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Question : According to Raghav, his weight is more than 64 kg but less than 74 kg. His sister does not agree with Raghav and she thinks that his weight is more than 60 kg but less than 69 kg. His mother's view is that his weight cannot be more than 68 kg. His father's view is that his weight cannot be more than 67 kg. If all are them are correct in their estimation, then what is the average of different probable weights of Raghav measured (in kg)?
Option 1: 66
Option 2: 67
Option 3: 68
Option 4: 65
Correct Answer: 66
Solution : Let $x$ be the weight of Raghav. According to Raghav, $64 < x < 74$ -----------(i) According to his sister, $60 < x < 69$ ---------(ii) According to his father, $x \leq 67$ --------(iii) According to his mother, $x \leq 68$ --------(iv) Taking the intersection
Question : Comprehension:
Read the following passage and answer the questions.
All foodstuffs change. Green fruits become ripe and eggs go bad or rotten. It is the enzymes naturally present in each food which bring about the complex chemical changes that lead first to ripening and then to rotting.
How does one control the activity of enzymes, bacteria, yeasts and moulds in food? All of them require air, moisture and a certain temperature, usually somewhere near the body temperature, to be active. Depriving them of one or more of these will suppress them. All microorganisms can be killed by heat sterilisation. This simply means heating the food to high enough temperatures by boiling, deep or shallow frying, roasting, baking and, for milk particularly, pasteurisation. After such sterilisation, if the food is sealed in airtight containers, it can be kept for a long time. A certain water content in food is necessary for microorganisms to be active. Drying in the sun is a simple way of bringing down the moisture level so low that the enzymes and microorganisms cannot flourish.
Some chemicals can suppress undesirable activity. The addition of salt, vinegar, spices and oil or sugar syrup are other ways of preventing foods from going bad. If heating kills, freezing inactivates the enzymes and microorganisms. This is what happens in a refrigerator, in which fruits, vegetables and milk can be kept for fairly long periods. For meat and fish, even colder temperatures, below freezing point, are necessary for preservation. All foods which are kept cold in this way, once taken out and returned to room temperature, are again subject to spoilage and change.
Question: Which of these is NOT required for the growth of bacteria?
Option 1: Air
Option 2: Optimum temperature
Option 3: Chemicals
Option 4: Moisture
Correct Answer: Chemicals
Solution : The third option is the correct choice.
As stated at the start of the second paragraph, bacteria require air, optimum temperature, and moisture to be active. Thus, bacteria do not require chemicals to be active.
Question : Directions: In the following question, select the related number from the given alternatives. 21 : 3 :: 574 : ?
Option 1: 23
Option 2: 82
Option 3: 97
Option 4: 113
Correct Answer: 82
Solution : Given: 21 : 3 :: 574 : ?
Like, 21 : 3→21 ÷ 7 = 3 Similarly, for 574 : ?→574 ÷ 7 = 82
So, 574 is related to 82. Hence, the second option is correct.
Question : In the context of modern Indian history, the expression Bombay Plan (1944) was a proposal on:
Option 1: economic development
Option 2: Panchayati Raj
Option 3: transfer of power
Option 4: administrative reorganisation
Correct Answer: economic development
Solution : The correct answer is economic development.
The "Bombay Plan" was a unique economic plan created by a group of business leaders and experts in January 1944 for India. At first, it was just shared privately among a few people. However, due to the
Question : Directions: Six characters A, B, C, 1, 2, and 3 are written on different faces of a dice. Two positions of this dice are shown in the figure. Find the character on the face opposite to C.
Option 1: A
Option 2: 2
Option 3: 3
Option 4: B
Correct Answer: 2
Solution : Taking dice positions 1 and 2 with 1 as the common face.
Moving clockwise from the common face with 1 –
So, the opposite pairs are –
Therefore, the opposite face of the C is 2. Hence, the second option is correct.
Question : If the arithmetic mean of $3a$ and $4b$ is greater than 50, and $a$ is twice $b$, then the smallest possible integer value of $a$ is:
Option 1: 20
Option 2: 18
Option 3: 21
Option 4: 19
Correct Answer: 21
Solution : According to the question, $\frac{3a+4b}{2}>50$ $\Rightarrow3a+4b>100$ $\Rightarrow3a+\frac{4a}{2}>100 (\because a = 2b)$ $\Rightarrow3a+2a>100$ $\Rightarrow5a>100$ $\Rightarrow a>20$ $\therefore$ Minimum value of $a = 21$ Hence, the correct answer is 21.
Question : The sum of 10 numbers is 686. What is their average?
Option 1: 67.5
Option 2: 65.5
Option 3: 68.6
Option 4: 66.6
Correct Answer: 68.6
Solution : The sum of 10 numbers is 686. $\therefore$ The average of these 10 numbers $=\frac{\text{Sum of all the observations}}{{\text{Total number of observations}}}=\frac{686}{10}= 68.6$ Hence, the correct answer is 68.6.
Question : Directions: In the given question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
She tries to adjust _____ her relations.
Option 1: at
Option 2: so
Option 3: with
Option 4: for
Correct Answer: with
Solution : The correct choice is the third option.
The preposition with is the correct choice in this sentence because it is used to indicate the manner in which someone adjusts or accommodates himself. In this case, with suggests that she is trying to adapt to her
Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the product of the two given numbers?
Option 1: 160
Option 2: 240
Option 3: 200
Option 4: 320
Correct Answer: 240
Solution : Let the numbers be x and y. So, x3 – y3 = 6272 and (x – y) = 8 Cubing both sides of the given expression, (x – y) = 8, ⇒ (x – y)3 = 83 ⇒ x3 –
Question : Which of the following set of angles forms a triangle?
Option 1: 60°, 70°, 80°
Option 2: 60°, 70°, 30°
Option 3: 60°, 40°, 80°
Option 4: 60°, 50°, 80°
Correct Answer: 60°, 40°, 80°
Solution : The sum of all angles of the triangle should be 180°. From the above-given options, only option 2 satisfies the condition. Option 2: 60°, 40°, 80° Sum of angles = 60° + 40° + 80° = 180° Hence, the correct answer is 60°,
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