Staff Selection Commission Combined Graduate Level Exam
Question : Select the INCORRECT formula from the following options.
Option 1: $\operatorname{cosec}^2 \theta-\cot ^2 \theta=1$
Option 2: $\sin ^2 \theta+\cos ^2 \theta=1$
Option 3: $\sec ^2 \theta+\cos ^2 \theta=1$
Option 4: $\sec ^2 \theta-\tan ^2 \theta=1$
Correct Answer: $\sec ^2 \theta+\cos ^2 \theta=1$
Solution : $\sec^2 \theta = \frac{1}{\cos^2 \theta}$ But, $\sec ^2 \theta+\cos ^2 \theta\neq1$ Hence, the correct answer is $\sec ^2 \theta+\cos ^2 \theta=1$.
Question : $(113^2+ 115^2 + 117^2- 113×115 - 115×117 -117×113)$ is equal:
Option 1: 0
Option 2: 4
Option 3: 8
Option 4: 12
Correct Answer: 12
Solution : Use the formula: $a^2 + b^2 + c^2 - ab - bc - ca = \frac{1}{2}((a-b)^2 + (b-c)^2 + (c-a)^2)$ Now, $(113^2+ 115^2 + 117^2- 113×115 - 115×117 -117×113)$ $=\frac{1}{2}[(113-115)^2 + (115-117)^2 + (117-113)^2]$ $=\frac{1}{2}[(-2)^2 + (-2)^2 + (4)^2]$ $=\frac{1}{2}(4 + 4 + 16)$ $=\frac{1}{2}(24)$
Question : If the measure of one angle of a right triangle is 30º more than the measure of the smallest angle, then the measure of the smallest angle is:
Option 1: 90º
Option 2: 60º
Option 3: 30º
Option 4: 75º
Correct Answer: 30º
Solution : Given: The measure of one angle of a right triangle is 30º more than the measure of the smallest angle. Let the smallest angle be $x$. So, the other angle = $(x+30°)$ According to the question, $x+(x+30°)+90°=180°$ ⇒ $2x=180°–120°$ ⇒ $x=\frac{60°}{2}$ ⇒ $x=30°$ Hence, the
Question : A sum of Rs. 5,000 is divided into two parts such that the simple interest on the first part for $4 \frac{1}{5}$ years at $6 \frac{2}{3} \%$ p.a. is double the simple interest on the second part for $2 \frac{3}{4}$ years at 4% p.a. The ratio of the second part to the first part is:
Option 1: 11:14
Option 2: 11 : 13
Option 3: 14 : 11
Option 4: 13 : 11
Correct Answer: 14 : 11
Solution : Let the first part of the sum as $x$ and the second part as $5000 - x$. Given that the simple interest on the first part is double the simple interest on the second part. $x \times \frac{21}{5} \times \frac{20}{3} \% = 2
Question : NIN (National Institute of Nutrition ) Central Office is located at
Option 1: Hyderabad
Option 2: Mumbai
Option 3: Bengaluru
Option 4: Kolkata
Correct Answer: Hyderabad
Solution : The correct option is Hyderabad.
the National Institute of Nutrition (NIN) is an Indian research institute that is part of the Indian Council of Medical Research (ICMR). The central office of the National Institute of Nutrition is located in Hyderabad, Telangana, India.
Question : What is the volume of the largest sphere that can be carved out of a wooden cube of sides 21 cm?$\left(\pi=\frac{22}{7}\right)$
Option 1: 3851 cm3
Option 2: 6858 cm3
Option 3: 4851 cm3
Option 4: 5821 cm3
Correct Answer: 4851 cm3
Solution : The largest sphere that can be carved out of a cube of side 21 cm will have a diameter of 21 cm. So, the radius of the sphere, $r$ = $\frac{21}{2}$ cm Now the volume of the sphere = $\frac{4}{3}\pi r^3$ = $\frac{4}{3}×\frac{22}{7}×\frac{21}{2}×\frac{21}{2}×\frac{21}{2}$
Question : The 'Kannauj assembly' organised by Harsha was held in honour of
Option 1: Fa-Hien
Option 2: Itsing7
Option 3: Hieun-Tsang
Option 4: Megasthenes
Correct Answer: Hieun-Tsang
Solution : The correct option is - Hieun-Tsang
The Kannauj assembly organized by King Harshavardhana was held in honor of the Chinese Buddhist monk Hieun-Tsang. Hieun-Tsang was a renowned Buddhist scholar, traveler, and translator who journeyed to India in the 7th century CE during the Tang Dynasty
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (26, 14, 170) (31, 7, 18)
Option 1: (11, 5, 17)
Option 2: (34, 10, 72)
Option 3: (21, 9, 60)
Option 4: (14, 6, 24)
Correct Answer: (21, 9, 60)
Solution : Given: (26, 14, 170); (31, 7, 18)
In the given sets, add the first and the third numbers. The resultant is the square of the second number. (26, 14, 170)→26 + 170 = 196; (14)2 = 196 (31, 7, 18)→31 + 18
Question : Direction: If NOTE is written as PQVG, then TIME is written as?
Option 1: VQOG
Option 2: VKOG
Option 3: VOKG
Option 4: VGKO
Correct Answer: VKOG
Solution : Given: NOTE is coded as PQVG: N + 2 = P ; O + 2 = Q ; T + 2 = V ; E + 2 = G
Similarly, TIME will be coded as: T + 2 = V ; I + 2 =
Question : If $5A=12B=13C$, then find $A: B: C$.
Option 1: $60:65:156$
Option 2: $65:156:60$
Option 3: $156:65:60$
Option 4: $3:12:5$
Correct Answer: $156:65:60$
Solution : Given: $5A=12B=13C$ Let $5A=12B=13C=k$ $⇒A=\frac{k}{5},B=\frac{k}{12},C=\frac{k}{13}$ Ratio of $A:B:C=\frac{k}{5}:\frac{k}{12}:\frac{k}{13}$ $⇒A:B:C=\frac{1}{5}:\frac{1}{12}:\frac{1}{13}$ LCM of $(5, 12, 13) = 780$ Multiplying with it, we get, $⇒A:B:C=\frac{780}{5}:\frac{780}{12}:\frac{780}{13}$ $\therefore A : B : C = 156:65:60$ Hence, the correct answer is $156:65:60$.
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