Staff Selection Commission Combined Graduate Level Exam
Question : Directions: Three statements are followed by three conclusions numbered I, II, and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements. Statements: Few chips are cakes. All cakes are ice creams. All ice creams are sweets. Conclusions: (I) Some sweets are cakes. (II) Some ice creams are cakes. (III) All cakes are sweets.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: All conclusions I, II and III follow
Option 4: Either conclusion I or conclusion III follows
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 sweets are cakes – From the Venn diagram, it is evident that some parts of the circle representing
Question : A difference curve measures _______ level of satisfaction derived from different combinations of commodities X and Y.
Option 1: same
Option 2: higher
Option 3: lower
Option 4: minimum
Correct Answer: same
Solution : The correct answer is the same.
An indifference curve evaluates the same amount of enjoyment gained from different commodity X and Y pairings. In other words, it depicts the combinations of products X and Y that offer a similar amount of satisfaction or utility
Question : $ \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}+\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}=$________.
Option 1: $2 \sin \theta$
Option 2: $2 \cos \theta$
Option 3: $ 2 \operatorname{cosec} \theta $
Option 4: $2 \sec \theta$
Correct Answer: $ 2 \operatorname{cosec} \theta $
Solution : Given: $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}+\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}$ = $ \frac{(1+\cos \theta) + (1-\cos \theta)}{\sqrt{(1-\cos \theta)(1+\cos \theta)}}$ = $ \frac{2}{\sqrt{(1-\cos^2 \theta)}}$ = $\frac{2}{\sin \theta}$ = $ 2 \operatorname{cosec} \theta $ Hence, the correct answer is $ 2 \operatorname{cosec} \theta $.
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
Please switch of the fan.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The first option is the correct answer.
Switch-off means to turn off or deactivate an electrical device or system. This is the only option that fits the sentence.
Hence, the correct sentence is: "Please switch off the fan."
Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows the given statements. Statements: All F is K. All W is K. Conclusions: I. All W is F. II. Some K is not W. III. Some F is W.
Option 1: Both conclusions I and III follow
Option 2: Both conclusions II and III follow
Option 3: Only conclusion I follows
Option 4: Neither conclusion follows
Correct Answer: Neither conclusion follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All W is F – From the Venn diagram, it is evident that there is no direct relation between W and F. So,
Question : Select the most appropriate option to fill in the blank. Vishal is going to read the story_____
Option 1: load
Option 2: allow
Option 3: aloud
Option 4: allowed
Correct Answer: aloud
Solution : The third option is the correct choice.
Aloud means to read or speak audibly so others can hear. In the context of reading a story, the appropriate word is aloud, as it signifies reading audibly.
The meanings of the other options are as follows:
Load
Question : In the figure given below, PQ is the diameter of the circle with centre O. If $\angle QOR=100^{\circ}$, then the measure of $\angle PSR$ is:
Option 1: $160^{\circ}$
Option 2: $80^{\circ}$
Option 3: $40^{\circ}$
Option 4: $100^{\circ}$
Correct Answer: $40^{\circ}$
Solution : Given: $\angle POR = 100^\circ$ Now, POQ is a straight line. ⇒ $\angle POR + \angle QOR = 180^\circ$ ⇒ $100^\circ+\angle POR = 180^\circ$ ⇒ $\angle POR = 180^\circ- 100^\circ = 80^\circ$ Theorem: The angle subtended by an arc at the centre is double the
Question : 60 kg of alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is:
Option 1: 53 kg
Option 2: 44 kg
Option 3: 80 kg
Option 4: 24 kg
Correct Answer: 44 kg
Solution : Given: Alloy A = 60 kg Alloy B = 100 kg Alloy A has lead and tin in the ratio of 3 : 2. Alloy B has tin and copper in the ratio of 3 : 2. According to the question statements, In 60
Question : Reshma covers 45 km at a speed of 15 km/hr by bicycle, 80 km at a speed of 40 km/hr by car, and another 6 km at a speed of 2 km/hr on foot. Find her average speed for the whole journey (correct to 2 decimal places).
Option 1: 16.38 km/hr
Option 2: 43.50 km/hr
Option 3: 18.36 km/hr
Option 4: 15.25 km/hr
Correct Answer: 16.38 km/hr
Solution : Reshma covers 45 km at a speed of 15 km/hr by bicycle, 80 km at a speed of 40 km/hr by car, and another 6 km at a speed of 2 km/hr on foot. $\text{Average speed}=\frac{\text{Total distance}}{{\text{Total time}}}$ ⇒ $\text{Average speed}=\frac{45+80+6}{\frac{45}{15}+\frac{80}{40}+\frac{6}{2}}=\frac{131}{3+2+3}=\frac{131}{8}=16.38$ km/hr Hence, the
Question : Directions: From the given alternative words, select the word that cannot be formed using the letters of the given word. CIRCUMSTANCES
Option 1: DISTANCE
Option 2: STANCE
Option 3: MUSIC
Option 4: CIRCUS
Correct Answer: DISTANCE
Solution : Given: CIRCUMSTANCES
Now, let's compare all the option words with the word CIRCUMSTANCES – First option: DISTANCE; All the letters of DISTANCE are not present in the word CIRCUMSTANCES. D is not present in the word CIRCUMSTANCES. Second option: STANCE; All the letters of STANCE
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