Seven boxes M, N, O, P, Q, R and S are kept one over the other, but not necessarily in the same order. Only three boxes are kept above P. Only two boxes are kept between P and M. Only R is kept between S and Q. Only N is kept between O and M. Neither Q nor M is at the topmost position. Which box is kept between Q and O?
This is a box-stacking puzzle. We need to deduce the arrangement of seven boxes (M, N, O, P, Q, R, S) based on the given clues. We will build the arrangement step-by-step, considering all possibilities and eliminating them as new clues are introduced.
Clue 1: Only three boxes are kept above P.
This means P is at the 4th position from the top (or 4th from the bottom, if counting from the bottom up).
_ _ _ P _ _ _
Clue 2: Only two boxes are kept between P and M.
Since P is at position 4, M can be either above P or below P.
Case 1: M is above P.
_ M _ P _ _ _ (This would mean M is at position 2).
Case 2: M is below P.
_ _ _ P _ M _ (This would mean M is at position 7).
Clue 3: Neither Q nor M is at the topmost position.
This eliminates Case 1 where M would be at position 2, as there is one box above M. If M is at position 2, then position 1 is the topmost. This clue means M cannot be at position 1. This clue is consistent with both cases so far.
Let's re-evaluate Clue 3 with the full stack of 7 boxes. The positions are 1, 2, 3, 4, 5, 6, 7 from top to bottom.
From Clue 1: P is at position 4.
Position 1
Position 2
Position 3
Position 4: P
Position 5
Position 6
Position 7
From Clue 2: Two boxes between P and M.
If M is above P: M must be at position 1. (1-M, 2-?, 3-?, 4-P). This contradicts Clue 3 (M is not at the topmost position). So, M cannot be above P.
Therefore, M must be below P.
Position 1
Position 2
Position 3
Position 4: P
Position 5: ?
Position 6: ?
Position 7: M
Clue 4: Only N is kept between O and M.
Since M is at position 7, N must be at position 6 and O at position 5.
Position 1
Position 2
Position 3
Position 4: P
Position 5: O
Position 6: N
Position 7: M
Clue 5: Only R is kept between S and Q.
The remaining positions are 1, 2, and 3. The remaining boxes are S, Q, and R. Since R is between S and Q, these three boxes must occupy positions 1, 2, and 3 in the order S/Q, R, Q/S.
Position 1: S or Q
Position 2: R
Position 3: Q or S
Position 4: P
Position 5: O
Position 6: N
Position 7: M
Clue 6: Neither Q nor M is at the topmost position.
We already used the part about M. Now, Q cannot be at the topmost position (Position 1).
Therefore, S must be at Position 1, R at Position 2, and Q at Position 3.
The final arrangement from top to bottom is:
Position 1: S
Position 2: R
Position 3: Q
Position 4: P
Position 5: O
Position 6: N
Position 7: M
The question asks: Which box is kept between Q and O?
From our final arrangement, Q is at Position 3 and O is at Position 5. The box between them is at Position 4, which is P.
B) P — As per the final arrangement, P is at position 4, which is between Q (position 3) and O (position 5).
Each of the digits in the number 56137428 is arranged in ascending order from left to right. The position of how many digits will remain unchanged as compared to that in the original number?
To solve this problem, we need to compare the positions of digits in the original number with their positions after the digits are rearranged in ascending order. We will list the original number and its digits' positions, then rearrange the digits and list their new positions, and finally count how many digits retain their original position.
The given number is 56137428.
Let's list the digits with their corresponding positions:
The digits in the number 56137428 are {5, 6, 1, 3, 7, 4, 2, 8}.
Arranging these digits in ascending order gives: {1, 2, 3, 4, 5, 6, 7, 8}.
After arranging the digits in ascending order, the new number formed is 12345678.
Let's list the digits with their new corresponding positions:
Now, we compare the original positions with the new positions:
| Position | Original Digit | New Digit | Position Unchanged? |
|---|---|---|---|
| 1 | 5 | 1 | No |
| 2 | 6 | 2 | No |
| 3 | 1 | 3 | No |
| 4 | 3 | 4 | No |
| 5 | 7 | 5 | No |
| 6 | 4 | 6 | No |
| 7 | 2 | 7 | No |
| 8 | 8 | 8 | Yes |
Only the digit '8' remains in its original position (Position 8).
Therefore, only one digit's position remains unchanged.
Correct Option: A) One
The question asks for the raw material used to produce washing soda. Washing soda is chemically known as sodium carbonate (\(\text{Na}_2\text{CO}_3\)). The primary industrial method for its production is the Solvay process, which relies on specific raw materials.
D) NaCl is the primary raw material (brine) used in the Solvay process to produce washing soda (\(\text{Na}_2\text{CO}_3\)).
The question asks about the composition of adult human urine. To answer this, we need to recall the primary components and their approximate percentages in urine.
D) 95% water, 2.5% urea and 2.5% other waste products
This option accurately reflects the typical composition of adult human urine: approximately 95% water, about 2.5% urea (the primary nitrogenous waste), and 2.5% other dissolved waste products including salts, uric acid, creatinine, and trace amounts of ammonia.
