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Question : The pie chart given below shows the number of students studying in six schools. Total number of students studying in all these six schools are 9000. The number of students studying in a particular school is shown as a percentage of the total number of students studying in all these six schools. What is the difference between the number of students studying in schools A and B together and schools D and F together?
Option 1: 790
Option 2: 810
Option 3: 770
Option 4: 840
Correct Answer: 810
Solution : Number of students studying in schools A and B together = (5% + 35%) × 9000 = 40% × 9000 = 3600 Number of students studying in schools D and F together = (21% + 10%) × 9000 = 31% × 9000 = 2790 Required
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 482, 524, 576, ?, 710, 792
Option 1: 604
Option 2: 618
Option 3: 624
Option 4: 638
Correct Answer: 638
Solution : Given: 482, 524, 576, ?, 710, 792
The pattern is as follows – 482 + 42 = 524; 524 + 52 = 576; 576 + 62 = 638; 638 + 72 = 710; 710 + 82 = 792
So, 638 is the missing number. Hence,
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 1 : 8
Option 2: 27 : 64
Option 3: 125 : 218
Option 4: 343 : 512
Correct Answer: 125 : 218
Solution : Let's check the options – First option: 1 – 8→13 = 1; 23 = 8 Second option: 27 – 64→ 33 = 27; 43 = 64 Third option: 125 – 218→ 53 = 125; 63 = 216
Question : Directions: In the following question, some parts of the sentence may have some 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".
Last night I dream (1) / I was a Sheikh on the 169th floor (2) / of Burj Khalifa. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
Dreamt will replace dream, as the sentence indicates a past event. Hence, last night I dreamt, is the right usage.
Therefore, the correct sentence is: "Last night I dreamt I was a Sheikh on
Question : What is the surface area (in cm²) of a spherical sculpture whose radius is 35 cm? (Take $\pi=\frac{22}{7}$)
Option 1: 16540
Option 2: 15700
Option 3: 15400
Option 4: 14500
Correct Answer: 15400
Solution : The radius of spherical sculpture, $r$ = 35 cm Surface area of sphere = $4\pi r^2$ = $4×\frac{22}{7}×{35}^2$ = 15400 cm2 Hence, the correct answer is 15400.
Question : The largest freshwater lake in India is :
Option 1: Dal lake
Option 2: Bhimtal lake
Option 3: Wular lake
Option 4: Nainital lake
Correct Answer: Wular lake
Solution : The correct answer is Wular Lake.
Wular Lake is located in the Indian state of Jammu and Kashmir and is the largest freshwater lake in India. It is fed by the river Jhelum. It was formed as a result of tectonic activity and is
Question : At what rate percent per annum will a sum of INR 15, 625 amount to INR 21, 952 in three years, if the interest is compounded annually?
Option 1: 12%
Option 2: 8%
Option 3: 9%
Option 4: 10%
Correct Answer: 12%
Solution : Principal (P) = INR 15, 625 Time (T) = 3 years Amount (A) = INR 21, 952 Amount = $P(1 + \frac{R}{100})^T$ Let the rate of interest per annum be $R$. 21952 = 15625$(1 + \frac{R}{100})^3$ ⇒ $\frac{21952}{15625} = (1 + \frac{R}{100})^3$ ⇒ $\sqrt[3]{(\frac{21952}{15625})} =
Question : What is the average of all prime numbers between 30 and 50?
Option 1: 36.5
Option 2: 39.8
Option 3: 38.5
Option 4: 34.2
Correct Answer: 39.8
Solution : Prime numbers between 30 and 50 are 31, 37, 41, 43, and 47. Required average = $\frac{31 + 37 + 41 + 43 + 47}{5}$ = 39.8 Hence, the correct answer is 39.8.
Question : A policeman noticed a thief from 300 m. The thief started running and the policeman was chasing him. The thief and the policeman ran at speeds of 8 km/h and 9 km/h, respectively. What was the distance between them after 3 minutes?
Option 1: 225 m
Option 2: 250 m
Option 3: 300 m
Option 4: 200 m
Correct Answer: 250 m
Solution : Given: Distance between the policeman and the thief = 300 m Speed of the policeman = 9 km//h = $9×\frac{5}{18}=\frac{5}{2}$ m/s Speed of the thief = 8 km//h = $8×\frac{5}{18}=\frac{20}{9}$ m/s Relative speed of the policeman and the thief = 9 – 8 =
Question : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}=$?
Option 1: $\operatorname{cosec}\theta$
Option 2: $\sec\theta$
Option 3: $2\cos\theta$
Option 4: $2\sec\theta$
Correct Answer: $2\sec\theta$
Solution : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}$ $=\frac{1-\cos ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}$ $=\frac{(1-\cos \theta)(1+\cos \theta)}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}$ $=\frac{1-\cos \theta}{\cos \theta}+\frac{1+\cos \theta}{\cos \theta}$ $=\frac{1-\cos \theta+1+\cos \theta}{\cos \theta}$ $=\frac{2}{\cos \theta}$ $=2\sec\theta$ Hence, the correct answer is $2\sec\theta$.
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