This problem can be solved by setting up a system of two linear equations based on the given information: the sum of two numbers and their difference. We can then solve these equations simultaneously to find the values of the two numbers.
A) 32, 13 — As calculated, the two numbers are 32 and 13.
Refer to the following letter series and answer the question.
JFVIEJEM VEFOJVEJJV MEX
How many such consonants are there each of which is immediately preceded by a vowel and also immediately followed by a vowel?
To solve this problem, we need to identify all consonants in the given letter series that satisfy two conditions simultaneously: they must be immediately preceded by a vowel and immediately followed by a vowel. We will first list all vowels and consonants, then scan the series for the pattern "Vowel - Consonant - Vowel".
Correct Option: D) Two
The question asks about the number of languages included in the Indo-Aryan language family according to the 2001 census data on Scheduled and Non-Scheduled Languages. This requires specific knowledge of linguistic classifications based on official Indian census reports.
Correct Option: C) 21
The question asks to identify the type of water currents that flow from lower latitudes (tropical zones) to higher latitudes (temperate and sub-polar zones). This involves understanding the basic classification and characteristics of ocean currents based on their temperature relative to the surrounding water.
A) warm currents — Warm currents originate in tropical or subtropical regions and flow towards higher latitudes. They are warmer than the surrounding ocean water and tend to bring milder temperatures to coastal areas they affect.
To determine the nature and height of the image formed by a concave mirror, we will use the mirror formula and the magnification formula. The mirror formula relates the object distance, image distance, and focal length, while the magnification formula relates the image height, object height, image distance, and object distance.
Identify the given values:
Calculate the image distance (\(v\)) using the mirror formula:
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]Substitute the known values:
\[ \frac{1}{-16} = \frac{1}{v} + \frac{1}{-24} \]\[ -\frac{1}{16} = \frac{1}{v} - \frac{1}{24} \]\[ \frac{1}{v} = -\frac{1}{16} + \frac{1}{24} \]Find a common denominator (48):
\[ \frac{1}{v} = \frac{-3}{48} + \frac{2}{48} \]\[ \frac{1}{v} = \frac{-1}{48} \]\[ v = -48 \, \text{cm} \]The negative sign for \(v\) indicates that the image is formed on the same side as the object, which means it is a real image. Real images formed by mirrors are always inverted.
Calculate the magnification (\(m\)) and image height (\(h_i\)) using the magnification formula:
The magnification formula is given by:
\[ m = \frac{h_i}{h_o} = -\frac{v}{u} \]Substitute the values of \(u\) and \(v\):
\[ m = -\frac{(-48 \, \text{cm})}{(-24 \, \text{cm})} \]\[ m = -\frac{48}{24} \]\[ m = -2 \]Now, use the magnification to find the image height:
\[ \frac{h_i}{h_o} = m \]\[ \frac{h_i}{1.0 \, \text{cm}} = -2 \]\[ h_i = -2 \times 1.0 \, \text{cm} \]\[ h_i = -2.0 \, \text{cm} \]The negative sign for \(h_i\) indicates that the image is inverted. The height of the image is \(2.0 \, \text{cm}\).
Conclusion:
The image formed is inverted and its height is 2.0 cm.
D) inverted, 2.0 cm
The question asks for the full form of 'STI' in the context of the 'Tech NEEV @ 75' initiative and the establishment of STI Hubs for Scheduled Tribes. This requires knowledge of common acronyms used in government initiatives related to science and technology.
B) Science, Technology and Innovation
This is the universally accepted full form of STI in the context of government policies, research, and development initiatives, especially those aimed at fostering growth and empowerment through scientific and technological advancements and innovative solutions.
If α and β are the roots of the equation 6x2+x−15 = 0, where α > β, then the value of (α – β) is:
\( \frac{20}{3} \)
\( \frac{19}{6} \)
\( \frac{1}{6} \)
\( \frac{1}{3} \)
We are given a quadratic equation and its roots \(\alpha\) and \(\beta\), with the condition \(\alpha > \beta\). We need to find the value of \((\alpha - \beta)\). We can solve this by either finding the roots of the quadratic equation directly or by using the relationships between the roots and coefficients of a quadratic equation.
B) \(\frac{19}{6}\) is the correct value for \((\alpha - \beta)\).
The question asks about the month in which the Baisakhi festival is celebrated in India. This requires knowledge of Indian festivals and their traditional calendar timings.
Correct Option: C) April is the month in which the Baisakhi festival is celebrated in India.
A 280 m long train overtakes a man moving at a speed of 8 km/h (in same direction) in 16 seconds. How much time (in seconds) will it take this train to completely cross another 380 m long train, moving in the opposite direction at a speed of 37 km/h?
This problem involves relative speed concepts. First, we'll use the information about the train overtaking a man to find the speed of the train. Then, we'll use this train's speed along with the second train's speed and lengths to calculate the time taken for them to cross each other when moving in opposite directions.
Convert speeds to m/s:
Speed of man \( = 8 \, \text{km/h} \)
\[ 8 \, \text{km/h} = 8 \times \frac{5}{18} \, \text{m/s} = \frac{40}{18} \, \text{m/s} = \frac{20}{9} \, \text{m/s} \]Calculate the relative speed of the train with respect to the man:
Since the train overtakes the man moving in the same direction, the relative speed is the difference between their speeds.
Let the speed of the train be \( S_T \, \text{m/s} \).
Relative speed \( = (S_T - \frac{20}{9}) \, \text{m/s} \)
Use the first scenario to find the train's speed:
The train is 280 m long and overtakes the man in 16 seconds.
Distance covered by the train to overtake the man is its own length.
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]\[ 280 = \left(S_T - \frac{20}{9}\right) \times 16 \]\[ S_T - \frac{20}{9} = \frac{280}{16} \]\[ S_T - \frac{20}{9} = \frac{35}{2} \]\[ S_T = \frac{35}{2} + \frac{20}{9} \]\[ S_T = \frac{315 + 40}{18} = \frac{355}{18} \, \text{m/s} \]Convert the speed of the second train to m/s:
Speed of the second train \( = 37 \, \text{km/h} \)
\[ 37 \, \text{km/h} = 37 \times \frac{5}{18} \, \text{m/s} = \frac{185}{18} \, \text{m/s} \]Calculate the relative speed of the two trains:
The trains are moving in opposite directions, so their relative speed is the sum of their speeds.
Relative speed \[= \frac{355}{18} + \frac{185}{18} = \frac{355 + 185}{18} = \frac{540}{18} = 30 \, \text{m/s}\]
Calculate the total distance to be covered:
The first train is 280 m long and the second train is 380 m long.
Total distance \( = 280 + 380 = 660 \, \text{m} \)
Calculate the time taken for the trains to cross each other:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} \]\[ \text{Time} = \frac{660}{30} = 22 \, \text{seconds} \]Correct Option: C) 22
This is a direction sense problem. We need to visualize the relative positions of the poles based on the given statements and then determine the final position of pole R with respect to pole B.
C) North-east. Based on the step-by-step analysis, pole R is located to the north-east of pole B.