Staff Selection Commission Combined Graduate Level Exam
Question : In the following figure, the length of arc AB is equal to five times the radius $r$ of the circle. Find the area of sector AOB.
Option 1: $2.5 r^2$
Option 2: $\frac{1}{2}r^2$
Option 3: $3r^2$
Option 4: $2r^2$
Correct Answer: $2.5 r^2$
Solution : Length of the arc AB = $5r$ Radius of the circle = $r$ Given: Length of arc = $5r$ ⇒ $\frac{\theta}{360^\circ }\times 2\pi r=5r$ ⇒ $\theta = \frac{360^\circ}{2\pi} \times 5$ Area of sector with angle $\theta$ = $\frac{\theta}{360^\circ}\pi r^2$ =$\frac{\frac{360^\circ}{2\pi} \times 5}{360^\circ}\pi r^2$ =
Question : Direction: In the following question a word is followed by four other words, one of which can not be formed by using the letters of the given word. Find this word.
DISTANCE
Option 1: DANCE
Option 2: STAND
Option 3: SANE
Option 4: TEASE
Correct Answer: TEASE
Solution : Given:
First option: DANCE;
All the letters of the above word are present in the given word DISTANCE.
Second option: STAND;
Third option: SANE;
All the letters of the above
Question : Parts of the following sentence are given as options. Identify the segment that contains a grammatical error.
Either of these two roads lead to the post office.
Option 1: Either of these
Option 2: the post office
Option 3: lead to
Option 4: two roads
Correct Answer: lead to
Solution : The correct choice is the third option.
Explanation: The correct form should be "leads to" to maintain subject-verb agreement. In the original sentence, the subject "either of these two roads" is singular, so the verb "lead" should be singular as well.
Question : Identify the segment that contains a grammatical error. A misunderstanding has crept between he and his sister.
Option 1: And his sister
Option 2: Between he
Option 3: Has crept
Option 4: A misunderstanding
Correct Answer: Between he
Solution : The second option is correct.
Question : If $x = 32.5$, $y = 34.6$ and $z = 30.9$, then the value of $x^3+y^3+z^3-3xyz$ is $0.98k$, where $k$ is equal to:
Option 1: 1033
Option 2: 933
Option 3: 1026
Option 4: 921
Correct Answer: 1033
Solution : Given that $x = 32.5$, $y = 34.6$ and $z = 30.9$ Use the identity, $x^3+y^3+z^3-3xyz=\frac{1}{2}[x+y+z][(x-y)^2+(y-z)^2+(z-x)^2]$ $⇒0.98k=\frac{1}{2}[32.5+34.6+30.9][(32.5-34.6)^2+(34.6-30.9)^2+(30.9-32.5)^2]$ $⇒\frac{1}{2}[98][(-2.1)^2+(3.7)^2+(-1.6)^2]=0.98k$ $⇒49[4.41+13.69+2.56]=0.98k$ $⇒49[20.66]=0.98k$ $⇒k=1033$ Hence, the correct answer is 1033.
Question : If the average of 41 consecutive odd numbers is 49, what is the largest number?
Option 1: 89
Option 2: 91
Option 3: 93
Option 4: 95
Correct Answer: 89
Solution : The average of 41 consecutive odd numbers is 49. Since the average of an arithmetic progression (AP) with an odd number of terms is the same as its middle term, Middle term = 21st term = 49 Largest number = last term = 41
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
There be a long queue for entry into the exhibition ground.
(1) for entry into
(2) No Error
(3) There be a long queue
(4) the exhibition ground
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third option.
The error is due to the incorrect subject-verb agreement, as the queue is a singular subject so it should be followed by a singular verb, i.e., is. The phrase there be a long queue is not grammatically accurate,
Question : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O and A, respectively. The length of BC is:
Option 1: $2 \sqrt{118} $ cm
Option 2: $2 \sqrt{119} $ cm
Option 3: $2 \sqrt{113} $ cm
Option 4: $2 \sqrt{117}$ cm
Correct Answer: $2 \sqrt{119} $ cm
Solution : Since AB $\perp$ BC and AQ $\perp$ OC, AQBC is a rectangle with sides AQ = BC and AB = QC. ⇒ AP = AB = QC = 7 cm and OC = OP = 17 cm Also, AO = AP +
Question : A laptop is sold for Rs. 54,000 after giving a discount of 20%. What is the list price (in Rs.) of the laptop?
Option 1: 69,500
Option 2: 67,500
Option 3: 70,000
Option 4: 64,800
Correct Answer: 67,500
Solution : Given: A laptop is sold for Rs. 54,000 after giving a discount of 20%. Let the list price be $x$. The selling price of the laptop = 80% of the list price 54000 = $\frac{80x}{100}$ ⇒ $x$ = Rs. 67,500 Hence, the correct answer is
Question : Select the most appropriate ANTONYM of the underlined word. The love between them is blooming.
Option 1: Flourishing
Option 2: Sprouting
Option 3: Growing
Option 4: Fading
Correct Answer: Fading
Solution : The correct answer is the fourth option.
While blooming suggests the growth and flourishing of love, fading indicates the opposite, that the love is diminishing or losing its intensity. Fading is the antonym of blooming. It means that something is diminishing or losing intensity.
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