Staff Selection Commission Combined Graduate Level Exam
Question : It is given that ABC $\cong$ PQR, AB = 5 cm, $\angle$B = $40^{\circ}$, and $\angle$A = $80^{\circ}$. Which of the following options is true?
Option 1: PQ = 5 cm and $\angle$R = $60^{\circ}$
Option 2: QR = 5 cm and $\angle$R = $60^{\circ}$
Option 3: QR = 5 cm and $\angle$Q = $60^{\circ}$
Option 4: PQ = 5 cm and $\angle$P = $60^{\circ}$
Correct Answer: PQ = 5 cm and $\angle$R = $60^{\circ}$
Solution : $\angle$C = $180^{\circ}-40^{\circ}-80^{\circ}$ = $60^{\circ}$ Since ABC $\cong$ PQR, AB = PQ = 5 cm $\angle$A = $\angle$P = $80^{\circ}$ $\angle$B = $\angle$Q = $40^{\circ}$ $\angle$C = $\angle$R = $60^{\circ}$ Hence, the correct answer is PQ = 5
Question : Direction: A man is facing in the south direction. He turns 135° in the anticlockwise direction and then 180° in the clockwise direction. In which direction is he facing now?
Option 1: South-East
Option 2: South-West
Option 3: North-East
Option 4: North-West
Correct Answer: South-West
Solution : As in the starting, the man was facing in the south direction. He turns in the anticlockwise direction (135°) and then in the clockwise direction (180°).
As per the given information, his movement will look as follows –
According to the above diagram, he
Question : Select the correct indirect form of the given sentence. She said to me, “You will speak at the conference tomorrow.”
Option 1: She told me that I would speak at the conference that day.
Option 2: She told me that I might speak at the conference the next day.
Option 3: She told me that I will speak at the conference the today.
Option 4: She told me that I would speak at the conference the next day.
Correct Answer: She told me that I would speak at the conference the next day.
Solution : Here, the correct option is the fourth option.
Indirect speech involves reporting what someone said without quoting their exact words.
Narration Conversion:
Question : $\triangle \mathrm{ABC}$ is a right-angle triangle at $\mathrm{B}$. If $\tan \mathrm{A}=\frac{5}{12}$, then $\sin \mathrm{A}+\sin \mathrm{B}+\sin \mathrm{C}$ will be equal to:
Option 1: $1 \frac{5}{13}$
Option 2: $2 \frac{4}{13}$
Option 3: $3 \frac{1}{13}$
Option 4: $2 \frac{1}{13}$
Correct Answer: $2 \frac{4}{13}$
Solution : Given, $\tan\mathrm{A}=\frac{5}{12}$ Using Pythagoras theorem, $AC^2 = AB^2+BC^2$ ⇒ $AC^2 = 5^2 + 12^2$ ⇒ $AC^2 = 25 + 144$ ⇒ $AC^2 = 169$ ⇒ $AC = 13$ units ⇒ $\sin \mathrm{A} = \frac{5}{13},$ $\sin \mathrm{B} = 1$ and $\sin\mathrm{C} = \frac{12}{13}$ So, $\sin
Question : If $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$, then the value of $\sin ^4 \theta-\cos ^4 \theta$ is:
Option 1: $\frac{5}{12}$
Option 2: $\frac{12}{13}$
Option 3: $\frac{11}{12}$
Option 4: $\frac{5}{13}$
Correct Answer: $\frac{12}{13}$
Solution : Given, $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$ or, $2(\sin \theta+\cos \theta)=3(\sin \theta-\cos \theta)$ or, $5\cos \theta = \sin \theta$ We know that $\sin^2 A+\cos^2 A=1$ Using $5\cos \theta = \sin \theta$, we get $25\cos^2 \theta +\cos^2 \theta=1$ or, $\cos^2 \theta = \frac{1}{26}$ Since $(a^2-b^2)=(a-b)(a+b)$ $\sin ^4
Question : Directions: The student strength of a college in Arts, Science, and Commerce from 2004-05 to 2007-08 sessions is shown in the following bar graph. Study the graph and answer the question.
The ratio of the average number of students in Arts to the average number of students in Commerce is:
Option 1: $12:5$
Option 2: $10:7$
Option 3: $7:4$
Option 4: $48:35$
Correct Answer: $12:5$
Solution : Total number of students in arts = 600 + 550 + 550 + 700 = 2400 Total number of students in commerce = 200 + 250 + 300 + 250 = 1000 Number of given years = 4 Average total number of students in arts
Question : In January 2022, who was named for the Rachael Heyhoe Flint Trophy for ICC Women's Cricketer of the Year?
Option 1: Mithali Raj
Option 2: Elyse Perry
Option 3: Lizelle Lee
Option 4: Smriti Mandhana
Correct Answer: Smriti Mandhana
Solution : The correct option is Smriti Mandhana.
Smriti Mandhana (India) has been awarded the Rachael Heyhoe Flint Trophy as the ICC Women's Cricketer of the Year.
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error."
He discussed (1) / the murder case (2) / with his juniors. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : There are no errors in the sentence.
The sentence means that he talked about the murder case with his colleagues who are younger than him. It is grammatically accurate and conveys the intended meaning of the sentence.
Therefore, the correct choice is the fourth option.
Question : Who discovered electron?
Option 1: E. Goldstein
Option 2: J. J. Thomson
Option 3: Ernest Rutherford
Option 4: J. Chadwick
Correct Answer: J. J. Thomson
Solution : The correct option is - J. J. Thomson
The electron was the first subatomic particle to be discovered, and J. J. Thomson, a British physicist and recipient of the Nobel Prize in Physics, is credited with its discovery. While examining cathode rays,
Question : Select the most appropriate ANTONYM of the given word.
SUPPRESS
Option 1: Abolish
Option 2: Release
Option 3: Quash
Option 4: Contain
Correct Answer: Release
Solution : The correct choice is the second option.
The word suppress implies the action of restraining, holding back, or preventing something, and its opposite, release, denotes the act of setting something free, allowing it, or making it available.
The meanings of the other options are
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