The question asks to identify the lead actor in the 2017 Bollywood movie 'Toilet - Ek Prem Katha'. This requires general knowledge about popular Indian cinema and the actors involved in prominent films.
Correct Option: B) Akshay Kumar played the lead role of Keshav in the movie 'Toilet - Ek Prem Katha'. The film addressed the issue of open defecation and promoted sanitation in rural India.
This is a direction sense problem. We need to trace Pavani's path by considering her initial direction and subsequent turns. Visualizing the directions (North, South, East, West) and how turns affect them is key.
C) North. As determined in the step-by-step analysis, after turning left from facing East, Pavani will be walking towards the North direction.
The problem asks us to find the electric charge given the work done and the potential difference. We can use the fundamental relationship between work done, potential difference, and electric charge.
Correct Option: C) 3 Coulomb
The question asks to identify the sport associated with PN Prakash. This requires general knowledge about prominent Indian sports personalities.
A) Shooting: PN Prakash is an accomplished Indian pistol shooter. He has won several medals for India in shooting events, including at the Commonwealth Games and other international competitions. Therefore, he is related to shooting.
The question asks to identify the novel for which David Grossman won the Man Booker International Prize in 2017. This requires knowledge of literary awards and the specific works associated with them.
David Grossman, an Israeli author, won the Man Booker International Prize in 2017 for his novel A Horse Walks Into a Bar. The prize recognizes the best work of translated fiction from around the world.
C) A Horse Walks Into a Bar — David Grossman won the Man Booker International Prize 2017 for his novel A Horse Walks Into a Bar. The novel was translated from Hebrew by Jessica Cohen.
Solve the following equation to find x:
\(\frac{x-5}{3}-\frac{x-2}{4}=\frac{7}{2}\)
To solve the given linear equation, we need to find a common denominator for the fractions on the left side, combine them, and then isolate the variable \(x\).
\[ \frac{x-5}{3} - \frac{x-2}{4} = \frac{7}{2} \]
The denominators are 3 and 4. The LCM of 3 and 4 is 12.
Multiply the first fraction by \(\frac{4}{4}\) and the second fraction by \(\frac{3}{3}\):
\[ \frac{4(x-5)}{12} - \frac{3(x-2)}{12} = \frac{7}{2} \]
\[ \frac{4(x-5) - 3(x-2)}{12} = \frac{7}{2} \]
\[ \frac{4x - 20 - 3x + 6}{12} = \frac{7}{2} \]
\[ \frac{x - 14}{12} = \frac{7}{2} \]
\[ 12 \times \frac{x - 14}{12} = 12 \times \frac{7}{2} \]
\[ x - 14 = 6 \times 7 \]
\[ x - 14 = 42 \]
\[ x = 42 + 14 \]
\[ x = 56 \]
D) The calculated value of \(x\) is 56, which matches option D.
A tank has two inlets which can fill it in 4 hours and 6 hours, respectively. An outlet can empty the full tank in 8 hours. Both inlet taps are opened for an hour and closed. Then the three pipes are opened together.
The remaining part of the tank fills in:
5\( \frac{1}{3} \) hours
2 hours
3\( \frac{1}{4} \) hours
3 hours
This problem involves calculating the work done by pipes (filling and emptying) over time. We will determine the individual filling/emptying rates, calculate the amount of tank filled in the initial phase, find the remaining capacity, and then calculate the time required to fill the remaining part with all pipes working simultaneously.
The first inlet fills the tank in 4 hours.
\[ \text{Rate of Inlet 1} = \frac{1}{4} \text{ tank/hour} \]The second inlet fills the tank in 6 hours.
\[ \text{Rate of Inlet 2} = \frac{1}{6} \text{ tank/hour} \]The outlet empties the tank in 8 hours.
\[ \text{Rate of Outlet} = \frac{1}{8} \text{ tank/hour} \]Both inlet taps are opened for an hour.
\[ \text{Amount filled in 1 hour} = \left( \frac{1}{4} + \frac{1}{6} \right) \times 1 \text{ hour} \]\[ = \left( \frac{3+2}{12} \right) = \frac{5}{12} \text{ of the tank} \]The total capacity is 1. So, the remaining part is:
\[ \text{Remaining part} = 1 - \frac{5}{12} = \frac{12-5}{12} = \frac{7}{12} \text{ of the tank} \]When both inlets and the outlet are open, the net filling rate is:
\[ \text{Combined rate} = \text{Rate of Inlet 1} + \text{Rate of Inlet 2} - \text{Rate of Outlet} \]\[ = \frac{1}{4} + \frac{1}{6} - \frac{1}{8} \]\[ = \frac{6+4-3}{24} = \frac{7}{24} \text{ tank/hour} \]Time = Remaining part / Combined rate
\[ \text{Time} = \frac{\frac{7}{12}}{\frac{7}{24}} = \frac{7}{12} \times \frac{24}{7} = 2 \text{ hours} \]Correct Option: B) 2 hours
This problem involves trigonometry, specifically using angles of elevation and depression to find unknown heights and distances. We will use the tangent function in right-angled triangles formed by the house, chimney, and the river width.
Let the height of the house be \(H = 15 \text{ m}\). Let the height of the chimney be \(h\). Let the width of the river be \(x\).
From the angle of depression: The angle of depression from the roof of the house to the base of the chimney is \(30^\circ\). Consider the right-angled triangle formed by the roof of the house, the base of the chimney, and the point directly below the roof on the same bank as the chimney. In this triangle:
\[ \tan(30^\circ) = \frac{\text{Height of house}}{\text{Width of river}} = \frac{H}{x} \] \[ \frac{1}{\sqrt{3}} = \frac{15}{x} \] \[ x = 15\sqrt{3} \text{ m} \]To find the approximate value of \(x\):
\[ x \approx 15 \times 1.732 \approx 25.98 \text{ m} \]So, the width of the river is approximately \(26 \text{ m}\).
From the angle of elevation: The angle of elevation from the base of the house to the top of the chimney is \(60^\circ\). Consider the right-angled triangle formed by the base of the house, the top of the chimney, and the point directly below the top of the chimney on the same bank as the house. In this triangle:
\[ \tan(60^\circ) = \frac{\text{Height of chimney}}{\text{Width of river}} = \frac{h}{x} \] \[ \sqrt{3} = \frac{h}{x} \] \[ h = x\sqrt{3} \]Substitute the value of \(x\) from step 2 into the equation for \(h\):
\[ h = (15\sqrt{3}) \times \sqrt{3} \] \[ h = 15 \times 3 \] \[ h = 45 \text{ m} \]Thus, the approximate width of the river is \(26 \text{ m}\) and the height of the chimney is \(45 \text{ m}\).
D) 26 m and 45 m
The question asks to identify the largest producer of saffron among the given Indian states. This requires knowledge of agricultural geography and crop distribution in India.
Correct Option: B) Jammu and Kashmir is renowned for its saffron production, particularly in the Pampore region, often referred to as the "Saffron Town of Kashmir." The unique agro-climatic conditions of the Kashmir Valley, including its specific soil type (known as "Karewas"), altitude, and temperature fluctuations, are ideal for saffron cultivation. It is the only state in India where saffron is grown on a commercial scale, making it the largest producer by a significant margin.
The question asks to identify the first brand ambassador of Sikkim. This is a factual recall question related to current affairs or general knowledge about Indian states and their promotional activities.
D) A. R. Rahman — In 2018, the renowned music composer A. R. Rahman was appointed as the first brand ambassador of Sikkim. His role was to promote the state's tourism and business potential, both nationally and internationally. This appointment was made during the 'Red Panda Winter Festival' in Gangtok.