Staff Selection Commission Combined Graduate Level Exam
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 the mirror image properties, closer things appear closer to the mirror in the reflection. So, according to the above property and the information provided, the mirror is placed on the right side of the figure (on line MN). So, the left side of the
Question : Direction: If each of the letters in the English alphabet is assigned an odd numerical value beginning with A = 1, B = 3, and so on, what will be the total value of the letters for the word HOTEL?
Option 1: 95
Option 2: 115
Option 3: 125
Option 4: 105
Correct Answer: 115
Solution : Given:
A = 1; B = 3
Let's find the even numerical value of all alphabets →
Question : Choose the most appropriate meaning of the underlined word in the given sentence.
The students have decided to conspire to steal the test papers.
Option 1: Enact
Option 2: Moderate
Option 3: Plot
Option 4: Assist
Correct Answer: Plot
Solution : The correct solution is the third option.
Explanation: In the context provided, the word conspire is associated with a group of students planning to steal test papers. Conspire means to secretly plan or plot together to commit an unlawful or harmful act. Therefore, the most
Question : If $\cos\theta = \frac{x^2\:-\:y^2}{x^2\:+\:y^2}$, then the value of $\cot\theta$ is equal to:
Option 1: $\frac{2xy}{x^{2}\:-\:y^{2}}$
$\frac{2xy}{x^2\:+\:y^2}$
$\frac{x^{2}\:+\:y^{2}}{2xy}$
$\frac{x^{2}\:-\:y^{2}}{2xy}$
Solution : Let right angle triangle at B and $\angle C = \theta$. $\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{CB}{AC} = \frac{x^{2}\:-\:y^{2}}{x^{2}\:+\:y^{2}}$ Applying Pythagoras' theorem, $(x^{2}+y^{2})^{2} =(x^{2}-y^{2})^{2}+(\text{Height})^{2}$ $⇒x^{4}+y^{4}+2x^{2}y^{2} =x^{2}+y^{2}-2x^{2}y^{2} +(\text{Height})^{2}$ $⇒4x^{2}y^{2} = (\text{Height})^{2}$ $⇒\sqrt{4x^{2}y^{2}} = \text{Height}$ $⇒2xy = \text{Height}$ So, $\cot\theta = \frac{\text{Base}}{\text{Height}} = \frac{x^{2}\:-\:y^{2}}{2xy}$ Hence, the correct
Question : Comprehension: In the given passage, some words have been left out. Read the passage carefully and select the most appropriate option to fill in each blank.
During the pandemic, remote working has kept the work going across _____ (1) Almost every industry got shut down physically during the lockdowns, but the work-from-home model tried to ______ (2) the effect of the lockdown when it came to jobs. In the future also, many businesses across the globe, including the information technology industry, are _______ (3) continuing with the hybrid model. Remote working has replaced geography as a major hiring ________ (4), with 90 percent of senior executives expected to work from home. As a result, 76 percent of US organisations are more likely to _______ (5) outside the city or even state, according to a Talent Works poll of recruiting managers conducted across the US, quoted by an FE report. Select the most appropriate option to fill in the blank number 1.
Option 1: sectors
Option 2: fields
Option 3: sections
Option 4: areas
Correct Answer: sectors
Solution : The first option is the correct answer.
The sentence discusses the impact of remote working across different domains or categories of the economy. Sectors refers to distinct areas or branches of the economy, such as the technology sector, healthcare sector, etc.
The meanings of the
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 6
Option 2: 24
Option 3: 64
Option 4: 120
Correct Answer: 64
Solution : Let's check each option – First option: 6; It is a multiple of 6. (6 × 1 = 6) Second option: 24; It is a multiple of 6. (6 × 4 = 24) Third option: 64; It is not a multiple of 6. Fourth option:
Question : Directions: Select the option that is related to the fourth term in the same way as the first term is related to the second term and the fifth term is related to the sixth term. 169 : 14 :: ? : 16 :: 289 : 18
Option 1: 205
Option 2: 230
Option 3: 225
Option 4: 125
Correct Answer: 225
Solution : Given: 169 : 14 :: ? : 16 :: 289 : 18
Like, (14 – 1)2 = (13)2 = 169 (18 – 1)2 = (17)2 = 289 Similarly, (16 – 1)2 = (15)2 = 225
So, 225 is the
Question : Directions: Study the following histogram of marks in mathematics (out of 50) of students in a class and answer the following question.
If the passing marks in math are 31, the number of students who failed in math is:
Option 1: 10
Option 2: 15
Option 3: 20
Option 4: 25
Correct Answer: 15
Solution : The passing marks are 31, and students who failed are those who scored less than 31. The number of students who failed was 15 and they scored between 25 and 30. Hence, the correct answer is 15.
Question : For any acute angle $\theta, \sin \theta+\sin^2 \theta=1$, then the value of $\cos^2 \theta+\cos^4 \theta=$___________.
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Correct Answer: 1
Solution : Given: $\sin \theta+\sin ^2 \theta=1$ ⇒ $\sin\theta = 1- \sin^2\theta$ ⇒ $\sin \theta = \cos^2\theta$ $\cos^2 \theta+\cos^4 \theta= \sin\theta + \sin^2\theta = 1$ Hence, the correct answer is 1.
Question : Three numbers are in the ratio 5 : 7 : 12. If the sum of the first and the third numbers is greater than the second number by 50. The sum of the three numbers is:
Option 1: 125
Option 2: 120
Option 3: 95
Option 4: 85
Correct Answer: 120
Solution : Let the first number be 5x, the second number be 7x, and the third number be 12x. According to the question, 5x + 12x = 7x + 50 ⇒ 10x = 50 $\therefore$ x = 5 The required sum of the numbers is: 5x +
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