To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will examine the relationship between consecutive terms.
Therefore, the missing number is 50.
Correct Option: D) 50
The question asks about the purpose of the Pradhan Mantri Krishi Sinchayee Yojana (PMKSY). To answer this, one needs to recall the primary objectives and focus areas of this specific government scheme.
Correct Option: D) Agriculture & irrigation — The Pradhan Mantri Krishi Sinchayee Yojana (PMKSY) was launched by the Indian Government with the primary objective of extending the coverage of irrigation and improving water use efficiency in a focused manner. Its motto is 'Har Khet Ko Pani' (More Crop Per Drop), directly linking it to agriculture and irrigation.
To determine how a body's weight changes when moved from the equator to the poles, we need to consider the factors affecting the acceleration due to gravity (\(g\)). These factors include the Earth's rotation (centrifugal force) and its non-spherical shape (oblateness).
Correct Option: D) increases
When a body is taken from the equator to the North or South poles, the acceleration due to gravity (\(g\)) increases. This is because the centrifugal force due to Earth's rotation is zero at the poles and maximum at the equator, and the poles are closer to the Earth's center than the equator. Since weight is directly proportional to \(g\), the body's weight increases.
The question asks about the anatomical connection of the vas deferens before it forms the urethra. This requires knowledge of the male reproductive and urinary systems.
Correct Option: D) urinary bladder — The vas deferens (after forming the ejaculatory duct) joins the urethra, which is the tube that carries urine from the urinary bladder out of the body. Thus, it unites with a tube coming from the urinary bladder to form this common passage.
The fumes of NO2 are ________ in colour.
The question asks about the characteristic color of nitrogen dioxide (NO₂) fumes. This is a direct recall question from basic chemistry knowledge regarding common gases and their properties.
B) brown. Nitrogen dioxide (NO₂) gas is distinctly brown in color. This is a fundamental property taught in chemistry.
This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the statements to determine how Lata and Aditya are related. We can draw a family tree or list the relationships step-by-step.
C) cousins — Lata is the daughter of Avani, who is the sister of Dinesh. Dinesh is the father of Aditya. Thus, Avani is Aditya's aunt, and Lata is Aditya's cousin.
Pb + CuCl2 → PbCl2 + Cu. The given reaction is an example of a ________ reaction.
decomposition
double displacement
combination
displacement
To identify the type of reaction, we need to analyze how the reactants transform into products. We will look for patterns such as combination, decomposition, displacement, or double displacement.
Correct Option: D) displacement
This problem involves calculating work rates of pipes. We'll determine the individual filling rates of pipes X and Y, and the combined filling/emptying rate when all three pipes (X, Y, and Z) are open. From these, we can find the emptying rate of pipe Z and then the time it takes for Z to empty the full tank.
Pipe X can fill the tank in 60 minutes. So, in 1 minute, pipe X fills:
\[ \text{Rate}_X = \frac{1}{60} \text{ of the tank} \]Pipe Y can fill the tank in 75 minutes. So, in 1 minute, pipe Y fills:
\[ \text{Rate}_Y = \frac{1}{75} \text{ of the tank} \]When all three pipes are used, the tank is full in 50 minutes. Since Z is an outlet pipe, its rate will be subtracted from the filling rates of X and Y. Let \(\text{Rate}_Z\) be the emptying rate of Z.
The combined rate is:
\[ \text{Rate}_{X+Y-Z} = \frac{1}{50} \text{ of the tank} \]The combined rate of filling pipes X and Y minus the emptying rate of pipe Z equals the overall combined rate:
\[ \text{Rate}_X + \text{Rate}_Y - \text{Rate}_Z = \text{Rate}_{X+Y-Z} \]\[ \frac{1}{60} + \frac{1}{75} - \text{Rate}_Z = \frac{1}{50} \]First, find a common denominator for 60 and 75. The least common multiple (LCM) of 60 and 75 is 300.
\[ \frac{5}{300} + \frac{4}{300} - \text{Rate}_Z = \frac{1}{50} \]\[ \frac{9}{300} - \text{Rate}_Z = \frac{1}{50} \]\[ \frac{3}{100} - \text{Rate}_Z = \frac{1}{50} \]\[ \text{Rate}_Z = \frac{3}{100} - \frac{1}{50} \]\[ \text{Rate}_Z = \frac{3}{100} - \frac{2}{100} \]\[ \text{Rate}_Z = \frac{1}{100} \text{ of the tank per minute} \]If pipe Z empties \(\frac{1}{100}\) of the tank in 1 minute, then it will empty the full tank (1 whole tank) in:
\[ \text{Time}_Z = \frac{1}{\text{Rate}_Z} = \frac{1}{\frac{1}{100}} = 100 \text{ minutes} \]B) 100 minutes
How many isomers does C6H14 have?
To determine the number of isomers for a given alkane, we need to systematically draw all possible structural arrangements (constitutional isomers) of the carbon skeleton, ensuring that no two structures are identical. The formula C₆H₁₄ corresponds to an alkane (C₆H₂₆₂ = C₆H₁₄), which means it will only contain single bonds and no rings.
Hexane (n-hexane): CH₃-CH₂-CH₂-CH₂-CH₂-CH₃
The five unique isomers are:
There are no other possible arrangements for C₆H₁₄.
Correct Option: D) 5
The question asks to identify the winner of the 2017-18 Ranji Trophy tournament. This requires knowledge of past winners of this specific Indian domestic cricket competition.
D) Vidarbha — Vidarbha won the 2017-18 Ranji Trophy by defeating Delhi in the final. This was their first-ever Ranji Trophy title.