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Question 1 of 5
1. Question
Consider the following statements:
I. The selling price of 40 articles is equal to the cost price of 32 articles, so the profit is 25%.
II. The cost price of 12 articles is equal to the selling price of 9 articles, so the profit is 33.33%.Which of the statements are correct?
Correct
Answer: (b)
Explanation
Let the cost price (C.P.) of one article be ₹1.
Statement I:
Selling price (S.P.) of 40 articles = C.P. of 32 articles
⇒ 40 × S.P. = 32 × 1
⇒ S.P. per article = 32/40 = ₹0.8Since the cost price is ₹1 and selling price is ₹0.8, there is a loss, not a profit.
Loss % = (1 − 0.8)/1 × 100 = 20% loss, not 25% profit.
→ Statement I is incorrect.Statement II:
C.P. of 12 articles = S.P. of 9 articles
⇒ 12 × 1 = 9 × S.P.
⇒ S.P. per article = 12/9 = ₹1.333…Profit % = (1.333 − 1)/1 × 100 = 33.33% profit.
→ Statement II is correct.Incorrect
Answer: (b)
Explanation
Let the cost price (C.P.) of one article be ₹1.
Statement I:
Selling price (S.P.) of 40 articles = C.P. of 32 articles
⇒ 40 × S.P. = 32 × 1
⇒ S.P. per article = 32/40 = ₹0.8Since the cost price is ₹1 and selling price is ₹0.8, there is a loss, not a profit.
Loss % = (1 − 0.8)/1 × 100 = 20% loss, not 25% profit.
→ Statement I is incorrect.Statement II:
C.P. of 12 articles = S.P. of 9 articles
⇒ 12 × 1 = 9 × S.P.
⇒ S.P. per article = 12/9 = ₹1.333…Profit % = (1.333 − 1)/1 × 100 = 33.33% profit.
→ Statement II is correct. -
Question 2 of 5
2. Question
The difference between compound interest and simple interest on a sum for two years at 10% per annum, where the interest is compounded annually, is Rs.36. If the interest were compounded half-yearly, the difference in the two interests would be nearly?
Correct
Answer: (b)
The difference between compound interest and simple interest on a sum for two years at 10% per annum compounded annually is given as ₹36.
For 2 years, the difference between compound interest (CI) and simple interest (SI) is given by the formula:
CI – SI = P × (r/100)²
36 = P × (10/100)²
36 = P × (1/100)
P = ₹3600Now, if interest is compounded half-yearly,
Rate per half-year = 5%
Number of half-years = 4CI = P × [(1 + 0.05)⁴ – 1]
= 3600 × (1.21550625 – 1)
= 3600 × 0.21550625
= ₹775.82SI for 2 years = P × r × t = 3600 × 10 × 2 / 100 = ₹720
Difference = CI – SI = 775.82 – 720 = ₹55.82 ≈ ₹56
Hence, the difference in the two interests when compounded half-yearly is nearly ₹56.
Incorrect
Answer: (b)
The difference between compound interest and simple interest on a sum for two years at 10% per annum compounded annually is given as ₹36.
For 2 years, the difference between compound interest (CI) and simple interest (SI) is given by the formula:
CI – SI = P × (r/100)²
36 = P × (10/100)²
36 = P × (1/100)
P = ₹3600Now, if interest is compounded half-yearly,
Rate per half-year = 5%
Number of half-years = 4CI = P × [(1 + 0.05)⁴ – 1]
= 3600 × (1.21550625 – 1)
= 3600 × 0.21550625
= ₹775.82SI for 2 years = P × r × t = 3600 × 10 × 2 / 100 = ₹720
Difference = CI – SI = 775.82 – 720 = ₹55.82 ≈ ₹56
Hence, the difference in the two interests when compounded half-yearly is nearly ₹56.
-
Question 3 of 5
3. Question
Two statements S1 and S2 are given below followed by a question.
S1. The area of a square is 144 square units.
S2. The perimeter of the square is 48 units.Question: What is the side length of the square?
