To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets (Parentheses), Orders (Exponents/Powers and Square Roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
The given expression is:
\[ 22 \times (63 \div 7) \div 6 - \{7 \times 5 + 4 - (3 - 5) \div 2\} \]Step 1: Evaluate the innermost brackets.
For the first part: \( (63 \div 7) \)
\[ 63 \div 7 = 9 \]For the second part: \( (3 - 5) \)
\[ 3 - 5 = -2 \]Substitute these values back into the expression:
\[ 22 \times 9 \div 6 - \{7 \times 5 + 4 - (-2) \div 2\} \]Step 2: Evaluate the operations within the curly braces \(\{...\}\).
Inside the curly braces, we have: \( 7 \times 5 + 4 - (-2) \div 2 \)
Perform multiplication and division first, from left to right:
Substitute these back into the expression inside the curly braces:
\[ 35 + 4 - (-1) \]Now perform addition and subtraction from left to right:
So, the expression inside the curly braces evaluates to \( 40 \).
Step 3: Substitute this value back into the main expression.
\[ 22 \times 9 \div 6 - 40 \]Step 4: Perform multiplication and division from left to right in the first part of the expression.
Step 5: Perform the final subtraction.
\[ 33 - 40 = -7 \]Thus, the value of the entire expression is \( -7 \).
D) -7 is the correct answer, as calculated by following the order of operations.
All 35 students of a class are standing in a straight row facing north. Ram is 17th from the right end, while Rakesh is 17th from the left end. Somi is exactly between Ram and Rakesh. What is the position of Somi from the left end?
To find Somi's position from the left end, we first need to determine the positions of Ram and Rakesh from the left end. Then, we can find the number of students between them and use this information to locate Somi, who is exactly in the middle.
C) 18 th
To find the cost of the canvas needed to cover the cuboidal box completely, we first need to calculate the total surface area of the box. Since the dimensions are given in meters and centimeters, we must convert all dimensions to a consistent unit (meters). Then, we can use the formula for the total surface area of a cuboid and multiply it by the cost per square meter of the canvas.
Given dimensions:
Convert height from centimeters to meters:
\[ H = 90 \text{ cm} = \frac{90}{100} \text{ m} = 0.9 \text{ m} \]The formula for the total surface area of a cuboid is:
\[ \text{Total Surface Area} = 2(LB + BH + HL) \]\[ \text{Total Surface Area} = 2((2.5 \text{ m})(2 \text{ m}) + (2 \text{ m})(0.9 \text{ m}) + (0.9 \text{ m})(2.5 \text{ m})) \]\[ \text{Total Surface Area} = 2(5 \text{ m}^2 + 1.8 \text{ m}^2 + 2.25 \text{ m}^2) \]\[ \text{Total Surface Area} = 2(9.05 \text{ m}^2) \]\[ \text{Total Surface Area} = 18.1 \text{ m}^2 \]The cost of the canvas is Rs 80 per \(\text{m}^2\).
Total cost = Total Surface Area \(\times\) Cost per \(\text{m}^2\)
\[ \text{Total Cost} = 18.1 \text{ m}^2 \times \text{Rs } 80/\text{m}^2 \]\[ \text{Total Cost} = \text{Rs } 1448 \]C) 1,448 is the correct option, as calculated by finding the total surface area of the cuboid and multiplying it by the given cost per square meter.
We need to determine the shortest person among the six friends (A, L, V, P, Q, M) based on the given height comparisons. We will establish the relative heights of the friends step-by-step to find the shortest one.
P is taller than only four other friends: This implies that P is the second tallest person. If there are six friends, and P is taller than four, then one person is taller than P. So, the order is: \(\text{Tallest} > \text{P} > \text{Friend}_1 > \text{Friend}_2 > \text{Friend}_3 > \text{Friend}_4\).
V is taller than only one friend: This means V is the second shortest person. So, the order is: \(\text{Tallest} > \text{Friend}_1 > \text{Friend}_2 > \text{Friend}_3 > \text{V} > \text{Shortest}\).
Combining the information from steps 1 and 2, we can place P and V in the sequence:
\(\text{Tallest} > \text{P} > \text{Friend}_1 > \text{Friend}_2 > \text{V} > \text{Shortest}\)
The remaining friends are A, L, Q, and M. We know P is the second tallest and V is the second shortest.
Q is taller than M but shorter than A: This gives us the sequence \(\text{A} > \text{Q} > \text{M}\).
A is not the tallest: Since P is the second tallest, the tallest person is not A. This means A must be one of the two friends between P and V.
Let's use the sequence from step 3: \(\text{Tallest} > \text{P} > \text{Friend}_1 > \text{Friend}_2 > \text{V} > \text{Shortest}\)
From \(\text{A} > \text{Q} > \text{M}\), and knowing A is not the tallest, A, Q, M must fit into the remaining slots. The only possible place for A, Q, M is in the middle or shorter positions.
Since A is not the tallest, A cannot be the first position. P is the second position. So A, Q, M must be among the remaining four positions.
We have \(\text{A} > \text{Q} > \text{M}\). V is the second shortest. So M must be the shortest, as it is shorter than Q, which is shorter than A. If M were not the shortest, then V would be shorter than M, which contradicts V being taller than only one friend.
Let's refine the sequence:
So, \(\text{Tallest} > \text{P} > \text{_} > \text{_} > \text{V} > \text{_}\)
The remaining friends are A, L, Q, M.
We know \(\text{A} > \text{Q} > \text{M}\). A is not the tallest. This means A cannot be the first position. P is the second position. So A must be in the 3rd or 4th position.
