Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements. Statements: Some dietitians are surgeons. All surgeons are therapists. No therapist is a physician. Conclusion: (I) Some therapists are dietitians. (II) No dietitian is a physician.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusions I and II follow
Option 4: Neither conclusion I nor II follows
Correct Answer: Only conclusion I follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some therapists are dietitians – From the Venn diagram, it is evident that the two circles representing therapists and dietitians overlap and
Question : Given below are four jumbled sentences. Pick the option that gives their correct order.
The immediate context of the Dunkirk evacuation was Germany's invasion of the Low Countries and northern France in May 1940. P. The Dutch defenders fell back westward, and by noon on May 12 German tanks were on the outskirts of Rotterdam. Q. Queen Wilhelmina and her government left the country for England on May 13, and the next day the Dutch army surrendered to the Germans. R. On May 10 the German blitzkrieg attack on the Netherlands began with the capture by parachutists of key bridges deep within the country, with the aim of opening the way for mobile ground forces. S. The invasion of Belgium also began on May 10, when German airborne troops landed on the fortress of Eben Emael, immediately opposite Maastricht, and on bridges over the Albert Canal. On May 11 the Belgian front was broken, and German tanks ran on westward while Belgian, French, and British divisions fell back to a line between Antwerp and Namur.
Option 1: QPRS
Option 2: PRSQ
Option 3: PSRQ
Option 4: RPQS
Correct Answer: RPQS
Solution : The correct choice is the fourth option.
The context helps identify that the paragraph is about the German invasion of the countries and northern France. Thus, to state the information provided chronologically, we follow the below steps:
Question : Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur, respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur, respectively. If X is moving at 45 km/hr, the speed of Y is:
Option 1: 60 km/hr
Option 2: 58 km/hr
Option 3: 54 km/hr
Option 4: 64.8 km/hr
Correct Answer: 54 km/hr
Solution : We know, $\frac{\text{Speed of X}}{\text{Speed of Y}}=\sqrt{\frac{\text{Time taken by Y after crossing X}}{\text{Time taken by X after crossing Y}}}$ $⇒\frac{45}{\text{Speed of Y}}=\sqrt{\frac{\text{3 hour 20 min}}{\text{4 hour 48 min}}}=\sqrt{\frac{\text{200 min}}{\text{288 min}}}=\sqrt{\frac{100}{144}}$ $⇒\frac{45}{\text{Speed of Y}}=\frac{10}{12}$ $\therefore \text{Speed of Y}=54$ km/hr Hence, the correct answer is 54
Question : Parts of the following sentence are given as options. Identify the part that contains a grammatical error. If there is no error, select 'No Error'.
You never know when / you are going to stumble to a / jewel in the most unexpected corner.
Option 1: You never know when
Option 2: you are going to stumble to a
Option 3: jewel in the most unexpected corner.
Option 4: No Error
Correct Answer: you are going to stumble to a
Solution : The error lies in the second option.
The preposition to is incorrect in this context. The correct idiom is stumble upon, which means to discover or find something unexpectedly. So, the phrase should be stumble upon a
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement."
The offerings were placed (on the alter).
(1) on the altar
(2) on the steps.
(3) on the platform.
(4) No improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option "on the altar."
An "altar" is a raised platform or table used in religious ceremonies for making offerings or sacrifices. Therefore, when describing where the offerings were placed, "on the altar" is the appropriate phrase to
Question : If $0^{\circ}< \theta< 90^{\circ}$ and $\operatorname{cosec \theta} =\cot^{2}\theta$, then the value of expression $\operatorname{cosec^{4}\theta}–\operatorname{2cosec^{2}\theta}-\cot^{2}\theta$ is equal to:
Option 1: $2$
Option 2: $0$
Option 3: $1$
Option 4: $3$
Correct Answer: $0$
Solution : $\operatorname{cosec \theta} =\cot^{2}\theta$ $⇒\operatorname{cosec \theta} = \operatorname{cosec^2 \theta} -1$ Squaring both sides, we get, $⇒\operatorname{cosec^2 \theta} =\operatorname{cosec^4 \theta} -2\operatorname{cosec^2 \theta} +1$ $⇒\operatorname{cosec^4 \theta} -3\operatorname{cosec^2 \theta} +1=0$ $⇒\operatorname{cosec^4 \theta} -3\operatorname{cosec^2 \theta} +\operatorname{cosec^2 \theta} -\cot^2\theta =0$ [$\because1 = \operatorname{cosec^2 \theta}-\cot^2\theta$] $⇒\operatorname{cosec^4 \theta} -2\operatorname{cosec^2 \theta} -\cot^2\theta =0$ Hence,
Question : Directions: Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group? 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: 8 – 72
Option 2: 11 – 143
Option 3: 7 – 63
Option 4: 9 – 99
Correct Answer: 8 – 72
Solution : Let's check the options – First option: 8 – 72; 82 = 64; 64 + 8 × 2 = 64 + 16 = 80 ≠ 72 Second option: 11 – 143; 112 = 121; 121 + 11 × 2 = 121
Question : Red soil found in India in which regions?
Option 1: Eastern Region only
Option 2: Southern Region only
Option 3: Eastern and Southern part of the Deccan Plateau
Option 4: None of these
Correct Answer: Eastern and Southern part of the Deccan Plateau
Solution : The correct answer is the Eastern and Southern parts of the Deccan Plateau.
Red soil is made up of an alluvium red layer, a thin layer of highly organic and organic-mineral soil and a lot of clay. This
Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Option 1: 105
Option 2: 101
Option 3: 108
Option 4: 103
Correct Answer: 108
Solution : Given: A metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each We know, The volume of a cone = $\ \frac {1}{3}\pi r^2h$, where $r$ and $h$ are the radius and height of the cone
Question : 51% of a whole number is 714. What is 25% of that number?
Option 1: 350
Option 2: 450
Option 3: 550
Option 4: 250
Correct Answer: 350
Solution : Let the number be $x$. According to the question, $x × \frac{51}{100} = 714$ ⇒ $x = 1400$ Now, 25% of that number is $1400 × \frac{25}{100} = 350$ Hence, the correct answer is 350.
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