Staff Selection Commission Combined Graduate Level Exam
Question : The following pie chart represents the units of electricity sold to various categories in a month by an Electricity Supplier. Electricity sold to various categories of a town
The central angle of the sector corresponding to supply for Industries is:
Option 1: $48^\circ$
Option 2: $25^\circ$
Option 3: $46^\circ$
Option 4: $90^\circ$
Correct Answer: $90^\circ$
Solution : Given: Percentage of industries = 25% Central angle $=\frac{\text{Given value of Industries}}{100}\times360^\circ=\frac{25}{100}\times360^\circ=90^\circ$ Hence, the correct answer is $90^\circ$.
Question : $\frac{\sec A(\sec A+\tan A)(1-\sin A)}{\left(\operatorname{cosec}^2 A-1\right) \sin ^2 A}$ is equal to:
Option 1: $\cot A$
Option 2: $\cos A$
Option 3: $\sec ^2 A$
Option 4: $\cos ^2 A$
Correct Answer: $\sec ^2 A$
Solution : $\frac{\sec A(\sec A+\tan A)(1-\sin A)}{\left(\operatorname{cosec}^2 A-1\right) \sin ^2 A}$ = $\frac{\frac{1}{\cos A}(\frac{1}{\cos A}+\frac{\sin A}{\cos A})(1-\sin A)}{\left(\operatorname{cot}^2 A\right) \sin ^2 A}$ = $\frac{\frac{1}{\cos^2 A}(1+\sin A)(1-\sin A)}{\left(\frac{\cos^2A}{\sin^2A}\right) \sin ^2 A}$ = $\frac{(1-\sin^2 A)}{\cos^4 A}$ = $\frac{\cos^2 A}{\cos^4 A}$ = $\frac{1}{\cos^2A}$ = $\sec^2A$ Hence, the correct
Question : Directions: In a certain code language, GHOST is written as VVSMM, and EATER is written as THXFK. How will HANDS be written in that language?
Option 1: UGRFN
Option 2: NFRGV
Option 3: WHRGN
Option 4: VGRGN
Correct Answer: UGRFN
Solution : Given: GHOST is written as VVSMM, and EATER is written as THXFK.
Add the consecutive natural numbers, in decreasing order (starting from 6) to the place value of the letters of the given words, and then reverse the order of the letters to get the
Question : Select the option that expresses the given sentence in active voice.
Were the cakes being baked by them?
Option 1: Were they baking the cakes?
Option 2: Did the cakes baked by them?
Option 3: Were they baking the cake?
Option 4: Was cakes being baked by them?
Correct Answer: Were they baking the cakes?
Solution : The correct option is the first option.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.
The structure of
Question : When a discount of 25% is given on a cruise trip, the profit is 41%. If the discount is 26%, then the profit is:
Option 1: 39.12%
Option 2: 67%
Option 3: 94.88%
Option 4: 11.24%
Correct Answer: 39.12%
Solution : Let the cost price be Rs. 100. When profit % = 41, selling price = 100 + 41 = Rs. 141 When discount = 25%, selling price = 75% of Marked price Marked price = $\frac{141}{\frac{75}{100}}$ = $\frac{141}{\frac{3}{4}}$ = $\frac{141 × 4}{3}$ = Rs. 188
Question : R jogs at twice the speed of walking and runs at twice the speed of jogging. From his home to office, he covers half of the distance by walking and the rest by jogging. From his office to home, he covers half the distance jogging and the rest by running. What is his average speed (in km/hr) in a complete round from his home to office and back home if the distance between his office and home is 10 km and he walks at the speed of 5 km/hr?
Option 1: $\frac{90}{8}$
Option 2: $\frac{60}{8}$
Option 3: $\frac{60}{9}$
Option 4: $\frac{80}{9}$
Correct Answer: $\frac{80}{9}$
Solution : R's jogging speed = 5 × 2 = 10 km/hr R's running speed = 10 × 2 = 20 km/hr Now, At the time of going to his office time taken $= \frac{5}{5} + \frac{5}{10} =1 + 0.5 = 1.5$ hours At the time of
Question : Which strait separates Australia and Tasmania ?
Option 1: Bass
Option 2: Bab-el-Mandeb
Option 3: Palk
Option 4: Berring
Correct Answer: Bass
Solution : The correct option is - Bass.
The Australian mainland and the island state of Tasmania are separated by Bass Strait. The strait is the only maritime entry point into the economically significant Port Phillip Bay and offers the most direct waterway between the Great Australian
Question : The table given below shows the marked price and value of the discount of 7 articles.
What is the average marked price of all the articles?
Option 1: 824.12
Option 2: 814.12
Option 3: 742.85
Option 4: 704.15
Correct Answer: 742.85
Solution : $\therefore$ Average Marked price $= \frac{1100+700+900+600+400+500+1000}{7}=\frac{5200}{7}= 742.85$ Hence, the correct answer is 742.85.
Question : If $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 5
Correct Answer: 6
Solution : Given: $x=\sqrt[3]{28}$ and $y=\sqrt[3]{27}.$ To find $x+y–\frac{1}{x^{2}+xy+y^{2}}$ Multiplying and dividing by $(x–y)$ $=x+y–\frac{(x–y)}{(x–y)(x^{2}+xy+y^{2})}$ $=x+y–\frac{(x–y)}{(x^{3}–y^{3})}$ $=x+y–\frac{(x–y)}{(28–27)}$ $=x+y–x+y$ $=2y$ $=2×\sqrt[3]{27}$ $=2×3 = 6$ Thus, $x+y-\frac{1}{x^{2}+xy+y^{2}}=6$ Hence, the correct answer is 6.
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. 5 : 45 :: 3 : 3 :: 6 : ?
Option 1: 90
Option 2: 106
Option 3: 110
Option 4: 96
Correct Answer: 96
Solution : Given: 5 : 45 :: 3 : 3 :: 6 : ?
Like, 5 : 45→5 × (5 – 2)2 = 5 × (3)2 = 5 × 9 = 45 3 : 3→3 × (3 – 2)2 = 3 × (1)2
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