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Question : The ratio of the volume of the two cones is 2 : 3, and the ratio of the radii of their bases is 1 : 2. The ratio of their heights is:
Option 1: 3 : 8
Option 2: 8 : 3
Option 3: 4 : 3
Option 4: 3 : 4
Correct Answer: 8 : 3
Solution : Let their radii be $x$ and $2x$ and their heights be $h$ and $H$ respectively. According to the question, $\frac{V_1}{V_2}=\frac{\frac{1}{3}\pi r_1^2 h_1}{\frac{1}{3}\pi r_2^2 h_2}$ ⇒ $\frac{V_1}{V_2}=\frac{r_1^2 h_1}{r_2^2 h_2}$ ⇒ $\frac{2}{3}=\frac{x^2 h}{(2x)^2 H}$ ⇒ $\frac{2}{3}=\frac{x^2 h}{4x^2 H}$ ⇒ $\frac{h}{H}=\frac{8}{3}$ Hence, the correct answer is
Question : If $p^{3}-q^{3}=(p-q)[(p+q)^{2}-xpq$, then the value of $x$ is:
Option 1: 1
Option 2: –1
Option 3: 2
Option 4: –2
Correct Answer: 1
Solution : Given: $p^{3}-q^{3}=(p-q)[(p+q)^{2}–xpq]$ ⇒ $p^{3}-q^{3}=(p-q)(p^{2}+q^{2}+2pq–xpq)$ ⇒ $p^{3}-q^{3}=(p-q)(p^{2}+q^{2}+pq(2-x)$ ----(1) We know the formula of $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$ Comparing this with equation (1), we have: ⇒ $(2-x)=1$ ⇒ $x=1$ Hence, the correct answer is 1.
Question : The enzyme that converts glucose to ethyl alcohol is:
Option 1: Invertase
Option 2: Maltase
Option 3: Zymase
Option 4: Diastase
Correct Answer: Zymase
Solution : The correct option is - Zymase
Zymase is a complex of enzymes found in yeast cells, and it plays a key role in the fermentation process that converts glucose (or other sugars) into ethanol (ethyl alcohol) and carbon dioxide.
Question : Select the most appropriate option to fill in the blank.
The peanut stove, which is so often seen on the __________, just outside the fruit shops, makes us think of the familiar street scene at home.
Option 1: Runway
Option 2: Building
Option 3: Market
Option 4: Foothpath
Correct Answer: Foothpath
Solution : The correct choice is the fourth option.
Footpath is a path or track that is laid on the side of roads for people to walk on. This helps convey that the peanut stove, which was present on the path where people walk, makes them think
Question : Direction: If Ramya's rank is 22nd out of 46 students, what is her rank from the last?
Option 1: 26
Option 2: 25
Option 3: 32
Option 4: 24
Correct Answer: 25
Solution : Given:
This means that there are 21 students ahead of Ramya.
Then, Ramya's rank from the last is 46 – 21 = 25
Hence, the second option is correct.
Question : Directions: In each of the following, questions, 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. M can be represented by 01, 23, etc, and E can be represented by 58, 88 etc. Similarly, you have to identify the set for the word given in each question. LANE
Option 1: 11, 66, 33, 96
Option 2: 11, 67, 32, 97
Option 3: 31, 87, 32, 97
Option 4: 31, 66, 33, 97
Correct Answer: 31, 87, 32, 97
Solution : Given: LANE
Number representations of each letter – L→11, 31 A→66, 87, 99 N→32 E→58, 79, 88, 97
First option: 11, 66, 33, 96; N and E cannot be represented as 33 and 96 respectively. Second option: 11, 67, 32, 97; A
Question : Directions: If A means add, B means divide, C means multiply and D means subtract, then 180 B 36 C 5 A 8 D 32 = ?
Option 1: 0
Option 2: 3
Option 3: 1
Option 4: 2
Solution : Given: 180 B 36 C 5 A 8 D 32 = ?
On replacing the letters with mathematical signs, the equation becomes – = 180 ÷ 36 × 5 + 8 – 32 = 5 × 5 + 8 – 32 = 25 + 8
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at line MN as shown.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on Line MN). So, the left side of the reflected image will appear
Question : Directions: A graph showing the price of rice in India during the years 2000 to 2003 is given below. Study the graph carefully and answer the questions.
The maximum difference in price between any two years was in the month of:
Option 1: January
Option 2: November
Option 3: March
Option 4: December
Correct Answer: December
Solution : From the given table in question, Difference = 23 – 5 = 18 So, the maximum difference in price between any two years was in the month of December. Hence, the answer is December.
Question : The prehistoric period in the early development of human beings is commonly known as the_______.
Option 1: Old Stone Age
Option 2: Mesolithic Age
Option 3: Iron Age
Option 4: New Stone Age
Correct Answer: Old Stone Age
Solution : The correct answer is the Old Stone Age.
The prehistoric period in the early development of human beings is commonly known as the Old Stone Age. The Stone Age can be defined as the prehistoric period or era when humans made tools
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