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Question : If $a+b+c=9$ (where $a,b,c$ are real numbers), the minimum value of $a^2+b^2+c^2$ is:
Option 1: 100
Option 2: 9
Option 3: 27
Option 4: 81
Correct Answer: 27
Solution : Given: If $a+b+c=9$ (where $a,b,c$ are real numbers). For the minimum value, $a=b=c$ ⇒ $3a = 9$ ⇒ $a = \frac{9}{3}=3$ Similarly, $b=3$ and $c=3$ Replacing $a$, $b$, and $c$ with their values, the equation, $a+b+c=9$, is satisfied. So, the minimum value of ($a^{2}+b^{2}+c^{2}$) is
Question : Which of the following was known as an organisation of merchants in the inscriptions of the Pallavas?
Option 1: Nagaram
Option 2: Sangathana
Option 3: Ur
Option 4: Sabha
Correct Answer: Nagaram
Solution : The correct answer is Nagaram.
"Nagaram" was the name of the merchant association. Rich landowners and merchants usually held authority over these gatherings. In South India, these types of village assemblies endured for generations.
Question : Which tributary of the Indus River originates near the Rohtang Pass at an altitude of 4,000 metres above mean sea level?
Option 1: Chenab
Option 2: Musi
Option 3: Beas
Option 4: Indravati
Correct Answer: Beas
Solution : The correct option is Beas.
The tributary of the Indus River that originates near the Rohtang Pass at an altitude of 4,000 metres above mean sea level is the Beas River. The Beas River flows through the northern part of India and eventually joins
Question : If A is 48% more than B and C is 60% less than the sum of A and B, then A is what percentage more than C? (Correct to one decimal place.)
Option 1: 50.8
Option 2: 49.2
Option 3: 50.2
Option 4: 49.8
Correct Answer: 49.2
Solution : Given: A is 48% more than B and C is 60% less than the sum of A and B. Let the value of B be 100. Then, the value of A = $100\times \frac{148}{100}$ = 148 According to the question, C = 40% of (A
Question : Select the most appropriate option to substitute the underlined segment in the given sentence. If there is no need to substitute it, select 'No substitution'.
He is not so a person that will betray a friend.
Option 1: as a person that
Option 2: No substitution
Option 3: such a person as
Option 4: so a person but
Correct Answer: such a person as
Solution : The correct choice is the third option.
The phrase "such a person as" is a valid substitution for it. In the context of the sentence, using "such a person as" emphasises the specific type or quality of the person in question.
Question : What is the Highest Common Factor of 25, 15, and 75?
Option 1: 7
Option 2: 15
Option 3: 25
Option 4: 5
Correct Answer: 5
Solution : 25 = 5 × 5 15 = 3 × 5 75 = 5 × 5 × 3 HCF of 25, 15, and 75 is 5. Hence, the correct answer is 5.
Question : Directions: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. 10, 18, 28, 40, ?
Option 1: 58
Option 2: 46
Option 3: 52
Option 4: 54
Correct Answer: 54
Solution : Given: 10, 18, 28, 40, ?
Add even consecutive numbers to the previous terms to obtain the missing term. 10 + 8 = 18; 18 + 10 = 28; 28 + 12 = 40; 40 + 14 = 54
So, 54 is the missing number
Question : Find the surface area of a sphere whose radius is 3.5 cm. Use $(\left.\pi=\frac{22}{7}\right)$.
Option 1: 154 cm2
Option 2: 152 cm2
Option 3: 146 cm2
Option 4: 160 cm2
Correct Answer: 154 cm2
Solution : Given, Radius = 3.5 cm The surface area of the sphere = $4\pi r^2$, where $r$ is the radius of the sphere. ⇒ Surface area = $4\times \frac{22}{7}\times 3.5\times 3.5=4\times 22\times 0.5\times 3.5=$ 154 cm2 Hence, the correct answer is 154 cm
Question : Insert the missing number 3, 18, 12, 72, 66, 396, ?.
Option 1: 300
Option 2: 380
Option 3: 350
Option 4: 390
Correct Answer: 390
Solution : Given: 3, 18, 12, 72, 66, 396, ? The pattern is: 3 × 6 = 18 18 – 6 = 12 12 × 6 = 72 72 – 6 = 66 66 × 6 = 396 396 – 6 = 390 Hence, the correct answer
Question : In an isosceles triangle, if the unequal angle is 4 times the sum of the equal angles, then each equal angle is:
Option 1: $25^{\circ}$
Option 2: $30^{\circ}$
Option 3: $21^{\circ}$
Option 4: $18^{\circ}$
Correct Answer: $18^{\circ}$
Solution :
In an isosceles triangle, two angles are equal. Let the equal angles be $\angle B$ and $\angle C$ ($\angle B=\angle C$). The third angle which is unequal is $\angle A$. Given that the unequal angle is $4$ times the sum of the equal angles. $=4(\angle
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