The question involves identifying the correct image to complete a sequence. The sequence consists of three images, each depicting a heart shape within a different orientation of a V or inverted V symbol.
Correct Option: A) Option A correctly completes the sequence by following the alternating pattern.
The question asks about the specific fund available to the Government of India for immediate use during emergencies or calamities. Understanding the purpose and operation of various government funds is crucial here.
Correct Option: A) The Contingency Fund of India is established under Article 267(1) of the Constitution. It is an imprest fund placed at the disposal of the President (on behalf of the executive) to meet unforeseen expenditures like natural calamities or emergencies, pending parliamentary authorization. This allows the government to act swiftly in times of crisis.
The question asks for the number of national parks in Uttarakhand as of 2018. This requires factual knowledge about the protected areas in the state.
Correct Option: D) 6
The problem asks us to evaluate an expression involving \(\sin\theta\) and \(\cos\theta\), given the value of \(\tan\theta\). We can solve this by either constructing a right-angled triangle to find the values of \(\sin\theta\) and \(\cos\theta\), or by dividing the numerator and denominator of the given expression by \(\cos\theta\) to express everything in terms of \(\tan\theta\).
We are given that \(\tan\theta = \frac{3}{5}\).
Consider the expression we need to evaluate:
\[ \frac{5\sin\theta+2\cos\theta}{5\sin\theta+3\cos\theta} \]To use the given \(\tan\theta\) value directly, we can divide both the numerator and the denominator by \(\cos\theta\). This is valid as long as \(\cos\theta \neq 0\). If \(\cos\theta = 0\), then \(\tan\theta\) would be undefined, which is not the case here.
Divide each term in the numerator and denominator by \(\cos\theta\):
\[ \frac{\frac{5\sin\theta}{\cos\theta} + \frac{2\cos\theta}{\cos\theta}}{\frac{5\sin\theta}{\cos\theta} + \frac{3\cos\theta}{\cos\theta}} \]Simplify the terms using the identity \(\tan\theta = \frac{\sin\theta}{\cos\theta}\):
\[ \frac{5\tan\theta + 2}{5\tan\theta + 3} \]Now, substitute the given value \(\tan\theta = \frac{3}{5}\) into the simplified expression:
\[ \frac{5\left(\frac{3}{5}\right) + 2}{5\left(\frac{3}{5}\right) + 3} \]Perform the multiplication:
\[ \frac{3 + 2}{3 + 3} \]Perform the addition:
\[ \frac{5}{6} \]Correct Option: D) \( \frac{5}{6} \)
The problem asks us to form a meaningful word using letters corresponding to specific numbers in the English alphabet sequence. We need to identify these letters, arrange them to form a word, and then find the second letter of that word.
The letters are T, A, G, E.
By rearranging these letters, we can form the word "GATE".
In the word "GATE", the second letter is 'A'.
Therefore, the second letter of the word is A.
C) A — As determined in the step-by-step analysis, the letters T, A, G, E form the word "GATE", and its second letter is 'A'.
To arrange rational numbers in ascending order, we need to compare them. The easiest way to compare fractions is to convert them to equivalent fractions with a common denominator. Once they have the same denominator, we can compare their numerators.
Correct Option: C) \(-\frac{5}{6}\)
The problem requires us to calculate the total cost of manufacturing cylindrical containers from a given rectangular sheet of metal. We need to determine how many containers can be made from the sheet by calculating the area of the sheet and the surface area of one container. Since the containers are without a lid, we will calculate the area of the base plus the lateral surface area for each container. Finally, we multiply the number of containers by the cost per container to find the total cost.
Convert all dimensions to a consistent unit.
The dimensions of the rectangular sheet are given in meters, and the container's diameter is in centimeters. Let's convert everything to centimeters.
Calculate the radius and height of one container.
Calculate the area of the rectangular sheet.
\[ \text{Area of sheet} = L \times W = 220 \text{ cm} \times 210 \text{ cm} = 46200 \text{ cm}^2 \]Calculate the material required for one container (without a lid).
A cylindrical container without a lid consists of a circular base and a lateral surface. The formula for the surface area of such a container is the area of the base plus the lateral surface area.
Substitute the values:
\[ A_{\text{container}} = \pi (7 \text{ cm})^2 + 2 \pi (7 \text{ cm})(14 \text{ cm}) \]\[ A_{\text{container}} = 49 \pi \text{ cm}^2 + 196 \pi \text{ cm}^2 \]\[ A_{\text{container}} = 245 \pi \text{ cm}^2 \]Using \(\pi = \frac{22}{7}\):\[ A_{\text{container}} = 245 \times \frac{22}{7} \text{ cm}^2 \]\[ A_{\text{container}} = 35 \times 22 \text{ cm}^2 \]\[ A_{\text{container}} = 770 \text{ cm}^2 \]Calculate the number of containers that can be made.
Divide the total area of the sheet by the material required for one container.
Calculate the total cost.
The cost of manufacturing one container is Rs. 50.
A) 3,000 is the correct total cost calculated based on the number of containers that can be made and the cost per container.
Work done in physics is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it is expressed as \(W = F \cdot d \cdot \cos(\theta)\), where \(W\) is work, \(F\) is force, \(d\) is displacement, and \(\theta\) is the angle between the force and displacement vectors. No work is done if the force is zero, displacement is zero, or the angle between force and displacement is 90 degrees.
Based on the analysis, only in the case of the donkey carrying a weight horizontally is the force supporting the weight perpendicular to the displacement of the weight, resulting in no work done on the weight by the donkey against gravity.
B) A donkey is carrying a weight on its back. In this scenario, the force exerted by the donkey to hold the weight is vertically upwards, while the displacement of the weight is horizontal. Since the angle between the force and displacement is \(90^\circ\), the work done by the donkey on the weight is zero, according to the formula \(W = F \cdot d \cdot \cos(90^\circ) = 0\).
The question asks to identify a specific program launched by Union Minister Uma Bharti in February 2018 for sustainable drinking water supply in rural Rajasthan. This requires knowledge of government schemes and their launch details.
Correct Option: A) Swajal Scheme
The Swajal Scheme was launched by the then Union Minister for Drinking Water and Sanitation, Uma Bharti, in February 2018. It was initiated as a pilot project in 115 aspirational districts across six states, including Rajasthan. The scheme aims to provide village communities with their own sustainable drinking water supply, managed by the community itself, with 90% of the project cost covered by the government and the remaining 10% by the community.
The question asks about the type of force that holds ions together in ionic compounds. Ionic compounds are formed between oppositely charged ions. We need to identify the fundamental force responsible for attraction between charged particles.
Correct Option: A) electrostatic forces — Electrostatic forces are the attractive or repulsive forces between electrically charged particles. Since ionic compounds consist of positively and negatively charged ions, the strong attraction holding them together is indeed an electrostatic force.