If A is in the 3rd position, then Q is in the 4th, and M must be the shortest. This fits perfectly.
So, the order becomes: \(\text{L} > \text{P} > \text{A} > \text{Q} > \text{V} > \text{M}\)
In this arrangement, L is the tallest. P is taller than A, Q, V, M (4 friends). V is taller than M (1 friend). Q is taller than M but shorter than A. A is not the tallest. All conditions are met.
Therefore, M is the shortest among all the friends.
Correct Option: D) M is the shortest among all the friends.
The question asks about the primary deity worshipped during the Hindu festival of Chhath Puja. To answer this, one needs to recall the core traditions and deities associated with this specific festival.
Correct Option: D) Lord Surya is the god worshipped during Chhath Puja. Devotees offer prayers to the setting and rising sun, seeking blessings for prosperity, health, and well-being of their family members.
Which of the following salts is used in black and white photography?
The question asks to identify the salt used in black and white photography. This requires knowledge of the chemical compounds historically and currently employed in photographic processes, particularly those sensitive to light.
D) AgBr — Silver bromide (\(\text{AgBr}\)) is the primary light-sensitive component in traditional black and white photographic emulsions. Its sensitivity to light allows it to capture images, which are then developed to produce photographs.
To solve this problem, we need to compare the original position of each letter in the given word with its position after arranging all the letters alphabetically. We will list the original word, then arrange its letters alphabetically, and finally count how many letters retain their original position.
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Letter | A | B | D | U | C | E | N | T |
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Letter | A | B | C | D | E | N | T | U |
| Position | Original Word | Alphabetical Order | Same Position? |
|---|---|---|---|
| 1 | A | A | Yes |
| 2 | B | B | Yes |
| 3 | D | C | No |
| 4 | U | D | No |
| 5 | C | E | No |
| 6 | E | N | No |
| 7 | N | T | No |
| 8 | T | U | No |
Therefore, 2 letters remain unchanged.
A) 2 is the correct answer because only the letters 'A' and 'B' retain their original positions after the word ABDUCENT is arranged alphabetically.
This is a direction sense problem. We need to track Rishabh's initial direction and subsequent turns to determine his final direction. We will assume standard cardinal directions (North, South, East, West) and that all turns are 90 degrees.
A) Following the sequence of turns, Rishabh is currently walking in the South direction.
This problem involves work and time. We will use the concept of efficiency (work done per day) to solve it. We'll first find the individual efficiencies of A, B, and C, then calculate the work done by them together, and finally determine the time B takes to complete the remaining work.
Calculate the efficiency of A:
Given that A, B, and C together can complete the work in 40 days, their combined one day's work is:
Given that B and C together can complete the work in 60 days, their combined one day's work is:
\[ (B+C)\text{'s 1 day's work} = \frac{1}{60} \]A's one day's work can be found by subtracting (B+C)'s work from (A+B+C)'s work:
\[ A\text{'s 1 day's work} = \frac{1}{40} - \frac{1}{60} = \frac{3-2}{120} = \frac{1}{120} \]So, A can complete the work alone in 120 days.
Calculate the efficiency of B:
We are given that B is 25% more efficient than A. This means B's efficiency is 125% of A's efficiency.
So, B can complete the work alone in 96 days.
Calculate the efficiency of C:
We know that \[(B+C)\text{'s 1 day's work} = \frac{1}{60}\] and \[B\text{'s 1 day's work} = \frac{1}{96}\].
So, C can complete the work alone in 160 days.
Calculate the work done by A, B, and C together in 30 days:
Their combined one day's work is \(\frac{1}{40}\).
Calculate the remaining work:
\[ \text{Remaining work} = 1 - \frac{3}{4} = \frac{1}{4} \]Calculate the time B takes to complete the remaining work:
B's one day's work is \(\frac{1}{96}\).
Correct Option: D) 24 days
This problem involves arranging six friends (P, Q, R, S, T, U) based on their heights using the given comparative statements. We will deduce their relative heights step-by-step to identify the shortest person.
P is taller than only one friend: This means P is the second shortest among the six friends. Let's denote height with '>'. So, we have:
\[ \text{_} > \text{P} > \text{_} \]There are 4 friends taller than P.
S is taller than only three friends: This means S is the fourth tallest, or third shortest. So, there are three friends taller than S and three friends shorter than S.
\[ \text{_} > \text{_} > \text{S} > \text{_} > \text{_} > \text{_} \]Combining the first two points, we can place P and S:
\[ \text{_} > \text{_} > \text{S} > \text{_} > \text{P} > \text{_} \]R is taller than P but shorter than Q: This gives us the relation \( \text{Q} > \text{R} > \text{P} \). Since P is the second shortest, R must be immediately taller than P. This also means Q is taller than R.
\[ \text{_} > \text{_} > \text{S} > \text{Q} > \text{R} > \text{P} > \text{_} \]U is taller than Q: This means \( \text{U} > \text{Q} \). Placing U in the sequence:
\[ \text{U} > \text{_} > \text{S} > \text{Q} > \text{R} > \text{P} > \text{_} \]Now we have five friends placed: U, S, Q, R, P. The only remaining friend is T, and there is one empty spot, which is the shortest position. Therefore, T must be the shortest.
The complete order from tallest to shortest is:
\[ \text{U} > \text{S} > \text{Q} > \text{R} > \text{P} > \text{T} \]From this arrangement, T is the shortest among all the friends.
C) T is the shortest among all the friends, as determined by the step-by-step deduction of their relative heights.