The question asks about a specific appointment in Indian cricket history. To answer this, one needs to recall the key personnel changes in the Indian Women's National Cricket Team's coaching staff around May 2021.
B) Ramesh Powar was appointed as the Head Coach of the Indian Women's National Cricket Team in May 2021. He had previously served in the same role in 2018.
Simplify \(\frac{2.46\times2.46-1.46\times1.46}{2.46-1.46}\), giving your answer as a fraction.
\(\frac{392}{10}\)
\(\frac{392}{10000}\)
\(\frac{392}{1000}\)
\(\frac{392}{100}\)
The problem asks us to simplify a given algebraic expression and present the answer as a fraction. The expression involves squares and differences, which suggests using the algebraic identity \((a^2 - b^2) = (a - b)(a + b)\).
Identify the structure of the numerator. The numerator is \(2.46 \times 2.46 - 1.46 \times 1.46\), which can be written as \((2.46)^2 - (1.46)^2\).
Apply the algebraic identity \(a^2 - b^2 = (a - b)(a + b)\) to the numerator. Let \(a = 2.46\) and \(b = 1.46\).
\[ (2.46)^2 - (1.46)^2 = (2.46 - 1.46)(2.46 + 1.46) \]Substitute this back into the original expression:
\[ \frac{(2.46 - 1.46)(2.46 + 1.46)}{2.46 - 1.46} \]Notice that \((2.46 - 1.46)\) appears in both the numerator and the denominator. Since \(2.46 - 1.46 \neq 0\), we can cancel this term:
\[ 2.46 + 1.46 \]Perform the addition:
\[ 2.46 + 1.46 = 3.92 \]The question asks for the answer as a fraction. Convert the decimal \(3.92\) into a fraction:
\[ 3.92 = \frac{392}{100} \]D) \(\frac{392}{100}\) is the simplified form of the given expression as a fraction.
The question asks to identify the likely pH of a solution that turns blue litmus paper red. This requires knowledge of how litmus paper reacts to acidic, basic, and neutral solutions, and the corresponding pH ranges.
C) 5 — A pH of 5 is less than 7, indicating an acidic solution. Acidic solutions turn blue litmus paper red. Therefore, this is the likely pH of the solution.
The given table shows the production of food grains (in tonnes) in a certain state of India for the period 2016-2020.
| Year |
Food grains
|
||||
| Wheat | Maize | Rice | Pulses | Beans | |
| 2016 | 410 | 680 | 500 | 390 | 280 |
| 2017 | 500 | 700 | 550 | 400 | 250 |
| 2018 | 550 | 500 | 580 | 380 | 300 |
| 2019 | 510 | 750 | 560 | 500 | 260 |
| 2020 | 600 | 800 | 600 | 510 | 300 |
In the year 2018, the total production of rice and beans is approximately what percentage of the total production of rice and beans in the year 2020?
To solve this problem, we need to calculate the total production of rice and beans for the year 2018 and for the year 2020. Then, we will find what percentage the 2018 total production is of the 2020 total production.
Correct Option: A) 97.8%
The problem asks for the location of the principal focus of a concave mirror given its radius of curvature, following the New Cartesian Sign Convention. We need to recall the relationship between the radius of curvature and the focal length of a spherical mirror and apply the sign convention correctly.
C) \(-6 \text{ cm}\) — The focal length of a spherical mirror is half its radius of curvature. For a concave mirror, both the radius of curvature and the focal length are negative according to the New Cartesian Sign Convention because they lie in front of the mirror (to the left of the pole). Thus, \(f = R/2 = (-12 \text{ cm})/2 = -6 \text{ cm}\).
The question asks to identify which right was declared a Fundamental Right by the Supreme Court of India in 2017. This requires knowledge of landmark judgments concerning Fundamental Rights in India.
Correct Option: C) Right to Privacy was declared a Fundamental Right by the Supreme Court of India in 2017 in the landmark Puttaswamy judgment. The Court held that privacy is an intrinsic part of Article 21 (Right to Life and Personal Liberty) and also flows through other fundamental rights.
To find the speed of the train, we need to determine the total distance covered by the train and the time taken. When a train passes through a tunnel, the total distance it covers is the sum of its own length and the length of the tunnel. Once we have the total distance and time, we can calculate the speed and then convert it to the required units (km/h).
B) The calculated speed of the train is 72 km/h, which matches this option.
When two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary, meaning their sum is 180°. We are given that these two angles are in the ratio 2:3. We can use this information to find the individual measures of the angles.
Let the two interior angles on the same side of the transversal be \(2x\) and \(3x\), since their ratio is given as 2:3.
According to the property of parallel lines intersected by a transversal, the sum of interior angles on the same side is 180° (they are supplementary).
\[ 2x + 3x = 180^\circ \]Combine the terms on the left side:
\[ 5x = 180^\circ \]Solve for \(x\):
\[ x = \frac{180^\circ}{5} \]\[ x = 36^\circ \]Now, calculate the measures of the two angles:
First angle \( = 2x = 2 \times 36^\circ = 72^\circ \)
Second angle \( = 3x = 3 \times 36^\circ = 108^\circ \)
The question asks for the greater of the two angles. Comparing \(72^\circ\) and \(108^\circ\), the greater angle is \(108^\circ\).
Correct Option: C) 108°
This question asks about the mechanism of water and mineral ion absorption by plant root cells from the soil. Understanding the principles of active transport, passive transport, diffusion, and osmosis is crucial here.
Correct Option: D) Ions move in first by active transport, followed by water along the concentration gradient
This question asks about the condition under which the primary deficit of the Government of India is zero. To answer this, we need to understand the definitions of fiscal deficit and primary deficit and how they relate to each other.
B) When the fiscal deficit is equal to the interest payment
As derived in the step-by-step explanation, the primary deficit is defined as the fiscal deficit minus interest payments. Therefore, if the primary deficit is zero, it means that the fiscal deficit is exactly equal to the interest payments made by the government on its past borrowings. This indicates that the government is borrowing only to pay off its past interest obligations and not for any new expenditure.