, Punjabi, and Malayalam are the languages. So, their circles will lie inside the circle of languages. But, all these three languages are not related to each other. So, their three circles will be drawn separately.
Therefore, the Venn diagram is
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