(136 ÷ 17) + (17 × 13) – (103 – 85) × (62 + 145) ÷ 23 =?
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
The given expression is:
\[ (136 \div 17) + (17 \times 13) - (103 - 85) \times (62 + 145) \div 23 \]Substitute these values back into the expression:
\[ 8 + 221 - 18 \times 207 \div 23 \]We have \(18 \times 207 \div 23\). First, perform multiplication:
Now, perform division:
Substitute this value back into the expression:
\[ 8 + 221 - 162 \]So, the final result is 67.
Correct Option: B) 67 is the correct answer after applying the BODMAS/PEMDAS rule correctly.
To calculate the units of energy consumed, we need to convert the power of the lamp from watts to kilowatts and then multiply it by the time it is used in hours. One unit of electrical energy is equivalent to one kilowatt-hour (kWh).
Since 1 kW = 1000 W, we divide the power in watts by 1000 to get power in kilowatts.
\[ P_{\text{kW}} = \frac{P_{\text{W}}}{1000} = \frac{120 \text{ W}}{1000} = 0.12 \text{ kW} \]Energy consumed (in units or kWh) is the product of power in kilowatts and time in hours.
\[ \text{Energy} = P_{\text{kW}} \times T_{\text{hours}} \]\[ \text{Energy} = 0.12 \text{ kW} \times 8 \text{ hours} \]\[ \text{Energy} = 0.96 \text{ kWh} \]Since 1 kWh = 1 unit, the energy consumed is 0.96 units.
C) 0.96 unit is the correct answer. The calculation shows that the lamp consumes 0.96 kWh, which is equivalent to 0.96 units of energy in one day.
The question asks for the year in which the Battle of Waterloo was fought. This is a direct factual recall question from world history.
Correct Option: B) 1815 — The Battle of Waterloo, which saw the decisive defeat of Napoleon Bonaparte by the forces of the Seventh Coalition (led by the Duke of Wellington and Gebhard Leberecht von Blücher), was fought on June 18, 1815.
The question asks to identify the item that does not belong to the group formed by the other items. This requires understanding the common characteristic shared by most items and identifying the outlier.
A) D (Cardboard) — Cotton, Wool, and Rayon are all types of fibers used in the textile industry. Cotton is a natural plant fiber, Wool is a natural animal fiber, and Rayon is a regenerated cellulosic fiber (derived from wood pulp). Cardboard, on the other hand, is a thick paper material used for packaging and construction, not typically classified as a textile fiber.
To find the current in a series circuit, first calculate the total equivalent resistance of the resistors connected in series. Then, use Ohm's Law, which states that current is equal to voltage divided by resistance (\(I = V/R\)), to find the total current flowing through the circuit.
Identify the given values:
Calculate the total equivalent resistance (\(R_{eq}\)) for resistors in series: When resistors are connected in series, their total resistance is the sum of individual resistances.
\[ R_{eq} = R_1 + R_2 \] \[ R_{eq} = 10 \, \Omega + 20 \, \Omega \] \[ R_{eq} = 30 \, \Omega \]Apply Ohm's Law to find the current (\(I\)): Ohm's Law is given by \(V = I \times R_{eq}\), which can be rearranged to find the current as \(I = V / R_{eq}\).
\[ I = \frac{V}{R_{eq}} \] \[ I = \frac{6 \, \text{V}}{30 \, \Omega} \] \[ I = 0.2 \, \text{A} \]Therefore, the current in the circuit is \(0.2 \, \text{A}\).
Correct Option: B) 0.2 A
If ‘+’ becomes ‘÷’ and ‘×’ becomes ‘+’ then what will be the value of ((36 + 6) + 6) × 12?
This problem involves substituting given symbol changes into a mathematical expression and then evaluating it using the correct order of operations (BODMAS/PEMDAS).
Correct Option: C) 13
To find the time taken, we need to use the fundamental formula relating distance, speed, and time. First, ensure that all units are consistent. The distance is given in meters, and the speed is in kilometers per hour. We should convert the speed to meters per second to get the time in seconds.
To convert km/hr to m/s, multiply by \(\frac{5}{18}\).
\[ S = 20 \times \frac{5}{18} \text{ m/s} = \frac{100}{18} \text{ m/s} = \frac{50}{9} \text{ m/s} \]The relationship between distance, speed, and time is:
\[ \text{Time} (T) = \frac{\text{Distance} (D)}{\text{Speed} (S)} \]Correct Option: A) 81 sec
A merchant incurred a loss of 5% by selling a book for ₹ 256.5. If he sells it for ₹ 310.5, find his gain percent or loss percent
To solve this problem, we first need to find the Cost Price (CP) of the book using the initial selling price and the loss percentage. Once the CP is known, we can calculate the new profit or loss when the book is sold at the new selling price, and then express it as a percentage.
A) Gain 15% — The calculations show that the merchant makes a gain of 15% when selling the book for ₹ 310.5.
Consider the following statement and assumptions and decide which of the assumptions is implicit from the given statement.
Statement:
The school management has introduced compulsory swimming sessions for children below Class V.
Assumptions:
I. Younger children learn swimming faster.
II. The school wishes to enhance the overall development of children.
Both assumptions I and II are implicit
Neither assumption I nor II is implicit
Only assumption II is implicit
Only assumption I is implicit
The task is to identify which of the given assumptions is implicitly made in the statement. An implicit assumption is something that is not stated directly but must be true for the statement to make sense or be logically valid. We need to evaluate each assumption independently against the statement.
Correct Option: C) Only assumption II is implicit
Which of the following events is celebrated every year on January 9 to mark the contribution of the overseas Indian community in the development of India?
Unnatiya Bharat Divas (UBD)
Overseas Indian Development Day (OIDD)
Akhil Bharatiya Divas (ABD)
Pravasi Bharatiya Divas (PBD)
The question asks to identify the specific event celebrated annually on January 9th that recognizes the contributions of the overseas Indian community to India's development. This is a factual question related to Indian national days and their significance.
D) Pravasi Bharatiya Divas (PBD) — This day is celebrated on January 9th each year to mark the contribution of the overseas Indian community to the development of India. The day commemorates the return of Mahatma Gandhi from South Africa to India in 1915.