Staff Selection Commission Combined Graduate Level Exam
Question : If $\sec\theta-\cos\theta=\frac{3}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec\theta$ is:
Option 1: $-\frac{1}{2}$
Option 2: $1$
Option 3: $2$
Option 4: $0$
Correct Answer: $2$
Solution : Given: $\sec\theta-\cos\theta$ = $\frac{3}{2}$ ⇒ $\frac{1}{\cos\theta}-\cos\theta=\frac{3}{2}$ Let $\cos\theta=x$ ⇒ $\frac{1}{x}-x=\frac{3}{2}$ ⇒ $2(1-x^2) = 3x$ ⇒ $2-2x^2 = 3x$ ⇒ $2x^2+3x - 2=0$ ⇒ $2x^2+4x-x-2 = 0$ ⇒ $2x(x+2)-1(x+2) = 0$ ⇒ $(x+2)(2x-1) = 0$ ⇒ $x = -2, \frac{1}{2}$ Neglecting the negative value, we get,
Question : The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.
Option 1: 8 m
Option 2: 0.04 m
Option 3: 0.08 m
Option 4: 0.008 m
Correct Answer: 0.08 m
Solution : Let the diameter of the base of the cylinder be $d$ cm. We know, The curved surface area of a right circular cylinder = $\pi dh$, where $h$ is the height of the cylinder. Here, $\pi dh=1408$ ⇒ $\frac{22}{7}×d×56=1408$ ⇒ $d=\frac{1408×7}{22×56}=8$ cm = 0.08
Question : Comprehension:
In the given passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
The word ‘diet’ is associated with the feeling of developing eating (1) _________ that are time-bound, coupled (2) ________ a strict food plan. But the (3) ________ meaning of diet is the food (4) _________ which a person follows daily. It (5) ________ creating a food plan that(6) _________ around your lifestyle, your work, (7) _________ quality of your sleep, your (8)__________ level, the kind of (9) _______ you do, your palate and your (10) ___________.
Question:
Select the most appropriate option to fill in blank No.3
Option 1: actual
Option 2: positive
Option 3: total
Option 4: confident
Correct Answer: actual
Solution : The first option is correct.
Let's look at the meaning of the given words:
Question : Of all microorganisms, the most adaptable and versatile are:
Option 1: Viruses
Option 2: Bacteria
Option 3: Algae
Option 4: Fungi
Correct Answer: Viruses
Solution : The correct option is Virus.
Viruses are not technically living organisms, but they are still considered microorganisms because they are very small and can only reproduce inside living cells. They are incredibly adaptable and can survive in a wide variety of environments, including extreme temperatures,
Question : Ultra violet radiations of the Sun do not reach the earth because, earth's atmosphere is surrounded by:
Option 1: Carbon dioxide
Option 2: Ammonia
Option 3: Chlorine
Option 4: Ozone
Correct Answer: Ozone
Solution : The correct answer is ozone.
Ozone layer present in stratosphere protects the earth from the harmful ultraviolet radiations of the sun. It majorly absorbs the UV b and UV c radiations which is the most severe. Although it is transparent to UV A radiations. Its
Question : Ethanol containing 5% water is known as
Option 1: rectified spirit
Option 2: denatured spirit
Option 3: methylated alcohol
Option 4: power alcohol
Correct Answer: rectified spirit
Solution : The correct option is rectified spirit.
Ethanol containing 5% water is known as rectified spirit. Rectified spirit, also known as rectified alcohol or neutral spirits, is an ethanol product that has been highly purified, often through distillation or other purification methods, to remove impurities
Question : What is the name of a metallic radioactive transuranic element with atomic number 101 in the actinide series, discovered in 1955?
Option 1: Seaborgium
Option 2: Nobelium
Option 3: Mendelevium
Option 4: Rutherfordium
Correct Answer: Mendelevium
Solution : The correct option is Mendelevium.
The metallic radioactive transuranic element with atomic number 101 in the actinide series, discovered in 1955, is called Mendelevium. It is named after Dmitri Mendeleev, the Russian chemist who is best known for creating the periodic table of elements. It
Question : Directions: In the following question, some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error. The number of that part is the answer. If a sentence is free from error, your answer is "No Error".
You need not tell a lie (1) / when the judge asked you where you were (2) / when the crime was committed. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
We use needn't have + past participle form to refer to events which happened but which the speaker considers were unnecessary. So, need not tell a lie should be replaced with need not have told.
Therefore,
Question : A sum of money at a fixed rate of simple interest amounts to INR 1630 in 3 years and to INR 1708 in 4 years. Find the sum (in INR).
Option 1: 1132
Option 2: 1296
Option 3: 1396
Option 4: 1448
Correct Answer: 1396
Solution : The difference in the amounts after 3 years and 4 years gives us the simple interest for 1 year. The simple interest for 1 year is INR 1708 – INR 1630 = INR 78 Interest for 3 years = (78 × 3) = INR 234
Question : Directions: From the given words, select the word that cannot be formed using the letters of the given word. PROXIMAL
Option 1: MOLAR
Option 2: AXIOM
Option 3: REALM
Option 4: APRIL
Correct Answer: REALM
Solution : Given: PROXIMAL
Let's compare the given options – First option: MOLAR; All the letters of MOLAR are present in the word PROXIMAL. Second option: AXIOM; All the letters of AXIOM are present in the word PROXIMAL. Third option: REALM; E is not present in the
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