Staff Selection Commission Combined Graduate Level Exam
Question : The mean of 100 items was 46. Later on, it was discovered that item 16 was misread as 61 and another item, 43, was misread as 34. It was also found that the number of items was 90 and not 100. Then, what is the correct mean?
Option 1: 50
Option 2: 50.7
Option 3: 52
Option 4: 52.7
Correct Answer: 50.7
Solution : Given: The average of 100 items is 46. An entry of 16 was misread as 61. Another entry of 43 was misread as 34. Total items were 90, not 100. The sum of 100 items = 100 × 46 = 4600 Difference made by the
Question : Directions: Read the graph and answer the following question:
In the case of, which soft drink was the average annual sale minimum during the period 1988-1993?
Option 1: Pep-up only
Option 2: Cool-sip only
Option 3: Dew-drop only
Option 4: Dew-drop and Cool-sip
Correct Answer: Dew-drop and Cool-sip
Solution : As per the given bar graph: 1) For Dew-drop The total annual sales = 10 + 15 + 25 + 15 + 30 + 25 = 120 lakh The number of years = 6 The average annual sales of Dew-drop during 1988-1993 =
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: CTES
Option 2: VDZC
Option 3: MKOJ
Option 4: RGTF
Correct Answer: VDZC
Solution : Let's check the options – First option: CTES; C + 2 = E; T – 1 = S Second option: VDZC; V + 4 = Z; D – 1 = C Third option: MKOJ; M + 2 = O; K – 1 = J Fourth
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).
I like tea and I like coffee.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The correct improvement for the sentence is: both tea and coffee
Explanation: This option is the correct improvement because it maintains the original meaning and structure of the sentence while emphasizing that the speaker likes both tea and coffee. It combines the two preferences without
Question : $\triangle ABC$ and $\triangle PQR$ are two triangles. AB = PQ = 6 cm, BC = QR =10 cm, and AC = PR = 8 cm. If $\angle ABC = x$, then what is the value of $\angle PRQ$?
Option 1: $(180 ^{\circ}–x)$
Option 2: $x$
Option 3: $(90 ^{\circ}–x)$
Option 4: $(90 ^{\circ}+x)$
Correct Answer: $(90 ^{\circ}–x)$
Solution : Given: $\triangle ABC$ and $\triangle PQR$ are two triangles. AB = PQ = 6 cm, BC = QR =10 cm and AC = PR = 8 cm. Also, $\angle ABC = x$. We know that the sum of all interior angles of the triangle
Question : If $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, then the value of $\frac{ab+bc+ca}{abc}$ is:
Option 1: $2$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{1}{2}$
Correct Answer: $\frac{1}{2}$
Solution : Given that $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, we can rewrite this equation as: $⇒\frac{2}{a}+1+\frac{2}{b}+1+\frac{2}{c}+1=4$ Simplifying, we get: $⇒\frac{2}{a}+\frac{2}{b}+\frac{2}{c}=1$ Multiplying through by $abc$, we get: $⇒2bc+2ac+2ab=abc$ Rearranging terms, we get: $⇒abc=2(ab+bc+ca)$ $\therefore\frac{ab+bc+ca}{abc}=\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
Question : Working together, A and B can do a job in 40 days, B and C in 36 days, and all three together in 24 days. In how many days can B alone do the job?
Option 1: 60
Option 2: 90
Option 3: 72
Option 4: 120
Correct Answer: 90
Solution : Let the total work = LCM of (40, 36, and 24) = 360 Efficiency of (A + B) = $\frac{360}{40}$ = 9 ----------------------------(1) Efficiency of (B + C) = $\frac{360}{36}$ = 10 --------------------------(2) Efficiency of (A + B + C) = $\frac{360}{24}$ = 15 ---------------------(3)
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).
She decided to go there, though her husband cautioned her on it.
(1) Against
(2) For
(3) About
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct answer is the first option.
The preposition on is not the most suitable choice for the sentence. When cautioning or warning someone, it's more common to use the preposition against.
Therefore, the correct sentence would be: She decided to go there, though
Question : The number of eggs normally released during one menstrual cycle is :
Option 1: 3
Option 3: 1
Correct Answer: 1
Solution : The correct answer is 1.
Only one egg is released during one menstrual cycle of 28 days. Egg is released during the ovulation phase of menstrual cycle. Menstrual cycle has 4 phases- Menstruation, the follicular phase, ovulation and the luteal phase. It is controlled by
Question : If $2 \frac{\cos ^2 x-\sec ^2 x}{\tan ^2 x}=a+b \cos 2 x$, then $a, b=$?
Option 1: $-\frac{3}{2}, -\frac{1}{2}$
Option 2: $\frac{3}{2}, \frac{1}{2}$
Option 3: $-3, -1$
Option 4: $3,1$
Correct Answer: $-3, -1$
Solution : $2 \frac{\cos ^2 x-\sec ^2 x}{\tan ^2 x}$ = $2 \frac{\cos ^2 x-\frac{1}{\cos ^2 x}}{\tan ^2 x}$ = $2 \frac{\cos ^4 x - 1}{\tan ^2 x\cos ^2 x}$ = $2 \frac{(\cos ^2 x - 1)(\cos ^2 x + 1)}{\frac{\sin^2 x}{\cos^2 x}\cos ^2 x}$ We
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