Staff Selection Commission Combined Graduate Level Exam
Question : Select the correct homonym from the given options to fill in the blank. Which________does the minister take to reach the Assembly?
Option 1: root
Option 2: rot
Option 3: route
Option 4: riot
Correct Answer: route
Solution : The third option is the correct choice.
Route refers to a course or path taken to reach a particular destination. In the given sentence, the context suggests that the question is about the path or course the minister takes to reach the Assembly, making route
Question : Directions: If A ÷ B means that A is the father of B, A – B means that A is the mother of B, and A + B means that A is the brother of B then which of the following expressions shows that P is the mother of R?
Option 1: Q – P + R
Option 2: P – Q + R
Option 3: P – Q ÷ R
Option 4: R + P – Q
Correct Answer: P – Q + R
Solution : Let's check the given options – First option: Q – P + R According to the given expression, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the
Question : A is chasing B in the same interval of time. A jumps 8 times, while B jumps 6 times. But the distance covered by A in 7 jumps is the same as that of B in 5 jumps. The ratio between the speeds of A and B is ________.
Option 1: 32 : 24
Option 2: 30 : 56
Option 3: 20 : 21
Option 4: 28 : 36
Correct Answer: 20 : 21
Solution : Distance covered in 7 jumps of A = Distance covered in 5 jumps of B Distance covered in 8 jumps of the A = $\frac{5}{7} \times 8$ jumps of the B = $\frac{40}{7}$ jumps of B So, the required ratio = $\frac{40}{7}$ :
Question : The table given below shows the number of officers working in six companies.
What is the ratio of number of officers working in Q to the number of officers working in R?
Option 1: $7 : 5$
Option 2: $6 : 7$
Option 3: $7 : 4$
Option 4: $5 : 7$
Correct Answer: $5 : 7$
Solution : Number of officers working in Q = 250 Number of officers working in R = 350 So, the required ratio = $250 : 350 = 5 : 7$ Hence, the correct answer is $5 : 7$.
Question : Directions: In the following question, four number pairs are given. In each pair, the number on the left side of (–) is related to the number on the right side of (–) with some Logic/Rule/Relation. Three pairs are similar based on the same Logic/Rule/Relation. Select the odd one out from the given alternatives. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations can be performed on 13, such as adding /subtracting /multiplying, etc., to 13. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Option 1: 12 – 50
Option 2: 8 – 36
Option 3: 10 – 44
Option 4: 18 – 76
Correct Answer: 12 – 50
Solution : Let's check the options – First option: 12 – 50; 12 × 4 = 48; 48 + 4 = 52 ≠ 52 Second option: 8 – 36; 8 × 4 = 32; 32 + 4 = 36 Third option: 10 – 44; 10
Question : A cycle dealer offers a discount of 10% and still makes a profit of 26%. What does he pay for a cycle whose marked price is Rs. 840?
Option 1: Rs. 600
Option 2: Rs. 650
Option 3: Rs. 700
Option 4: Rs. 750
Correct Answer: Rs. 600
Solution : Given: Discount percentage = 10%, gain percentage = 26% and marked price (MP) = Rs. 840 So, the selling price (SP) = $\frac{\text{Marked Price}×(100-\text{Profit%)}}{100}$ = $\frac{840(100-10)}{100}$ = Rs. 756 To gain 26%, Cost price = $\frac{\text{Selling Price} × 100}{100+\text{Gain%}}=\frac{756×100}{100+26}$ = Rs. 600 Hence, the
Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All the medicines are capsules. Some capsules are bangles. Some bangles are toothpaste. Conclusions: I. Some bangles are medicines. II. Some toothpaste are capsules. III. Some medicines are bangles. IV. Some medicines are toothpaste.
Option 1: Only conclusions III and IV follow
Option 2: None of the conclusions follow
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and II follow
Correct Answer: None of the conclusions follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some bangles are medicines – From the Venn diagram, it is evident that there is no direct relation between bangles and
Question : An important greenhouse gas other than methane being produced from the agricultural fields is
Option 1: Nitrous oxide
Option 2: Ammonia
Option 3: Sulphur dioxide
Option 4: Arsine
Correct Answer: Nitrous oxide
Solution : The correct answer is Nitrous oxide
Other than methane, nitrous oxide is the most significant greenhouse gas produced by agricultural land. The decomposition of nitrogenous molecules in the soil produces this colourless and odourless gas. Nitrous oxide is a powerful greenhouse gas that is
Question : If $7 \cot P = 24$, then find $\sin P$.
Option 1: $\frac{625}{7}$
Option 2: $\frac{24}{25}$
Option 3: $\frac{49}{625}$
Option 4: $\frac{7}{25}$
Correct Answer: $\frac{7}{25}$
Solution : Given: $7 \cot P = 24$ ⇒ $\cot P = \frac{24}{7}$ We know, $\operatorname{cosec}^2P - \cot^2P =1$ ⇒ $\operatorname{cosec}^2P=1+(\frac{24}{7})^2$ ⇒ $\operatorname{cosec}^2P= \frac{49+576}{49}=\frac{625}{49}$ ⇒ $\operatorname{cosec}P=\sqrt{\frac{625}{49}}=\frac{25}{7}$ $\therefore \sin P=\frac{1}{\operatorname{cosec}P} =\frac{7}{25}$ Hence, the correct answer is $\frac{7}{25}$.
Question : Using $\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$, find the value of $\tan 15°$.
Option 1: $\sqrt{3}+1$
Option 2: $\sqrt{3}-1$
Option 3: $2-\sqrt{3}$
Option 4: $2+\sqrt{3}$
Correct Answer: $2-\sqrt{3}$
Solution : Given: $\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$ ⇒ $\tan (45°-30°)=\frac{\tan 45°-\tan 30°}{1+\tan 45° \tan 30°}$ ⇒ $\tan15° = \frac{(1-\frac{1}{\sqrt3})}{(1+\frac{1}{\sqrt3})}$ ⇒ $\tan15° = \frac{(\sqrt3-1)}{(\sqrt3+1)}$ After rationalizing, ⇒ $\tan15°=2-\sqrt{3}$ Hence, the correct answer is $2-\sqrt{3}$.
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