Staff Selection Commission Combined Graduate Level Exam
Question : ABCD is a trapezium with AD and BC parallel sides and E is a point on BC. The ratio of the area of ABCD to that of AED is:
Option 1: $\mathrm{\frac{AD}{BC}}$
Option 2: $\mathrm{\frac{BE}{EC}}$
Option 3: $\mathrm{\frac{AD+BE}{AD+CE}}$
Option 4: $\mathrm{\frac{AD+BC}{AD }}$
Correct Answer: $\mathrm{\frac{AD+BC}{AD }}$
Solution :
The area of a trapezium, $\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$ $\text{Area}_{ABCD} = \mathrm{\frac{1}{2} \times (AD + BC) \times EF}$ The area of triangle AED, $\text{Area}_{AED} = \mathrm{\frac{1}{2} \times AD \times EF}$ The ratio of the area of ABCD to that of AED, $\mathrm{\frac{\text{Area}_{ABCD}}{\text{Area}_{AED}} = \frac{\frac{1}{2} \times (AD + BC) \times EF}{ \frac{1}{2} \times AD \times EF} = \frac{AD + BC}{AD}}$ Hence, the correct answer is $ \mathrm{\frac{AD + BC}{AD}}$.
Question : Directions: A sentence or a part of the sentence is printed in bold. Below are alternatives to the bold part that may improve the sentence. Choose the correct alternative. In case no improvement is needed, choose "No Improvement".
Internet providers would not block content because it would not to be make economic sense and consumers would stand for it.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The correct choice is the third option.
The phrase not make economic sense should replace not to make economic sense, as modal verbs are to be followed by the base form of the main verb. Here, would is a modal verb and it should be followed by the base form of the main verb, make.
So, the correct sentence is: Internet providers would not block content because it would not make economic sense and consumers would stand for it.
Question : Directions: Select the option that is related to the third word in the same way as the second word is related to the first word. (The words must be considered meaningful English words and must not be related to each other based on the number of letters/number of consonants/vowels in the word.) Cells : Tissue :: Organs : ?
Option 1: Kidney
Option 2: Lungs
Option 3: Body
Option 4: Heart
Correct Answer: Body
Solution : Given: Cells : Tissue :: Organs : ?
Like, a group of cells forms tissues. Similarly, a group of organs forms a body.
Hence, the third option is correct.
Question : Rubi goes to a multiplex at a speed of 3 km/h to see a movie and reaches 5 minutes late. If she travels at the speed of 4 km/h she reaches 5 minutes early, then the distance of the multiplex from her starting point is:
Option 1: 2 km
Option 2: 5 km
Option 3: 2 metres
Option 4: 5 metres
Correct Answer: 2 km
Solution : Let the distance be $x$ km. According to the question, Speed = $\frac{\text{Distance}}{\text {Time}}$ $\frac{x}{3}–\frac{x}{4}=\frac{5+5}{60}$ ⇒ $x=2$ Hence, the correct answer is 2 km.
Question : The bar graph given below shows the percentage distribution of the total production of six different types of cars by a car manufacturing company over 2 years. If 75% of the T-type cars produced each year were sold by the company, how many T-type cars remain unsold?
Option 1: 23500
Option 2: 22000
Option 3: 24125
Option 4: 25000
Correct Answer: 24125
Solution : According to the question, 75% of the T-type cars are sold. Now, if 75% of the T-type cars produced each year were sold by the company, the number of T-type cars remain unsold = 350000 $\times$ (90 – 75)% $\times$ (100 – 75)% $+$ 440000 $\times$ (95 – 85)% $\times$ (100 – 75)% = 24125 Hence, the correct answer is 24125.
Question : The climatic zones are classified on the basis of
Option 1: distance from equator
Option 2: elevation
Option 3: rainfall
Option 4: distance from the sea
Correct Answer: rainfall
Solution : The correct option is - rainfall
The maximum and minimum temperatures, temperature range, total and seasonal distribution of precipitation, and other factors are used to classify the climatic zones. The most well-known classification scheme was initially created by Wladimir Koppen based on these parameters.
Question : If, $\frac{r}{13}+\frac{13}{r}=1$, then the value of $r^3$ is:
Option 1: –2157
Option 2: 2197
Option 3: 2157
Option 4: –2197
Correct Answer: –2197
Solution : $\frac{r}{13}+\frac{13}{r}=1$ We know that if $x+\frac{1}{x} = 1$, then $x^3 = -1$ Let $\frac{r}{13} = x$ The equation becomes, $x+\frac{1}{x} = 1$ ⇒ $x^2-x+1=0$ $x^3+1^3=(x+1) (x^2-x+1)$ ⇒ $x^3+1^3 =0$ ⇒ $x^3 = -1$ ⇒ $(\frac{r}{13})^3 = -1$ ⇒ $r^3 = -2197$ Hence, the correct answer is –2197.
Question : Muddy water is treated with alum in purification process, it is same as
Option 1: Emulsification
Option 2: Absorbtion
Option 3: Adsorbtion
Option 4: Coagulation
Correct Answer: Coagulation
Solution : The correct answer is coagulation.
When the suspended particles in any liquid solution form a precipitate and settle down, then this process is known as coagulation. The most common example of it is coagulation of blood which forms a blood clot and stops bleeding. Similarly when alum is added to the muddy water it reacts with the impurities of the water and forms a solid precipitate which settles down at the bottom of water along with all the suspended dust particles.
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 45 : 15 :: 20 : 10 :: 125 : ?
Option 1: 20
Option 2: 25
Option 3: 28
Option 4: 24
Correct Answer: 25
Solution : Given: 45 : 15 :: 20 : 10 :: 125 : ?
Like, 45 : 15→(45 × 5) = 225; √225 = 15 20 : 10→(20 × 5) = 100; √100 = 10 Similarly, follow the same pattern for 125 : ?→(125 × 5) = 625; √625 = 25
So, 25 is related to 125. Hence, the second option is correct.
Question : Directions: Select the correct mirror image of the given combination when the mirror is placed at line MN as shown.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection. So, according to the above property and 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 as the right side and the right side will appear as the left side. However, the top and bottom of the reflected image will remain the same.
Thus, the correct mirror image of the given figure will be –
Hence, the second option is correct.
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