The question asks about the location of the principal focus in a convex mirror. To answer this, we need to recall the properties of convex mirrors, specifically how parallel rays of light behave upon reflection from their surface.
Correct Option: B) behind the mirror
The problem asks us to identify the odd one out among four given letter clusters based on their positions in the English alphabetical order. We need to find a pattern or rule that applies to three of the clusters and not to the fourth.
C) DGF is the odd one out because the difference between its first and second letters is +3, while for the other options, it is +4.
The average price of three items of furniture is Rs 15,765. If their prices are in the ratio 3:5:7, the price of the costliest item (in Rs) is
To find the price of the costliest item, we first need to determine the total price of the three items using their average price. Then, we can use the given ratio of their prices to find the individual prices and identify the costliest one.
The average price of three items is given as Rs 15,765.
\[ \text{Total Price} = \text{Average Price} \times \text{Number of Items} \]\[ \text{Total Price} = 15,765 \times 3 \]\[ \text{Total Price} = 47,295 \text{ Rs} \]The prices of the three items are in the ratio 3:5:7. Let the prices be \(3x\), \(5x\), and \(7x\) respectively.
The sum of the individual prices must equal the total price.
\[ 3x + 5x + 7x = 47,295 \]\[ 15x = 47,295 \]\[ x = \frac{47,295}{15} \]\[ x = 3,153 \]The costliest item corresponds to the largest part of the ratio, which is \(7x\).
\[ \text{Price of Costliest Item} = 7x \]\[ \text{Price of Costliest Item} = 7 \times 3,153 \]\[ \text{Price of Costliest Item} = 22,071 \text{ Rs} \]A) 22,071 — This is the price calculated for the item corresponding to the ratio 7, which is the costliest.
To find the missing number in the series, we need to identify the pattern or the rule governing the sequence of numbers. This often involves looking at the differences between consecutive terms.
C) 128 is the correct answer because it follows the established pattern of increasing differences by 2.
A man sold an article for ₹687 by first giving a d% discount on its marked price, and then another discount having the same nominal value (in ₹). If the marked price of the article is ₹1,145, then what is the value of d?
The problem involves calculating a discount percentage when two successive discounts are applied. One discount is a percentage (\(d\%\)) and the other is a fixed amount (same nominal value as the first discount's amount). We need to work backward from the selling price to find the value of \(d\).
Price after first discount \(= \text{MP} - D_1\).
We know that \(D_1 = \frac{d}{100} \times \text{MP}\).
So, Price after first discount \[= \text{MP} - \frac{d}{100} \times \text{MP} = \text{MP} \left(1 - \frac{d}{100}\right)\].
The second discount is \(D_1\). This discount is applied to the price after the first discount.
Selling Price (SP) \(= (\text{Price after first discount}) - D_1\).
Substituting the expressions:
\[ \text{SP} = \text{MP} \left(1 - \frac{d}{100}\right) - \frac{d}{100} \times \text{MP} \]Substitute MP = 1145 and SP = 687 into the equation:
\[ 687 = 1145 \left(1 - \frac{d}{100}\right) - \frac{d}{100} \times 1145 \]Let \(x = \frac{d}{100}\). The equation becomes:
\[ 687 = 1145 (1 - x) - 1145x \] \[ 687 = 1145 - 1145x - 1145x \] \[ 687 = 1145 - 2 \times 1145x \] \[ 2 \times 1145x = 1145 - 687 \] \[ 2290x = 458 \] \[ x = \frac{458}{2290} \] \[ x = \frac{1}{5} \]Since \(x = \frac{d}{100}\), we have:
\[ \frac{d}{100} = \frac{1}{5} \] \[ d = \frac{100}{5} \] \[ d = 20 \]C) 20
This question asks about the chemical reaction that occurs when Plaster of Paris is mixed with water. Understanding the chemical composition of Plaster of Paris and its reaction with water is key to answering this question.
Correct Option: C) It changes to gypsum.
AB and CD are parallel straight lines and HI is the transversal intersecting AB at E and CD at F. G is a point between the lines AB and CD but not on HI, such that m∠EGF = 65°. If \( \frac{2}{5} \) × m∠BEG = \( \frac{3}{5} \) × m∠DFG, and m∠DFG = \( \frac{1}{3} \) × m∠DFE, what is the measure of ∠FEG?
The question asks to identify the first President of the Indian National Congress (INC). This requires knowledge of the INC's foundational history and its early leadership.
C) Womesh Chandra Banerjee was indeed the first President of the Indian National Congress. He presided over the first session held in Bombay in 1885.
The question asks to identify the correct statements regarding the Arunachal Himalaya. We need to evaluate each statement based on geographical facts about the Himalayan ranges, specifically the eastern part.
Based on the evaluation, statements 1, 2, and 4 are correct, while statement 3 is incorrect.
Correct Option: A) Statements 1, 2 and 4 are correct.