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 question gives the analogy # : GJM :: FIL : % and asks which letter-clusters replace # and %. We need to find a single rule that converts the first cluster of each pair into the second, check it against the options, and confirm that the same rule links FIL to its pair.
Identify the given information:
Test # = XAD with GJM:
Using positions X = 24, A = 1, D = 4 and adding 9 to each (wrapping after Z):
\[ X(24)+9=33-26=7=G \] \[ A(1)+9=10=J \] \[ D(4)+9=13=M \]So, the rule is +9 for each letter.
Apply the rule to FIL:
\[ F(6)+9=15=O \] \[ I(9)+9=18=R \] \[ L(12)+9=21=U \]Therefore, % = ORU.
Correct Option: D) # = XAD, % = ORU — Each letter of the first cluster moves 9 places forward to give the second cluster: XAD → GJM and FIL → ORU. Hence, Option D is the correct answer.
A) # = XAD, % = MRU: This is incorrect because F + 9 gives O, not M.
B) # = XAD, % = ORP: This is incorrect because L + 9 gives U, not P.
C) # = YAD, % = ORU: This is incorrect because Y + 9 gives H, not G, so YAD does not pair with GJM.
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 gives two parallel lines AB and CD cut by the transversal HI at E and F, a point G between the lines with ∠EGF = 65°, and two relations between ∠BEG, ∠DFG and ∠DFE. We need to use the property that the angle at a point between two parallel lines equals the sum of the alternate angles, find ∠BEG and ∠DFE, and then use co-interior angles to find ∠FEG.
Identify the given information:
Use the angle property between parallel lines:
For a point G between two parallel lines, the angle EGF equals the sum of the angles BEG and DFG.
\[ \angle BEG+\angle DFG=65^\circ \]Express ∠BEG in terms of ∠DFG:
\[ \frac{2}{5}\angle BEG=\frac{3}{5}\angle DFG \] \[ \angle BEG=\frac{3}{2}\angle DFG \] \[ \frac{3}{2}\angle DFG+\angle DFG=65^\circ \] \[ \angle DFG=26^\circ,\ \angle BEG=39^\circ \]Find ∠DFE and ∠BEF:
\[ \angle DFE=3\times26^\circ=78^\circ \]Since ∠BEF and ∠DFE are co-interior angles, they add up to 180°.
\[ \angle BEF=180^\circ-78^\circ=102^\circ \]Find ∠FEG:
\[ \angle FEG=\angle BEF-\angle BEG \] \[ =102^\circ-39^\circ=63^\circ \]Correct Option: C) 63° — Using ∠BEG + ∠DFG = 65° with the given ratio gives ∠BEG = 39° and ∠DFG = 26°, so ∠DFE = 78° and ∠BEF = 102°. Therefore, ∠FEG = 102° − 39° = 63°. Hence, Option C is the correct answer.
A) 62°: This is incorrect because the correct value works out to 63°; this value cannot be obtained mathematically from the given data.
B) 52°: This is incorrect because 52° = 2 × 26° uses twice ∠DFG instead of subtracting ∠BEG from ∠BEF.
D) 69°: This is incorrect because the correct value works out to 63°; this value cannot be obtained mathematically from the given data.
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.