Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $A:B=7:9$ and $B:C =3:5$, then $A:B:C$ is equal to:
Option 1: $7:9:5$
Option 2: $21:35:45$
Option 3: $7:9:15$
Option 4: $7:3:15$
Correct Answer: $7:9:15$
Solution : Given: $A:B = 7:9$ Let $A = 7x$ and $B = 9x$ $B:C = 3:5$ or we can say $9:15$ (after multiplying by 3) Let $B=9x$ and $C=15x$ $A:B: C = 7x:9x:15x$ $\therefore$ $A:B:C = 7:9:15$ Hence, the correct answer is $7:9:15$
Question : Three partners P, Q, and K invest INR 1,000, INR 1,200, and INR 1,500 respectively, in a business. What should be the share of Q if the total profit is INR 666?
Option 1: INR 216
Option 2: INR 275
Option 3: INR 252
Option 4: INR 284
Correct Answer: INR 216
Solution : Given, three partners P, Q, and K invest INR 1,000, INR 1,200, and INR 1,500 respectively, in a business. Also, total profit = Rs. 666 Here, the share of profit of each individual is directly proportional to the individual's investment So, share of Q
Question : What is the value of $\sec 330°$?
Option 1: $2$
Option 2: $\frac{–2}{\sqrt3}$
Option 3: $–2$
Option 4: $\frac{2}{\sqrt3}$
Correct Answer: $\frac{2}{\sqrt3}$
Solution : Use the trigonometric identity, $\sec (360°-\theta)=\operatorname{sec} \theta$ The value of $\sec 330°$ is given as, $\sec 330°= \sec(360°- 30°)$ ⇒ $\sec 330°= \operatorname{sec} 30°$ ⇒ $\operatorname{sec} 30°=\frac{2}{\sqrt3}$ ⇒ $\sec 330°= \frac{2}{\sqrt3}$ Hence, the correct answer is $\frac{2}{\sqrt3}$.
Question : Select the most appropriate SYNONYM of the word 'Keen' from the given sentence.
I am eager and happy to visit the beautiful city of Darjeeling next month with my family.
Option 1: beautiful
Option 2: visit
Option 3: eager
Option 4: happy
Correct Answer: eager
Solution : The correct choice is the third option.
In the context of the sentence, the word keen is used to express enthusiasm or eagerness. The word eager carries a similar meaning and is the most suitable synonym in this context. Both keen and eager convey
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank. Data 1._______ the Pioneer spacecraft of NASA apparently prove the theory that the high surface temperature of Venus is 2.______ to an atmospheric greenhouse effect caused mainly by a blanket of carbon dioxide. Such a greenhouse 3.______ is created when energy in the form of sunlight easily passes through a planet's atmosphere, warms its 4.____ and is converted to heat radiation that is then held in by the atmosphere from top to bottom. Venus has a relatively thin atmosphere like the Earth's, but Venus' atmosphere consists of more than ninety percent carbon dioxide, compared to less than four percent in that of the 5.____ Select the most appropriate option to fill in the blank No. 4.
Option 1: atmosphere
Option 2: walls
Option 3: core
Option 4: surface
Correct Answer: surface
Solution : The fourth option is correct.
In the given context, the word surface would be used because it refers to the outermost layer or topmost part of the planet. When energy in the form of sunlight passes through a planet's atmosphere, it eventually reaches the surface.
Question : The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on a larger circle and B and C are the points on a smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Option 1: 60 cm
Option 2: 80 cm
Option 3: 75 cm
Option 4: 40 cm
Correct Answer: 80 cm
Solution : Given: Radius $OA = 50$ cm $OB = 34$ cm $BE = \frac{BC}{2} = \frac{32}{2} = 16$ Now, in $\triangle OBE$ $OE^2=OB^2-BE^2$ $⇒OE^2=34^2-16^2$ $⇒OE^2=1156-256=900$ $\therefore OE=30$ In $\triangle OAE$ $AE^2=OA^2-OE^2$ $⇒AE^2=50^2-30^2$ $⇒AE^2=2500-900=1600$ $\therefore AE=40$ $\therefore AD = AE×2 = 40×2= 80$ Hence, the correct
Question : Directions: Select the combination of letters that when sequentially placed in the blanks of the given series will make the series logically complete. F_HIEH_JDIF_ _JEL
Option 1: ELFX
Option 2: GGKC
Option 3: KGGG
Option 4: FGEL
Correct Answer: GGKC
Solution : Given: F_HIEH_JDIF_ _JEL
To fill the series we have to divide the series – F_HI / EH_J / DIF_ / _JEL
Let's check each option – First option: ELFX; FEHI / EHLJ / DIFF / XJEL (No repeated pattern
Question : Directions: Among the four answer figures, which one can be formed from the cut–out pieces given below in the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : The various parts of the figure can be numbered as follows –
The parts can be arranged in the following manner –
The above-compiled figure matches the figure given in the second option. Hence, the second option is correct.
Question : Parts of a sentence are given below in jumbled order. Arrange the parts in the correct order to form a meaningful sentence.
A. we need to understand where we are and, B. that will require significant investment C. where we are headed, and D. in our data and information infrastructure E. to stay ahead of these crises
Option 1: EACBD
Option 2: CEDAB
Option 3: BACDE
Option 4: BAEDC
Correct Answer: EACBD
Solution : The correct choice is the first option.
The sentence discusses the need to stay ahead of crises (part E), followed by the importance of understanding where we are (part A), where we are headed (part C), the significant investment required (part B)
Question : A bullet of mass 'm' and velocity 'a' is fired into a large block of wood of mass 'M'. The final velocity of the system is:
Option 1: $\frac{M}{m + M}a$
Option 2: $\frac{\vec{m}}{ m + M}a$
Option 3: $\frac{m + M}{m}a$
Option 4: $\frac{m + M}{M}a$
Correct Answer: $\frac{\vec{m}}{ m + M}a$
Solution : The correct option is $\frac{\vec{m}}{ m + M}a$.
The initial momentum of the bullet is 'ma' (mass 'm' times velocity 'a'). The initial momentum of the block is 0 since it is initially at rest.
After the collision, the bullet becomes
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