To solve this problem, we first need to arrange the given numbers in descending order. Then, we identify the number that is fifth from the right and the number that is fourth from the left in this new arrangement. Finally, we calculate the absolute difference between these two identified numbers.
The numbers are: 202, 323, 266, 182, 315, 285, 193, 217, 231, 186.
Descending order means arranging from the largest to the smallest.
323, 315, 285, 266, 231, 217, 202, 193, 186, 182.
Counting from the right end of the descending sequence:
1st from right: 182
2nd from right: 186
3rd from right: 193
4th from right: 202
5th from right: 217
So, the number fifth from the right is 217.
Counting from the left end of the descending sequence:
1st from left: 323
2nd from left: 315
3rd from left: 285
4th from left: 266
So, the number fourth from the left is 266.
The difference between the number fourth from the left (266) and the number fifth from the right (217) is:
\[ 266 - 217 = 49 \]Correct Option: B) 49
To identify the type of reaction, we need to analyze the reactants and products, specifically looking at how atoms or ions are exchanged and if a new phase (like a solid precipitate) is formed.
Analyze the reactants: We have sodium carbonate (\(\text{Na}_2\text{CO}_3\)) and calcium chloride (\(\text{CaCl}_2\)). Both are in aqueous solution (\(\text{aq}\)), meaning they are dissolved in water and exist as ions: \(\text{Na}^+\), \(\text{CO}_3^{2-}\), \(\text{Ca}^{2+}\), and \(\text{Cl}^-\) ions.
Analyze the products: We have calcium carbonate (\(\text{CaCO}_3\)) which is a solid (\(\text{s}\)), and sodium chloride (\(\text{NaCl}\)) which is in aqueous solution (\(\text{aq}\)).
Identify ion exchange: In the reaction, the positive ion (\(\text{Na}^+\)) from sodium carbonate combines with the negative ion (\(\text{Cl}^-\) from calcium chloride, forming sodium chloride. Simultaneously, the positive ion (\(\text{Ca}^{2+}\)) from calcium chloride combines with the negative ion (\(\text{CO}_3^{2-}\)) from sodium carbonate, forming calcium carbonate. This exchange of ions between two compounds is characteristic of a double displacement reaction.
Identify precipitate formation: One of the products, calcium carbonate (\(\text{CaCO}_3\)), is formed as a solid (precipitate) from the aqueous solutions of the reactants. This indicates that it is also a precipitation reaction.
Conclusion: Since there is an exchange of ions between two compounds and the formation of an insoluble solid (precipitate), the reaction is both a double displacement reaction and a precipitation reaction.
C) Double displacement and precipitation reaction. This accurately describes the given reaction where ions are exchanged between two compounds, leading to the formation of an insoluble solid (precipitate).
A) Only displacement reaction — A displacement (or single displacement) reaction involves one element displacing another element from a compound. For example, \(\text{A} + \text{BC} \rightarrow \text{AC} + \text{B}\). The given reaction involves two compounds exchanging ions, not a single element displacing another.
B) Combination and decomposition reaction — A combination reaction involves two or more reactants forming a single product (\(\text{A} + \text{B} \rightarrow \text{AB}\)). A decomposition reaction involves a single reactant breaking down into two or more products (\(\text{AB} \rightarrow \text{A} + \text{B}\)). The given reaction has two reactants forming two products, so it is neither a combination nor a decomposition reaction.
D) Displacement and combination reaction — As explained above, the reaction is not a displacement reaction or a combination reaction.
The problem asks us to identify a triad of letter pairs that follows the same pattern as two given triads. We need to analyze the positional values of the letters in the English alphabet for each pair and find the common rule.
Correct Option: D) US – QO – MK
What is the sum of 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xy + 5x – 2xy?
5x – 4y + 2xy + 9yz + 6zx
5x – 4y – 2xy + 9yz + 6zx
5x – 4y + 6xy + 9yz + 6zx
5x – 4y + 6xy + 9yz – 6zx
To find the sum of the given algebraic expressions, we need to combine like terms. Like terms are terms that have the same variables raised to the same powers. We will group these terms together and then perform the addition or subtraction as indicated by their coefficients.
Correct Option: A) \(5x - 4y + 2xy + 9yz + 6zx\)
This question asks about the trophic level of small carnivores or secondary consumers. To answer this, we need to understand the concept of trophic levels in an ecosystem and how organisms are classified within them based on their feeding relationships.
A) third trophic — Small carnivores are organisms that feed on primary consumers (herbivores). In an ecological food chain, producers (like plants) form the first trophic level. Primary consumers (herbivores) form the second trophic level. Secondary consumers (carnivores that eat herbivores) form the third trophic level. Therefore, small carnivores, being secondary consumers, are at the third trophic level.
The problem asks for the power of a convex lens given its focal length. We need to recall the formula relating power and focal length, paying attention to units and the sign convention for convex lenses.
A) +5.0 D is the correct answer. The power of a convex lens is positive, and when the focal length of 20 cm (0.2 m) is used in the power formula \(P = 1/f\), it yields +5.0 D.