Staff Selection Commission Combined Graduate Level Exam
Question : What is Gandhi's definition of Rama Raj ?
Option 1: The rule as it was during the time of Rama
Option 2: Sovereignty of the people based on pure moral authority
Option 3: The greatest good of all
Option 4: The absolute power concentrated in the hands of a king
Correct Answer: The greatest good of all
Solution : The correct option is - The greatest good of all
Gandhi envisioned a society where leaders ruled with a sense of duty, selflessness, and a commitment to the welfare of all citizens. In Rama Rajya, there would be no discrimination, and
Question : If $\cos^2 \theta=\frac{3}{4}$, where $\theta$ is an acute angle, then the value of $\sin \left(\theta+30^{\circ}\right)$ is:
Option 1: $1$
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\frac{1}{2}$
Option 4: $\frac{\sqrt{3}}{2}$
Correct Answer: $\frac{\sqrt{3}}{2}$
Solution : Given: $\cos^2 \theta=\frac{3}{4}$ ⇒ $\cos \theta=\pm\frac{\sqrt3}{2}$ $\theta$ is an acute angle i.e. it will be less than 90°. $\therefore \cos \theta=-\frac{\sqrt3}{2}$ will be rejected. ⇒ $\cos \theta=\frac{\sqrt3}{2}$ ⇒ $\theta = 30°$ Now we have to find $\sin \left(\theta+30^{\circ}\right)$ $ = \sin(30° + 30°) = \sin
Question : Select the sentences that contains no spelling errors.
Option 1: I heard raucouos laughter from the next room.
Option 2: I heard raocous laughter from the next room.
Option 3: I heard raucus laughter from the next room.
Option 4: I heard raucous laughter from the next room.
Correct Answer: I heard raucous laughter from the next room.
Solution : The correct choice is the fourth option.
Raucous is the correct spelling and it means loud and unpleasant.
Therefore, the correct sentence will be: I heard raucous laughter from the next room.
Question : AB is the chord of a circle such that AB = 10 cm. If the diameter of the circle is 20 cm, then the angle subtended by the chord at the centre is?
Option 1: $45^{\circ}$
Option 2: $60^{\circ}$
Option 3: $30^{\circ}$
Option 4: $90^{\circ}$
Correct Answer: $60^{\circ}$
Solution : Given: AB is the chord of a circle such that AB = 10 cm. The diameter of the circle is 20 cm. The line segment connecting any two points on the circle's circumference is known as the chord of a circle. In $\triangle AOC$, AO
Question : Directions: In the following question, some parts of the sentence may have 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".
In relationships, too, she seems too have subsisted (1) / on nothing but the emptiness of her (2) / heart to be the master of her life. (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.
The word "too" should be replaced with "to" as "too" is an adverb that means in excess or also. Here, "to" is used to form the perfect infinitive with "have". So, "she seems to have subsisted" would
Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?
Option 1: $a^2+b^2+c^2-3abc$
Option 2: $0$
Option 3: $3abc$
Option 4: $a^2+b^2+c^2-ab-bc-ca$
Correct Answer: $3abc$
Solution : Using the identity: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$. If $a + b + c = 0$, $a^3 + b^3 + c^3 - 3abc = 0$ ⇒ $a^3
Question : If $2 \sin \theta+2 \sin ^2 \theta=2$, then the value of $2 \cos ^4 \theta+2 \cos ^2 \theta$ is:
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 2
Solution : Given: $2 \sin \theta+2 \sin ^2 \theta=2$ ⇒ $2\sin\theta + 2\sin^2\theta = 2(\sin^2\theta + \cos^2\theta)$ ⇒ $2\sin\theta + 2\sin^2\theta = 2\sin^2\theta + 2\cos^2\theta$ ⇒ $2\sin\theta = 2\cos^2\theta$ ⇒ $\sin\theta = \cos^2\theta$ Putting the value in the given equation, $2 \cos ^4 \theta+2 \cos ^2 \theta$
Question : How many composite numbers are there from 53 to 97?
Option 1: 36
Option 2: 38
Option 3: 37
Option 4: 35
Correct Answer: 35
Solution : Given: The numbers are from 53 to 97. Numbers with more than two factors are called composite numbers. The composite number between 53 and 97 = 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77,
Question : Microorganisms are classified into how many major groups?
Option 1: 1
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : The correct option is 4
There are four main categories of microorganisms:
Question : Which of the following statement(s) is/are TRUE? I. $33^{3}>3^{33}$ II. $333>(3^{3})^{3}$
Option 1: Only I
Option 2: Only II
Option 3: Both I and II
Option 4: Neither I nor II
Correct Answer: Neither I nor II
Solution : $33^{3}$ = $33^{3}$ $3^{33} =(3^{11})^3$ Since $3^{11}$ is clearly greater than $33$, Thus, $3^{33} > 33^{3}$ So, statement I is false. Now, $(3^3)^3 = 27^3 = (729×27)>333$ So, statement II is also false. Hence, the correct answer is 'Neither I nor II'.
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