The question asks to identify the correct statement regarding waste excretion in plants. We need to evaluate each option based on the known physiological processes in plants.
Correct Option: D) In some plants, waste products are stored as resins.
When a set of numbers leaves the same remainder \(y\) when divided by a number \(x\), it means that if we subtract the remainder \(y\) from each number, the resulting numbers will be perfectly divisible by \(x\). In other words, \(x\) is a common factor of \((N_1 - y)\), \((N_2 - y)\), and \((N_3 - y)\). If \(x\) is the greatest such number, then \(x\) is the HCF (Highest Common Factor) of the differences between these numbers. We can find \(x\) by taking the HCF of the differences between the given numbers.
Let the given numbers be \(N_1 = 1833\), \(N_2 = 2482\), and \(N_3 = 3190\).
When these numbers are divided by \(x\), the remainder in each case is \(y\). This means:
\[ 1833 = q_1 x + y \]\[ 2482 = q_2 x + y \]\[ 3190 = q_3 x + y \]Subtracting the remainder \(y\) from each number makes them perfectly divisible by \(x\):
\[ 1833 - y = q_1 x \]\[ 2482 - y = q_2 x \]\[ 3190 - y = q_3 x \]This implies that \(x\) is a common factor of \((1833 - y)\), \((2482 - y)\), and \((3190 - y)\). Since \(x\) is the greatest number, \(x\) is the HCF of these three numbers.
An important property of HCF is that if \(x\) divides \(a\) and \(b\), then \(x\) also divides \((a-b)\). Therefore, \(x\) must divide the differences between these numbers:
\[ (2482 - y) - (1833 - y) = 2482 - 1833 = 649 \]\[ (3190 - y) - (2482 - y) = 3190 - 2482 = 708 \]\[ (3190 - y) - (1833 - y) = 3190 - 1833 = 1357 \]So, \(x\) is the HCF of 649, 708, and 1357.
Let's find the HCF of 649, 708, and 1357. We can use the prime factorization method or Euclidean algorithm.
First, find HCF of 649 and 708:
\[ 708 = 1 \times 649 + 59 \]\[ 649 = 11 \times 59 + 0 \]So, HCF(649, 708) = 59.
Now, find HCF(59, 1357):
\[ 1357 = 23 \times 59 + 0 \]So, HCF(649, 708, 1357) = 59. Therefore, \(x = 59\).
Now we need to find the remainder \(y\). We can divide any of the original numbers by \(x = 59\).
Let's divide 1833 by 59:
\[ 1833 = 59 \times 31 + 4 \]So, the remainder \(y = 4\).
Finally, we need to calculate the value of \((3x - 14y)\):
\[ 3x - 14y = 3(59) - 14(4) \]\[ = 177 - 56 \]\[ = 121 \]Correct Option: C) 121
Seven boxes A, B, C, D, E, F and G are kept one over the other, but not necessarily in the same order. D is kept third from the bottom. Only one box is kept between C and D. Only three boxes are kept between B and F. B is kept at one of the positions above F. A is kept immediately below G. How many boxes are kept between D and E?
The problem involves two parts. First, we need to find the value of \(x\) using the concept of proportion. If four numbers \(a, b, c, d\) are in proportion, then \[\frac{a}{b} = \frac{c}{d}\]. Once \(x\) is found, we use it in the second proportion to find the value of \(y\).
When \(x\) is added to 11, 14, 31, and 38, the new numbers are \((11+x)\), \((14+x)\), \((31+x)\), and \((38+x)\). Since these numbers are in proportion, we can write:
\[ \frac{11+x}{14+x} = \frac{31+x}{38+x} \]Cross-multiplying the equation:
\[ (11+x)(38+x) = (31+x)(14+x) \]\[ 11(38) + 11x + 38x + x^2 = 31(14) + 31x + 14x + x^2 \]\[ 418 + 49x + x^2 = 434 + 45x + x^2 \]Subtract \(x^2\) from both sides:
\[ 418 + 49x = 434 + 45x \]Subtract \(45x\) from both sides:
\[ 49x - 45x = 434 - 418 \]\[ 4x = 16 \]\[ x = \frac{16}{4} \]\[ x = 4 \]The second proportion is given as \(3x : y :: y : (8x - 5)\). This can be written as:
\[ \frac{3x}{y} = \frac{y}{8x - 5} \]Substitute \(x=4\) into the expression:
\[ \frac{3(4)}{y} = \frac{y}{8(4) - 5} \]\[ \frac{12}{y} = \frac{y}{32 - 5} \]\[ \frac{12}{y} = \frac{y}{27} \]Cross-multiplying gives:
\[ y^2 = 12 \times 27 \]\[ y^2 = 324 \]Take the square root of both sides:
\[ y = \sqrt{324} \]\[ y = 18 \]Since the problem states \(y > 0\), we take the positive root.B) The value of \(y\) is 18.
The given series is an alternating series, meaning it consists of two interleaved sub-series. We need to identify the pattern in each sub-series to find the missing term.
Let's write down the given series: 82, 23, 69, 30, 56, 37, 43, 44, 30, ?
