Staff Selection Commission Combined Graduate Level Exam
Question : If $\sin5\theta = \cos 20° (0°<\theta<90°)$, then the value of $\theta$ is:
Option 1: 4°
Option 2: 22°
Option 3: 10°
Option 4: 14°
Correct Answer: 14°
Solution : Given: $\sin5\theta = \cos 20° (0°<\theta<90°)$ We know, $\cos 20°=\cos(90°-70°)=\sin70°$ So, $\sin5\theta=\sin 70°$ $⇒5\theta=70°$ $\therefore \theta=14°$ Hence, the correct answer is 14°.
Question : What is the smallest number which can be added to 9454351626 so that it becomes divisible by 11?
Option 1: 1
Option 2: 6
Option 3: 5
Option 4: 4
Correct Answer: 6
Solution : A number is divisible by 11 if the difference between the sum of the digits at even places and the sum of the digits at odd places of a number is either 0 or divisible by 11. Now, the difference between the sums = (9
Question : A conical vessel (solid) is made of iron. Its base radius is 7 cm and its height is 15 cm. If the weight of the iron per cubic centimetre is 15 g, what is the weight of the vessel?
Option 1: 13.55 kg
Option 2: 12.55 kg
Option 3: 14.55 kg
Option 4: 11.55 kg
Correct Answer: 11.55 kg
Solution : Base radius of conical vessel = 7 cm Height of conical vessel = 15 cm Weight of the iron per cubic centimetre (density) = 15 g Volume of the Conical Vessel = $\frac{1}3\pi r^2h$ = $\frac{1}3\pi \times 7^2\times 15=770$ cm3 Weight of vessel
Question : Total deposits with Post Office savings organisations are included in which money supply aggregate?
Option 1: M1
Option 2: M3
Option 3: M4
Option 4: M2
Correct Answer: M4
Solution : The correct option is M4.
The deposits held with Post Office savings organisations are typically included in the broader money supply aggregate known as M2 or M3.
M4 is a monetary aggregate that includes a broader range of financial assets compared to M2 and
Question : Which is the largest gland in the human body?
Option 1: Liver
Option 2: Thyroid
Option 3: Pituitary
Option 4: Salivary gland
Correct Answer: Liver
Solution : The correct option is the Liver.
The liver is the largest gland in the human body. It performs various activities, including the production of bile for digestion, processing of nutrients, detoxifying toxic compounds, and regulation of other metabolic processes. The liver also stores and releases
Question : A balloon leaves from point P and rises at a uniform speed. After 6 minutes, an observer situated at a distance of $450\sqrt3$ metres from point P observes that the angle of elevation of the balloon is 60°. Assume that the point of observation and point P is on the same level. What is the speed (in m/s) of the balloon?
Option 1: 4.25
Option 2: 3.75
Option 3: 4.5
Option 4: 3.45
Correct Answer: 3.75
Solution : Given: Distance between the observer and the point P is $450\sqrt{3}$ m. After 6 minutes angle of elevation is 60°. So, $\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}$ $⇒\tan 60° = \frac{H}{450 \sqrt{3}}$ $⇒\sqrt{3} = \frac{H}{450 \sqrt{3}}$ $\therefore H =450×3 = 1350$ m Now, for the speed of the
Question : The disease that is caused by virus is
Option 1: Typhoid
Option 2: Cholera
Option 3: Common Cold
Option 4: Tetanus
Correct Answer: Common Cold
Solution : The correct option is common cold
The common cold is caused by a number of viruses, the most prevalent of which being rhinoviruses. Other viruses, such as adenoviruses and coronaviruses, also cause cold symptoms. It is a highly contagious respiratory infection with symptoms such
Question : The average of 25 numbers is 64. The averages of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the $12^{\text {th }}$ number is 61, and if the $12^{\text {th }}$ and $13^{\text {th }}$ numbers are excluded, then what is the average of the remaining numbers (correct to one decimal place)?
Option 1: 59.2
Option 2: 62.2
Option 3: 60.2
Option 4: 61.5
Correct Answer: 60.2
Solution : Sum of the 25 numbers = 64 × 25 = 1600 Sum of the first 13 numbers = 13 × 62.8 = 816.4 Sum of the last 13 numbers = 13 × 72.2 = 938.6 Number 13th = (Sum of the first 13 numbers +
Question : Directions: If A means –, C means ×, D means ÷, and E means +, then 14 C 3 A 12 E 4 D 2 = ?
Option 1: 6
Option 2: 17
Option 3: 28
Option 4: 32
Correct Answer: 32
Solution : Given: 14 C 3 A 12 E 4 D 2 = ?
After replacing the letters with mathematical signs, the equation becomes – = 14 × 3 –12 + 4 ÷ 2 = 14 × 3 –12 + 2 = 42 –12 + 2 =
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."
You should avoid (1) / to travel (2) / in the rush hour. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : There is an error in the second part of the sentence as "to travel" is not needed after "avoid." The verb "avoid" is followed by the gerund form of the verb, so it should be "avoid travelling" instead of "to travel."
The correct sentence is
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