Staff Selection Commission Combined Graduate Level Exam
Question : A wide inlet of the sea usually concave in shape, is termed as a:
Option 1: Strait
Option 2: Sound
Option 3: Bay
Option 4: Fjord
Correct Answer: Bay
Solution : The correct answer is Bay.
Bay is a coastal erosional landform formed by the marine wave actions. It is a large concave shaped land formation which encloses ocean water, having a medium sized opening which connects it with bigger ocean. It is smaller and less
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed on the right side of the figure.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per mirror image properties, closer things appear closer to the mirror in reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the reflected image will appear as the
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank. This book (1) _ writing practice to pre-schoolers to help them learn to write (2) _ of the English alphabet. Directional arrows, (3) _ with the letters and numbers, guide children in writing. (4) _ and copying activities encourage children to read and write letters and numbers (5) _ to count.
Select the most appropriate option to fill in the blank no 2.
Option 1: letter
Option 2: letters
Option 3: phrases
Option 4: words
Correct Answer: letters
Solution : The correct choice is the second option.
The most appropriate option to fill in the blank is letters, as the sentence discusses writing practice for pre-schoolers to help them learn to write. Specifically, the focus is on the English alphabet. Since the English
Question : If $k^4+\frac{1}{k^4}=47$, then what is the value of $k^3+\frac{1}{k^3}$?
Option 1: 4.5
Option 2: 54
Option 3: 18
Option 4: 9
Correct Answer: 18
Solution : Given, $k^4+\frac{1}{k^4}=47$ Adding 2 on both sides, ⇒ $k^4+\frac{1}{k^4}+2=47+2$ ⇒ $(k^2)^2+\frac{1}{(k^2)^2}+2\times k^2\times \frac{1}{k^2}=49$ ⇒ $(k^2+\frac{1}{k^2})^2=49$ ⇒ $k^2+\frac{1}{k^2}=7$ Again adding 2 on both sides, $k^2+\frac{1}{k^2}+2=7+2$ ⇒ $(k+\frac{1}{k})^2=9$ ⇒ $k+\frac{1}{k}=3$ cubing both sides, we get, ⇒ $k^3+\frac{1}{k^3}+3×k\times \frac{1}{k}(k+\frac{1}{k})=27$ ⇒ $k^3+\frac{1}{k^3}+3×3=27$ $\therefore k^3+\frac{1}{k^3}=27-9=18$ Hence, the correct answer is
Question : Directions: Select the odd group of numbers. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Option 1: 13 – 159
Option 2: 9 – 71
Option 3: 5 – 31
Option 4: 17 – 279
Correct Answer: 5 – 31
Solution : Let's check the options – First option: 13 – 159→(13)2 = 169; 169 – 10 = 159 Second option: 9 – 71→(9)2 = 81; 81 – 10 = 71 Third option: 5 – 31→(5)2 = 25; 25 – 10 =
Question : If areas of similar triangles $\triangle {ABC}$ and $\triangle {DEF}$ are $ {x}^2 \ \text{cm}^2$ and $ {y}^2 \ \text{cm}^2$, respectively, and EF = a cm, then BC (in cm) is:
Option 1: $\frac{y^2}{a^2 x^2}$
Option 2: $\frac{y}{a x}$
Option 3: $\frac{ax}{y}$
Option 4: $\frac{a^2 x^2}{y^2}$
Correct Answer: $\frac{ax}{y}$
Solution : Given: $\triangle{ABC}\sim\triangle{DEF}$ $\frac{\text{Area of}\triangle{ABC}}{\text{Area of}\triangle{DEF}}=\frac{{BC}^2}{{EF}^2}$ ⇒ $\frac{ {x}^2 }{{y}^2 }=\frac{{BC}^2}{{a}^2}$ ⇒ $\frac{ {x}}{ {y}}=\frac{{BC}}{{a}}$ $\therefore {BC} = \frac{{ax}}{{y}}$ Hence, the correct answer is $\frac{{ax}}{{y}}$.
Question : Which of the following hills and their regions are correctly matched?
Option 1: Patkai Hills – Western Ghats
Option 2: Mizo Hills – Eastern Ghats
Option 3: Shevaroy Hills – Western Ghats
Option 4: Javadi Hills – Eastern Ghats
Correct Answer: Javadi Hills – Eastern Ghats
Solution : The correct answer is Javadi Hills – Eastern Ghats.
Javadi Hills are correctly matched with their region, which is the Eastern Ghats. The Patkai Hills are part of the Purvanchal mountain range, which is the Himalayas' eastern extension. The Purvanchal
Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? × and +, 6 and 4
Option 1: 3 × 9 – 4 ÷ 2 + 6 = 8
Option 2: 8 × 6 + 4 ÷ 2 – 5 = –5
Option 3: 8 – 3 × 6 + 4 ÷ 1 = 18
Option 4: 7 × 6 – 4 + 9 ÷ 3 = –7
Correct Answer: 7 × 6 – 4 + 9 ÷ 3 = –7
Solution : Given: × and +, 6 and 4
Let's check the given options – First option: 3 × 9 – 4 ÷ 2 + 6 = 8 On interchanging the signs and numbers, we get –
Question : What is the remainder when $\left(x^{17}+1\right)$ is divided by $(x+1)$?
Option 1: $x$
Option 2: $x - 1$
Option 3: $0$
Option 4: $1$
Correct Answer: $0$
Solution : $\left(x^{17}+1\right)$ is divided by $(x +1)$ $P(x) = \left(x^{17}+1\right)$ Divisor = $x + 1$ $\therefore$ remainder = $P(- 1) = (- 1)^{17}+ 1= - 1 + 1 = 0$ Hence, the correct answer is $0$.
Question : Lady Ratan Tata Trophy is related to which game ?
Option 1: Basketball
Option 2: Hockey
Option 3: KhoKho
Option 4: Cricket
Correct Answer: Hockey
Solution : The correct option is - Hockey.
ndia hosts a national hockey competition for women called the Lady Ratan Tata Trophy. It bears Ratan Tata's name, an industrialist, philanthropist, and former chairman of Tata Sons
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