Staff Selection Commission Combined Graduate Level Exam
Question : If $x=\frac{1}{x-3},(x>0)$, then the value of $x+\frac{1}{x}$ is:
Option 1: $\sqrt{11}$
Option 2: $\sqrt{17}$
Option 3: $\sqrt{15}$
Option 4: $\sqrt{13}$
Correct Answer: $\sqrt{13}$
Solution : Given: $x=\frac{1}{x-3},(x>0)$ Or, $x^2-3x-1=0$ Or, $x=\frac{3\pm\sqrt{13}}{2}$ So, $x = \frac{3+\sqrt{13}}{2}$ Now, $x+\frac{1}x = \frac{3+\sqrt{13}}{2}+\frac{2}{3+\sqrt{13}}$ Rationalising, = $\frac{3+\sqrt{13}}{2}+\frac{2}{3+\sqrt{13}}\times \frac{3-\sqrt{13}}{3-\sqrt{13}}$ = $\frac{3+\sqrt{13}}{2}+2\times \frac{3-\sqrt{13}}{-4}$ = $\sqrt13$ Hence, the correct answer is $\sqrt{13}$.
Question : Directions: Three of the following four-letter clusters are alike in a certain way and one is different. Pick the odd one out.
Option 1: PTXB
Option 2: MQUY
Option 3: GKOS
Option 4: HKNQ
Correct Answer: HKNQ
Solution : Let's check the options – First option: PTXB; P + 4 = T; T + 4 = X; X + 4 = B Second option: MQUY; M + 4 = Q; Q + 4 = U; U + 4 = Y Third option: GKOS; G
Question : A train is running at a speed of 116 km/hr. The distance covered by the train (in metres) in 18 seconds is:
Option 1: 900 metres
Option 2: 1160 metres
Option 3: 508 metres
Option 4: 580 metres
Correct Answer: 580 metres
Solution : Given: The speed of the train is 116 km/hr. For converting it into m/sec, multiply with $\frac{5}{18}$. So, 116 km/hr = 116 × $\frac{5}{18}$ m/s = $\frac{580}{18}$ m/s $\therefore$ The distance covered in 18 seconds = Speed × Time = $\frac{580}{18}×18=580$ metres Hence, the
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the options given. Select the most appropriate option for each number. A new swarm of locusts entered Rajasthan’s Jaisalmer on Sunday. This is the fifth swarm to (1)______ the state in four days from (2)______ western border with Pakistan. Since the first locust swarm (3)______ the state’s Sri Ganganagar district on April 11, as many as 25 swarms (4)______ entered Rajasthan. Some swarms moved to Chhattisgarh and Madhya Pradesh, (5)______ which agricultural departments issued advisories to farmers asking them to be on high alert. Question: Select the most appropriate option to fill in the blank no. 4.
Option 1: having
Option 2: have
Option 3: to have
Option 4: has
Correct Answer: have
Solution : The correct choice is the second option.
The phrase, as many as 25 swarms have entered Rajasthan, is describing an action that started in the past and continues up to the present. In English grammar, this is expressed using the present perfect tense, which
Question : A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes?
Option 1: 4 : 7
Option 2: 7 : 8
Option 3: 7 : 12
Option 4: 2 : 3
Correct Answer: 7 : 8
Solution : Given, A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm where l = 18 cm, b = 36 cm and h = 72 cm It is melted and recast into 8 cubes of the same volume. We know
Question : Select the most appropriate option to improve the underlined segment in the given sentence. If there is no need to improve it, select 'No improvement'.
A hole is in my pocket.
Option 1: A hole are there
Option 2: A hole there is
Option 3: There is a hole
Option 4: No improvement
Correct Answer: There is a hole
Solution : The correct choice is the third option.
The pronoun "there" should be used to begin the sentence in order to make proper sentence structure. We use this pronoun to mention the things that exist.
Therefore, the correct sentence is: There is
Question : In an examination, the average marks of a student per paper were 71. If he had obtained 35 more marks in sciences; 11 more marks in history and 4 more marks in computer science, his average marks per paper would have been 76. How many papers were there in the examination?
Option 1: 10
Option 2: 12
Option 3: 18
Option 4: 15
Correct Answer: 10
Solution : Average marks of a student per paper = 71 Let $n$ be the number of papers. Total marks scored = $71n$ New average = 76 New total = $76n$ ⇒ $71n + 35 + 11 + 4 = 76n$ ⇒ $5n = 50$ ⇒ $n
Question : Which wildlife sanctuary has a project to conserve Rhinos in India?
Option 1: Bandipur
Option 2: Periyar
Option 3: Kaziranga
Option 4: Gir
Correct Answer: Kaziranga
Solution : The correct option is Kaziranga.
The one-horned Indian rhinoceros population is the focus of a specialist wildlife conservation programme at Kaziranga National Park in India. This iconic park in the Indian state of Assam is well-known for providing rhinos and other wildlife species with
Question : Which Indian religious festival has been included in the representative list of intangible cultural heritage of humanity by UNESCO, an organisation of the United Nations?
Option 1: Durga Puja
Option 2: Ramnavami
Option 3: Janmashtami
Option 4: Mahashtami
Correct Answer: Durga Puja
Solution : The correct option is Durga Puja.
Durga Puja is listed under the intangible cultural heritage of humanity by UNESCO. This is the main festival in West Bengal and is also celebrated in Bangladesh. It marks the worship of Goddess Durga, who symbolises the
Question : The radius of the incircle of an equilateral $\Delta$ ABC of side $2\sqrt{3}$ cm is $x$ cm. The value of $x$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $\sqrt{3}$
Correct Answer: $1$
Solution : The radius of the incircle of an equilateral triangle is given by the formula $r = \frac{a}{2\sqrt{3}}$, where $a$ is the side length of the triangle. Given that the length of the sides of the equilateral triangle ABC is $2\sqrt{3}$ cm. $x = \frac{2\sqrt{3}}{2\sqrt{3}} =
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
