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Question : How many solid spherical balls each of 33 cm radius can be made out of a solid spherical ball of radius 66 cm?
Option 1: 8
Option 2: 4
Option 3: 7
Option 4: 3
Correct Answer: 8
Solution : Volume of a sphere $=\frac{4}{3}\pi r^3$, where $r$ is the radius The volume of the larger sphere with a radius of 66 cm, $V_{\text{large}} = \frac{4}{3} \pi (66)^3$ The volume of the smaller sphere with a radius of 33 cm, $V_{\text{small}} = \frac{4}{3} \pi (33)^3$
Question : Directions: Select the correct combination of the mathematical signs to replace X in the below equation and thereby balance it. 9 X 3 X 6 X 2 X 9
Option 1: ÷, ×, =, ×
Option 2: ÷, ×, =, –
Option 3: ×, =, –, ÷
Option 4: ×, ÷, +, =
Correct Answer: ÷, ×, =, ×
Solution : Given: 9 X 3 X 6 X 2 X 9
Replace the given symbols in the options one by one with the original symbols in the given equation. First option: ÷, ×, =, × 9 ÷ 3 × 6 = 2 ×
Question : Directions: In a certain code language, CHILDREN is written as FKLOGUHQ, and SCHOOL is written as VFKRRO, how will CLASSROOM be written in that language?
Option 1: EMCTTTQQO
Option 2: EMCTTURRP
Option 3: FOEWWURRP
Option 4: FODVVURRP
Correct Answer: FODVVURRP
Solution : Given: The code for CHILDREN is FKLOGUHQ, and the code for SCHOOL is VFKRRO.
As for, CHILDREN is written as FKLOGUHQ – C + 3 = F; H + 3 = K; I + 3 = L; L + 3 = O; D + 3
Question : What are the last three digits of the multiplication 654321 × 123456?
Option 1: 376
Option 2: 344
Option 3: 324
Option 4: 352
Correct Answer: 376
Solution : To find the last three digits of a product, we can ignore the first two digits and multiply the remaining digits. Ignoring the first two digits of 654321 and 123456, we have 321 × 456. Multiplying these digits, we get 146376. Hence, the correct answer
Question : Select the correctly spelt word.
Option 1: Exeacutve
Option 2: Exacutive
Option 3: Exicutive
Option 4: Executive
Correct Answer: Executive
Solution : The correct choice is the fourth option.
The correct spelling is executive, which refers to a person or group having administrative or managerial authority in an organisation.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
You can play video games and paint or (draw) from anywhere.
(1) be drawing
(2) can draw
(3) could draw
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct choice is the fourth option, No improvement.
The verb form used is correct in the sentence and conveys the intended meaning.
Question : If $\tan ^2 \theta+\tan ^4 \theta=1$, then:
Option 1: $\cot ^2 \theta+\cot ^4 \theta=1$
Option 2: $\cos ^2 \theta+\cos ^4 \theta=1$
Option 3: $\sin ^2 \theta+\sin ^4 \theta=1$
Option 4: $\operatorname{cosec}^2 \theta+\sec ^4 \theta=1$
Correct Answer: $\cos ^2 \theta+\cos ^4 \theta=1$
Solution : $\tan ^2 \theta+\tan ^4 \theta=1$ ⇒ $\tan^2\theta(1+\tan^2\theta) = 1$ ⇒ $\tan^2\theta(1+\frac{\sin^2\theta}{\cos^2\theta}) = 1$ ⇒ $\frac{\sin^2\theta}{\cos^2\theta}(\frac{cos^2\theta + \sin^2\theta}{\cos^2\theta}) = 1$ ⇒ $\frac{\sin^2\theta}{\cos^2\theta}(\frac{1}{\cos^2\theta}) = 1$ ⇒ $\sin^2\theta = \cos^4\theta$ ⇒ $1-\cos^2\theta = \cos^4\theta$ ⇒ $\cos^4\theta + \cos^2\theta = 1$ Hence, the correct answer
Question : Who among the following belonged to the ancient chiefly family of the Cholas from Uraiyur, who captured the Kaveri delta from the Muttaraiyar in the middle of the ninth century?
Option 1: Gandaraditya
Option 2: Vijayalaya
Option 3: Parantaka I
Option 4: Aditya I
Correct Answer: Vijayalaya
Solution : The correct answer is Vijayalaya.
A minor ruling family called the Muttaraiyar had control over the Kaveri delta, and they were under the authority of the Pallava kings of Kanchipuram. In the middle of the ninth century, a leader named Vijayalaya, hailing from the
Question : The table given below shows the foreign trade by two countries in 5 different years.
What is the value of average foreign trade by country P in all 5 years?
Option 1: 155
Option 2: 745
Option 3: 149
Option 4: 135
Correct Answer: 149
Solution : Average foreign trade by country P in all 5 years = $\frac{220+200+125+115+85}{5}$ = $\frac{745}{5}$ = 149 Hence, the correct answer is 149.
Question : Select the INCORRECTLY spelt word.
Option 1: Puzzled
Option 2: Nasal
Option 3: Councel
Option 4: Embezzlement
Correct Answer: Councel
Solution : The correct answer to this question is the third option.
The appropriate spelling of: coucel should be counsel. In the place of 'c', 'ns' needs to be added.
In summary, "counsel" revolves around the theme of providing advice, guidance, or professional support. The specific context
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