The question asks to identify the Five-Year Plan in India where the removal of poverty was the primary objective. This requires knowledge of the objectives and focus areas of different Five-Year Plans.
A) Sixth - The Sixth Five-Year Plan (1980-1985) had "removal of poverty" (Garibi Hatao) and "technological self-reliance" as its foremost objectives. This plan focused on strengthening the infrastructure, agriculture, and industrial sectors to achieve these goals.
To find the marked price, we first need to calculate the selling price using the given cost price and profit percentage. Then, using the selling price and the discount percentage, we can determine the marked price.
The cost price (CP) is ₹480, and the profit is 10%.
\[ \text{Profit} = 10\% \text{ of CP} = 0.10 \times 480 = \text{₹}48 \]\[ \text{Selling Price (SP)} = \text{CP} + \text{Profit} = 480 + 48 = \text{₹}528 \]The shopkeeper sells the shoes at a discount of 34% on the marked price. This means the selling price is 100% - 34% = 66% of the marked price.
\[ \text{SP} = (100\% - \text{Discount}\% ) \times \text{MP} \]\[ 528 = (100\% - 34\%) \times \text{MP} \]\[ 528 = 66\% \times \text{MP} \]\[ 528 = 0.66 \times \text{MP} \]\[ \text{MP} = \frac{528}{0.66} \]\[ \text{MP} = \text{₹}800 \]C) ₹800 is the correct marked price. This is derived by first calculating the selling price from the cost price and profit, and then using the selling price and discount percentage to find the marked price.
This problem involves setting up and solving a system of linear equations based on the given age relationships at two different points in time: 16 years ago and the present. We will use variables to represent the current ages of the father and son and then translate the given conditions into algebraic equations.
Define variables for present ages:
Let the present age of the father be \(F\) years.
Let the present age of the son be \(S\) years.
Formulate equations based on the given conditions:
Condition 1: 16 years ago
16 years ago, the father's age was \(F - 16\).
16 years ago, the son's age was \(S - 16\).
According to the problem, 16 years ago, the father's age was 4 times the age of his son:
\[ F - 16 = 4(S - 16) \]\[ F - 16 = 4S - 64 \]\[ F = 4S - 64 + 16 \]\[ F = 4S - 48 \quad \text{(Equation 1)} \]Condition 2: Present ages
Now, the father is twice as old as his son:
\[ F = 2S \quad \text{(Equation 2)} \]Solve the system of equations:
We have two equations:
1) \(F = 4S - 48\)
2) \(F = 2S\)
Substitute Equation 2 into Equation 1:
\[ 2S = 4S - 48 \]\[ 48 = 4S - 2S \]\[ 48 = 2S \]\[ S = \frac{48}{2} \]\[ S = 24 \]Calculate the father's present age:
Substitute the value of \(S\) back into Equation 2:
\[ F = 2S \]\[ F = 2(24) \]\[ F = 48 \]Find the difference between their present ages:
Difference \( = F - S \)
\[ \text{Difference} = 48 - 24 \]\[ \text{Difference} = 24 \]D) 24 years
If ‘×’ means ‘÷’, ‘÷’ means ‘+’, ‘+’ means ‘−’, and ‘−’ means ‘×’, what will come in place of the question mark (?) in the following equation?
2 − (684 + 228 × 19) × 21 ÷ 4 =?
This problem involves substituting given symbol transformations into a mathematical expression and then evaluating the expression using the BODMAS/PEMDAS rule (Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction).
First, solve the operations inside the parenthesis.
Inside the parenthesis: \(684 - 228 \div 19\)
Perform division first:
\[ 228 \div 19 = 12 \]Now, perform subtraction:
\[ 684 - 12 = 672 \]Substitute this back into the equation:
\[ 2 \times 672 \div 21 + 4 = ? \]Next, perform multiplication and division from left to right.
Perform multiplication:
\[ 2 \times 672 = 1344 \]Now, perform division:
\[ 1344 \div 21 = 64 \]Finally, perform addition:
\[ 64 + 4 = 68 \]Thus, the value of the expression is 68.
B) 68
The given series consists of letter-clusters followed by numbers. We need to identify the pattern in both the letters and the numbers separately to find the next term in the series.
Correct Option: B) MRX 29
The problem presents a proportion involving algebraic expressions. We need to find an expression equivalent to 'z' by using the property of proportions that the product of the means equals the product of the extremes.
The given proportion is \(2xy^2 : 2x^2y :: 2x^2y : z\).
This can be written in fraction form as:
\[ \frac{2xy^2}{2x^2y} = \frac{2x^2y}{z} \]To solve for \(z\), we can cross-multiply:
\[ (2xy^2) \times z = (2x^2y) \times (2x^2y) \]Simplify the right side of the equation:
\[ 2xy^2 \cdot z = 4x^4y^2 \]Now, isolate \(z\) by dividing both sides by \(2xy^2\):
\[ z = \frac{4x^4y^2}{2xy^2} \]Perform the division:
Combine these results to find \(z\):
\[ z = 2x^3 \]A) \(2x^3\) is the correct expression for \(z\), as derived from the proportion.
This question tests the basic understanding of image formation by a concave mirror, specifically when the object is placed at infinity. We need to recall the rules of ray optics for concave mirrors.
Correct Option: D) focus
The question describes the positions of some people sitting in a row facing north and asks for the total number of people. We need to place each named person using the given conditions, keeping in mind that unnamed people may sit in between, and then count the total.
Identify the given information:
Place T, R and Z:
Take T's position as 0. Then R is at −1 (immediate left) and Z is at +2 (second to the right).
Place K:
Only three people sit between K and R, so K is 4 places away from R: at −5 or +3.
If K were at +3, S (third to the left of K) would be at 0, which is T's position. This is not possible.
Therefore, K is at −5.
Place S and V:
S is third to the left of K, so S is at −8.
S is second to the right of V, so V is at −10.
Count the total number of people:
The leftmost person is V (−10) and the rightmost is Z (+2).
\[ \text{Total}=2-(-10)+1 \] \[ =13 \]Final row (left to right): V, _, S, _, _, K, _, _, _, R, T, _, Z.
Therefore, 13 people are seated in the row.
Correct Option: C) 13 — Placing everyone gives the row V, _, S, _, _, K, _, _, _, R, T, _, Z from left to right, which has 13 seats in all. Hence, Option C is the correct answer.
A) 12: This is incorrect because the correct total works out to 13; this value cannot be obtained mathematically from the given conditions.
B) 14: This is incorrect because the correct total works out to 13; this value cannot be obtained mathematically from the given conditions.
D) 11: This is incorrect because the correct total works out to 13; this value cannot be obtained mathematically from the given conditions.
This question tests the understanding of how a concave mirror reflects a parallel beam of light that is not parallel to its principal axis. We need to recall the properties of reflection from a concave mirror, specifically concerning parallel rays.
Correct Option: A) principal focal plane. When a parallel beam of light is incident on a concave mirror and is not parallel to the principal axis, all the rays in that beam converge at a point in the focal plane. This plane is perpendicular to the principal axis and passes through the principal focus. The point of convergence will be on this plane, but not necessarily at the principal focus itself, as the beam is off-axis.
This question asks for the standard unit of electrical resistance. To answer this, we need to recall the fundamental units for various electrical quantities.
Correct Option: C) Ohm — The Ohm is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. It is defined as a volt per ampere (\(V/A\)).