Staff Selection Commission Combined Graduate Level Exam
Question : The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar raised so that its angle of elevation at the same point may be 45°, is:
Option 1: 63.4
Option 2: 86.6
Option 3: 126.8
Option 4: 173.2
Correct Answer: 63.4
Solution : Given: The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. In $\triangle DBC$, $\tan 30°=\frac{DB}{BC}$ $⇒\frac{1}{\sqrt3}=\frac{DB}{150}$ $⇒DB=\frac{150}{\sqrt3}$ $⇒DB=50\sqrt3$ In $\triangle ABC$, $\tan45°=\frac{AB}{BC}$ $⇒1=\frac{AB}{150}$ $⇒AB=150$ m Also, $AD = AB - DB$ $⇒AD=150 -
Question : In an election, 2% of persons enrolled in the voter list did not participate and 500 votes were invalid. Two candidates A and B fought the election and A defeated B by 200 votes. If 43% of the persons enrolled in the voter list cast their votes in favour of A, then what is the number of the total cast votes?
Option 1: 2450
Option 2: 2800
Option 3: 3000
Option 4: 3250
Correct Answer: 2450
Solution : Let the number of persons enrolled in the voter list be $x$. The 2% of the enrolled persons did not participate in the election, which implies that 98% of the total enrolled persons did participate. The total number of cast votes = $0.98x$ Included, 500
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation. 33 * 4 * 15 * 3 * 61 = 188
Option 1: +, ×, ÷, −
Option 2: ×, −, ÷, +
Option 3: +, −, ÷, ×
Option 4: ÷, ×, −, +
Correct Answer: ×, −, ÷, +
Solution : Given: 33 * 4 * 15 * 3 * 61 = 188
Replace * with the mathematical signs and solve the equations one by one using the BODMAS. First option: +, ×, ÷, – 33 + 4 × 15 ÷ 3 –
Question : From the top of a cliff 100 metres high, the angles of depression of the top and bottom of a tower are 45° and 60°, respectively. The height of the tower is:
Option 1: $\frac{100}{3}(3-\sqrt{3})$ m
Option 2: $\frac{100}{3}(\sqrt3-1)$ m
Option 3: $\frac{100}{3}(2\sqrt3-1)$ m
Option 4: $\frac{100}{3}(\sqrt3-\sqrt{2})$ m
Correct Answer: $\frac{100}{3}(3-\sqrt{3})$ m
Solution : Given: The top of a cliff 100 metres high, the angles of depression of the top and bottom of a tower are 45° and 60°. We know the trigonometric ratio, $tan\ \theta=\frac{\text{Height}}{\text{Base}}$. Let the height of the tower be $x$ m. In $\triangle AEC$,
Question : Direction: In the following question,one statement is given followed by two Conclusions I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given conclusions can be definitely be drawn from the given statement.
Statement : Every school should promote partnerships that will increase parental involvement and participation for promoting the growth of children.
Conclusions :
I. For the growth of the children , parents should ne involved in various school activities.
II. Involvement of parents in school activities has no influence on the growth of the children.
Option 1: Both I and II follow
Option 2: Only I follow.
Option 3: Only II follows.
Option 4: Neither I nor II follows.
Correct Answer: Only I follow.
Solution : Conclusion I: For the growth of the children , parents should be involved in various school activities. From the above statement, it can be said that parents should be involved for the growth of children.
Conclusion II: Involvement of parents in school activities
Question : Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A. We reached there at about 10 a.m. B. The first ride we took was the Fury Wheel. It was really big, all of us were yelling and crying! C. Yesterday, my friends and I went on a short picnic at an amusement park. D. Even though we had reached on time there was a serpentine queue for the tickets. I took the entrance ticket.
Option 1: CADB
Option 2: ABCD
Option 3: CDBA
Option 4: ADBC
Correct Answer: CADB
Solution : The correct choice is the first option: CADB.
Explanation:
Sentence C introduces the overall context, stating that the speaker and his friends went on a short picnic at an amusement park. It is followed by Sentence A, which provides information about the time of
Question : Directions: In a certain code language, PLANT is written as NRDVP, and SCORE is written as EURGT. How will GRIND be written in that language?
Option 1: TILFP
Option 2: SHLGQ
Option 3: UJKEO
Option 4: ITLPF
Correct Answer: TILFP
Solution : Given: PLANT is written as NRDVP and SCORE is written as EURGT.
Add 2 in the place value of the first two and last two letters and shuffle their position as shown and add 3 in the place value of the third letter of PLANT,
Question : AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm, then what is the length of PD?
Option 1: 14 cm
Option 2: 28 cm
Option 3: 21 cm
Option 4: 7 cm
Correct Answer: 7 cm
Solution : AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm The centroid of the triangle divides each of its medians in the ratio 2 : 1. ⇒ $\frac{\text{AP}}{\text{PD}} = \frac{2}{1}$ ⇒ $\frac{14}{\text{PD}} = \frac{2}{1}$ ⇒
Question : Directions: A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given folded paper is unfolded, it will look like –
Hence, the third option is correct.
Question : The percentage profit made when an article is sold for Rs. 78 is twice as much as when it is sold for Rs. 69. The cost of the article is:
Option 1: Rs. 60
Option 2: Rs. 51
Option 3: Rs. 55.50
Option 4: Rs. 70
Correct Answer: Rs. 60
Solution : Let the cost price of the article be Rs. x. The profit from selling it at Rs. 78 = twice the profit at Rs. 68. So, 78 – x = 2(69 – x) ⇒ 78 – x = 138 – 2x $\therefore$ x =
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