Staff Selection Commission Combined Graduate Level Exam
Question : What is the area (in unit squares) of the triangle enclosed by the graphs of $2 x+5 y=12, x+y=3$ and the x-axis?
Option 1: 2.5
Option 2: 3.5
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The area of a triangle enclosed by two lines and the x-axis can be found by determining the points where the lines intersect the x-axis and each other. The line $2x + 5y = 12$ intersects the x-axis when $y = 0$, which gives $x
Question : If $x-\frac{1}{x}=-6$, what will be the value of $x^5-\frac{1}{x^5}?$
Option 1: –8898
Option 2: –8896
Option 3: –8886
Option 4: –8892
Correct Answer: –8886
Solution : Given: $x-\frac{1}{x}=-6$ ----------------(equation1) Squaring both sides of equation 1, we get: ⇒ $x^2+\frac{1}{x^2}-2=(-6)^2$ ⇒ $x^2+\frac{1}{x^2}=38$ Cubing both sides of equation 1, we get: ⇒ $x^3-\frac{1}{x^3}-3×x×\frac{1}{x}(x-\frac{1}{x})=(-6)^3$ ⇒ $x^3-\frac{1}{x^3}=-216+3×(-6)$ ⇒ $x^3-\frac{1}{x^3}=-234$ Now, $(x^2+\frac{1}{x^2})(x^3-\frac{1}{x^3})=38×(-234)$ ⇒ $(x^5-\frac{1}{x^5})+(x-\frac{1}{x})=(-8892)$ ⇒ $(x^5-\frac{1}{x^5})+(-6)=(-8892)$ $\therefore(x^5-\frac{1}{x^5})= -8886$ Hence, the correct answer is –8886.
Question : A circular arc whose radius is 4 cm makes an angle of 45º at the centre. Find the perimeter of the sector formed. (Take $\pi=\frac{22}{7}$)
Option 1: $\frac{78}{7} \mathrm{~cm}$
Option 2: $\frac{72}{7} \mathrm{~cm}$
Option 3: $\frac{74}{7} \mathrm{~cm}$
Option 4: $\frac{76}{7} \mathrm{~cm}$
Correct Answer: $\frac{78}{7} \mathrm{~cm}$
Solution : A circular arc whose radius is 4 cm makes an angle of 45° at the centre. Here, radius($r$) = 4 cm and central angle($\theta$) = 45°. We know, The perimeter of the sector in circle = $2\pi r×(\frac{\theta}{360°})$ + 2 × $r$ = $2×\frac{22}{7}×4×\frac{45°}{360°}$
Question : Select the most appropriate indirect form of the given sentence.
“I finished my assignment two hours ago,” she said.
Option 1: She said that she finished my assignment two hours ago.
Option 2: She said that she had finished her assignment two hours before.
Option 3: She said that I finished my assignment two hours before.
Option 4: She said that she has finished her assignment two hours ago.
Correct Answer: She said that she had finished her assignment two hours before.
Solution : The second option is the correct choice.
Narration Conversion:
Question : Ramesh sold a book at a loss of 30%. If he had sold it for Rs. 140 more, he would have made a profit of 40%. The cost price of the book is:
Option 1: Rs. 280
Option 2: Rs. 200
Option 3: Rs. 260
Option 4: Rs. 300
Correct Answer: Rs. 200
Solution : Loss = 30% of cost price ⇒ Selling price = cost price – loss = 70% of cost price 70% of cost Price + Rs.140 = cost price + profit Profit = 40% of cost price ⇒ 70% of cost price + Rs. 140
Question : Directions: If 11 & 25 = 18, 12 & 20 = 16 then, what is the value of 4 & 50 = ?
Option 1: 42
Option 2: 17
Option 3: 27
Option 4: 37
Correct Answer: 27
Solution : Given: 11 & 25 = 18, 12 & 20 = 16, 4 & 50 = ?
Use the following operations in place of the given symbols & – Like, 11 & 25 = 18→(11 + 25) ÷ 2 = 36 ÷ 2 = 18 And,
Question : Two pie charts are given below. There are 6 departments in an office. Pie chart 1 shows the number of males in these 6 departments. The number of males in a particular department is shown as a percentage of total number of males in these 6 departments. Pie chart 2 shows the number of females in these 6 departments. The number of females in a particular department is shown as a percentage of the total number of females in these 6 departments. The difference between the number of males in B and C is 600 and the difference between the number of females in D and E is 900. What is the sum of the number of females in A, B, and F and the number of males in D, E, and A?
Option 1: 26,300
Option 2: 29,400
Option 3: 26,800
Option 4: 25,700
Correct Answer: 26,300
Solution : Given: The difference between the number of males in B and C is 600 and the difference between the number of females in D and E is 900. Male(1%) = $\frac{600}{3}$ = 200 males Females(1%) = $\frac{900}{3}$ = 300 females According to the question, The
Question : Directions: Select the option that represents the letters that, when sequentially placed from left to right in the blanks below, will complete the letter series. M_ _KS_ON_SMO_ K_ _ _NKS
Option 1: ONMNKOMS
Option 2: ONMKNSMO
Option 3: ONMMMMMO
Option 4: NMOKNSMO
Correct Answer: ONMKNSMO
Solution : Given: M_ _KS_ON_SMO_ K_ _ _NKS
To fill the series we have to divide the series – M_ _KS /_ON_S / MO_ K_ / _ _NKS
Let's check the options – First option: ONMNKOMS – MONKS / MONNS
Question : Select the correct direct form of the given sentence.
Rahul said that he had slipped and fallen on the marshy land.
Option 1: Rahul said, “I slipped and fallen on the marshy land.”
Option 2: Rahul said, “He have slipped and fallen on the marshy land.”
Option 3: Rahul said, “I slipped and fell on the marshy land.”
Option 4: Rahul said, “He slips and falls on the marshy land.”
Correct Answer: Rahul said, “I slipped and fell on the marshy land.”
Solution : The correct choice is the third option.
Question : Directions: Arrange the given words in the sequence in which they occur in a dictionary. 1. Feeble 2. From 3. Floor 4. Foam 5. Fluorescent
Option 1: 1, 3, 5, 4, 2
Option 2: 1, 5, 3, 4, 2
Option 3: 1, 3, 5, 2, 4
Option 4: 1, 5, 3, 2, 4
Correct Answer: 1, 3, 5, 4, 2
Solution : Given: 1. Feeble 2. From 3. Floor 4. Foam 5. Fluorescent
Step 1: Compare the first letter of each word. Since all the words start with the same letter F, move to the next letter. Step 2: The second letter
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