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Question : Find the length of the arc of the sector of a circle of diameter 7 cm with a central angle of $108^{\circ}$. [Use $\pi=\frac{22}{7}$]
Option 1: 6.6 cm
Option 2: 5.6 cm
Option 3: 13.2 cm
Option 4: 11.2 cm
Correct Answer: 6.6 cm
Solution : Diameter of circle = 7 cm So, radius, $r$ = 3.5 cm Angle subtended by arc, $\theta$ = 180° We know, length of arc of a circle = $\frac{\theta}{360°}\times 2\pi r$ = $\frac{108°}{360°}\times 2\pi ×\frac{7}2 = 6.6$ cm Hence, the correct answer is 6.6
Question : Directions: Select the letter cluster that will replace the question mark (?) in the following series. GMDR, EOBT, CQZV, ?, YUVZ
Option 1: ASXX
Option 2: BSYX
Option 3: ASXY
Option 4: BSXY
Correct Answer: ASXX
Solution : Given: GMDR, EOBT, CQZV, ?, YUVZ
Subtract 2 from the first and the third letters and add 2 to the second and fourth letters of the previous term to obtain the next term in the series – GMDR→G – 2 = E; M + 2
Question : If $a+b+c=0$, then the value of $\frac{a^{2}+b^{2}+c^{2}}{ab+bc+ca}$ is:
Option 1: 2
Option 2: –2
Option 3: 0
Option 4: 4
Correct Answer: –2
Solution : Given: $a+b+c=0$ We know that $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$ Putting the value of $a+b+c=0$, we have, ⇒ $(0)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$ ⇒ $a^{2}+b^{2}+c^{2}=–2(ab+bc+ca)$ ⇒ $\frac{(a^{2}+b^{2}+c^{2})}{(ab+bc+ca)}=–2$ Hence, the correct answer is –2.
Question : The bar graph shows the marks of a student in different subjects out of 100. His marks in physics are what percentage more than that in mathematics?
Option 1: 44%
Option 2: 35%
Option 3: 33%
Option 4: 28%
Correct Answer: 35%
Solution : Marks in physics = 54 Marks in mathematics = 40 Required percentage = $\frac{\text{Marks in physics - Marks in mathematics}}{\text{Marks in mathematics}}\times100$ = $\frac{54-40}{40}\times100$ = $\frac{14}{40}\times100$ = 35% Hence, the correct answer is 35%.
Question : The average of 16 numbers is 35. It was found later that four numbers 18, 17, 24, and 35 were taken by mistake. What is the new average after removing these numbers?
Option 1: 38.83
Option 2: 42.33
Option 3: 46.66
Option 4: 33.33
Correct Answer: 38.83
Solution : Given that the average of 16 numbers is 35, we can calculate the sum of those 16 numbers as follows: Sum = Average × Count ⇒ Sum = 35 × 16 = 560 So, Adjusted Sum = Sum – Sum of Mistaken Numbers ⇒ Adjusted
Question : Directions: A person starts delivering letters 3 km southwards and then turns right. He covers 4 km on this road and again turns right. He delivers letters for 3 km and completes his daily beat. Then he turns left for lunch at home which is 5 km away. How far does he have to travel to reach the post office after lunch?
Option 1: 15 km
Option 2: 10 km
Option 3: 9 km
Option 4: 8 km
Correct Answer: 9 km
Solution : Firstly, we will draw the diagram as per the given instructions –
Now, we have to find the distance the person has to travel to reach the post office after lunch.
In the figure, A is the starting point and E is the finishing
Question : Directions: A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. I can be represented by 12, 44, etc, and D can be represented by 75, 97, etc. Similarly, you have to identify the set for the word CHEAT.
Option 1: 10, 21, 68, 77, 56
Option 2: 34, 43, 95, 85, 96
Option 3: 41, 14, 76, 99, 79
Option 4: 22, 00, 87, 67, 67
Correct Answer: 41, 14, 76, 99, 79
Solution : Given: CHEAT
Number representations of each letter – C→03, 10, 22, 34, 41 H→00, 14, 21, 32, 43 E→59, 68, 76, 87, 95 A→58, 66, 77, 85, 99 T→55, 67, 79, 86, 98
First option: 10, 21, 68, 77, 56; T
Question : Identify the segment in the sentence which contains the grammatical error. If I want to gave you some advice, would you be interested?
Option 1: gave you some advice,
Option 2: be interested?
Option 3: If I want to
Option 4: would you
Correct Answer: gave you some advice,
Solution : The error lies in the first option.
The verb "gave" is incorrect in this context. The correct form should be "give" because it needs to match the infinitive "to" in the sentence. When the infinitive "to" is used, it
Question : Which of the following pairs of countries will host the 2023 FIFA Women’s World Cup?
Option 1: Canada and Mexico
Option 2: New Zealand and Austria
Option 3: France and Canada
Option 4: New Zealand and Australia
Correct Answer: New Zealand and Australia
Solution : The correct answer is New Zealand and Australia.
Australia and New Zealand jointly hosted the 2023 FIFA Women’s World Cup. The World Cup was held in July and August 2023. Spain won the 2023 FIFA Women’s World Cup. The final of
Question : What is the normal blood volume in human adult ?
Option 1: One litre
Option 2: Three Litres
Option 3: Five Litres
Option 4: Seven Litres
Correct Answer: Five Litres
Solution : The correct answer is Five Litres.
A normal adult's blood volume is around 5 litres (10.5 pints). This blood volume accounts for around 7% of a person's entire body weight. Blood volume is critical for general health and well-being. It aids in the transfer
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