Correct
Answer: Option (b)
Explanation:
Statement 1: Area = 144
⇒ Side² = 144 ⇒ Side = √144 = 12
→ So, side length = 12 (Answerable)Statement 2: Perimeter = 4 × side = 48 ⇒ Side = 12
→ So again, side = 12 (Answerable)Since each statement alone gives the answer,
the correct option is (b)Incorrect
Answer: Option (b)
Explanation:
Statement 1: Area = 144
⇒ Side² = 144 ⇒ Side = √144 = 12
→ So, side length = 12 (Answerable)Statement 2: Perimeter = 4 × side = 48 ⇒ Side = 12
→ So again, side = 12 (Answerable)Since each statement alone gives the answer,
the correct option is (b) -
Question 4 of 5
4. Question
A bag contains 9 black, 11 white, 13 orange, and 15 purple balls.
Consider the following statements:- The smallest number n such that any n balls drawn must include at least one full set of one colour is 46.
- The smallest number m such that any m balls drawn must include at least one ball of each colour is 40.
Which of the above statements is/are correct?
Correct
Answer: (d)
Explanation:
To guarantee at least one full set of a colour (i.e., all balls of some one colour are included), in the worst case you can draw up to one less than each colour without completing any:
8 black + 10 white + 12 orange + 14 purple = 44.
The next draw (45th) must complete one colour.
So the smallest such is 45, not 46.
→ Statement 1 is false.To guarantee at least one ball of each colour, the worst case is to avoid one colour entirely and draw all of the others. To maximize this, avoid the colour with the largest count (purple = 15). You could draw all black, white, and orange:
9 + 11 + 13 = 33 without getting purple.
The next draw (34th) must be purple.
So the smallest such is 34, not 40.
→ Statement 2 is false.Incorrect
Answer: (d)
Explanation:
To guarantee at least one full set of a colour (i.e., all balls of some one colour are included), in the worst case you can draw up to one less than each colour without completing any:
8 black + 10 white + 12 orange + 14 purple = 44.
The next draw (45th) must complete one colour.
So the smallest such is 45, not 46.
→ Statement 1 is false.To guarantee at least one ball of each colour, the worst case is to avoid one colour entirely and draw all of the others. To maximize this, avoid the colour with the largest count (purple = 15). You could draw all black, white, and orange:
9 + 11 + 13 = 33 without getting purple.
The next draw (34th) must be purple.
So the smallest such is 34, not 40.
→ Statement 2 is false. -
Question 5 of 5
5. Question
The stability of natural ecosystems depends on the diversity of species and their ability to adapt to environmental changes. When ecosystems lose variety—through deforestation, pollution, or monoculture farming—they also lose resilience. Climate change intensifies this loss by altering temperature and rainfall patterns, forcing species to migrate or perish. Ironically, many conservation and development strategies focus only on short-term productivity rather than long-term adaptability. Protecting biodiversity is not just about saving species; it is about safeguarding the natural mechanisms that maintain soil fertility, pollination, and pest control. The less diverse an ecosystem becomes, the more vulnerable it is to sudden collapse under environmental stress.
Q70. Which one of the following statements best reflects the central idea conveyed by the passage?
Correct
Answer: (a)
Explanation:
Option (a) is correct: The passage explicitly argues that ecosystem stability depends on diversity and that “the less diverse an ecosystem becomes, the more vulnerable it is to sudden collapse.” This directly links biodiversity loss to reduced resilience and long-term instability.
Option (b) is incorrect: While climate change is mentioned, the passage lists multiple causes—deforestation, pollution, and monoculture farming—so it is not the sole cause of species decline.
Option (c) is incorrect: The author criticises focusing on “short-term productivity rather than long-term adaptability,” making this option contrary to the passage’s message.
Option (d) is incorrect: The passage advocates protecting natural mechanisms, not increased human interference.
Hence, option (a) best captures the central idea.Incorrect
Answer: (a)
Explanation:
Option (a) is correct: The passage explicitly argues that ecosystem stability depends on diversity and that “the less diverse an ecosystem becomes, the more vulnerable it is to sudden collapse.” This directly links biodiversity loss to reduced resilience and long-term instability.
Option (b) is incorrect: While climate change is mentioned, the passage lists multiple causes—deforestation, pollution, and monoculture farming—so it is not the sole cause of species decline.
Option (c) is incorrect: The author criticises focusing on “short-term productivity rather than long-term adaptability,” making this option contrary to the passage’s message.
Option (d) is incorrect: The passage advocates protecting natural mechanisms, not increased human interference.
Hence, option (a) best captures the central idea.