Separate the series into two alternating sub-series:
Analyze Sub-series 1 (82, 69, 56, 43, 30):
This sub-series is an arithmetic progression where each term is 13 less than the previous term.
Analyze Sub-series 2 (23, 30, 37, 44, ?):
This sub-series is an arithmetic progression where each term is 7 more than the previous term.
To find the missing term, we need to apply the pattern of Sub-series 2 to its last known term:
The last term in Sub-series 2 is 44. The next term will be \(44 + 7\).
\[ 44 + 7 = 51 \]Therefore, the missing number is 51.
Correct Option: B) 51
Three chairs and two tables cost Rs 7,000 and five chairs and three tables cost Rs 11,000. What is the cost of four chairs and two tables?
This problem can be solved by setting up a system of two linear equations with two variables, representing the cost of a chair and a table. We can then solve these equations simultaneously to find the individual cost of a chair and a table. Finally, we use these values to calculate the cost of four chairs and two tables.
Let \(C\) be the cost of one chair and \(T\) be the cost of one table.
From the first statement, "Three chairs and two tables cost Rs 7,000", we can form the equation:
\[ 3C + 2T = 7000 \quad \text{(Equation 1)} \]From the second statement, "five chairs and three tables cost Rs 11,000", we can form the equation:
\[ 5C + 3T = 11000 \quad \text{(Equation 2)} \]To solve these equations simultaneously, we can use the elimination method. Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of \(T\) equal:
Multiply Equation 1 by 3:
\[ 3 \times (3C + 2T) = 3 \times 7000 \]\[ 9C + 6T = 21000 \quad \text{(Equation 3)} \]Multiply Equation 2 by 2:
\[ 2 \times (5C + 3T) = 2 \times 11000 \]\[ 10C + 6T = 22000 \quad \text{(Equation 4)} \]Subtract Equation 3 from Equation 4:
\[ (10C + 6T) - (9C + 6T) = 22000 - 21000 \]\[ 10C - 9C + 6T - 6T = 1000 \]\[ C = 1000 \]Substitute the value of \(C = 1000\) into Equation 1:
\[ 3(1000) + 2T = 7000 \]\[ 3000 + 2T = 7000 \]\[ 2T = 7000 - 3000 \]\[ 2T = 4000 \]\[ T = \frac{4000}{2} \]\[ T = 2000 \]So, the cost of one chair is Rs 1,000 and the cost of one table is Rs 2,000.
We need to find the cost of four chairs and two tables:
Cost \( = 4C + 2T \)
Cost \( = 4(1000) + 2(2000) \)
Cost \( = 4000 + 4000 \)
Cost \( = 8000 \)
Correct Option: B) 8,000
The question asks to identify a complex mixture of hydrocarbons found on Earth in liquid, gaseous, or solid forms, which can be refined into fuel. We need to evaluate each option based on this description.
Correct Option: B) Petroleum fits all the criteria: it is a complex mixture of hydrocarbons, found in liquid (crude oil), gaseous (natural gas associated with it), and sometimes solid (waxes within crude oil) forms, and is extensively refined into various fuels.
We are given the total power dissipated in a circuit with two identical resistors connected in parallel to a battery. We need to find the current flowing through each resistor. We can use the formula for power, Ohm's law, and the properties of parallel circuits to solve this problem.
Identify given values:
Calculate the total current from the battery:
The total power dissipated in a circuit is given by the formula \(P_{\text{total}} = V \times I_{\text{total}}\), where \(I_{\text{total}}\) is the total current drawn from the battery.
Determine the current in each resistor:
Since the two resistors are identical and connected in parallel, the total current from the battery will split equally between them. Therefore, the current through each resistor will be half of the total current.
D) 1.0 A — As calculated, the total current from the battery is 2 A, and since the two identical resistors are in parallel, this current divides equally, resulting in 1 A through each resistor.
The question asks to identify biodegradable substances from the given options. Biodegradable substances are those that can be decomposed by natural processes, primarily by microorganisms, into simpler, harmless substances.
To find the correct average, we first need to calculate the incorrect sum of observations. Then, we adjust this sum by subtracting the misread value and adding the correct value. Finally, we divide the corrected sum by the total number of observations to get the correct average.
The average of 10 observations is given as 46.
\[ \text{Incorrect Sum} = \text{Number of observations} \times \text{Incorrect Average} \]\[ \text{Incorrect Sum} = 10 \times 46 = 460 \]An observation was misread as 42 in place of 142. This means 42 was included in the sum, but 142 should have been.
To correct the sum, we subtract the misread value and add the correct value:
\[ \text{Correct Sum} = \text{Incorrect Sum} - \text{Misread Value} + \text{Correct Value} \]\[ \text{Correct Sum} = 460 - 42 + 142 \]\[ \text{Correct Sum} = 418 + 142 \]\[ \text{Correct Sum} = 560 \]The number of observations remains the same, which is 10.
\[ \text{Correct Average} = \frac{\text{Correct Sum}}{\text{Number of observations}} \]\[ \text{Correct Average} = \frac{560}{10} \]\[ \text{Correct Average} = 56 \]D) The correct average is 56.