The question asks for the full form of "NDC" in the context of a government agency. This is a direct knowledge-based question related to Indian polity and governance.
Correct Option: B) National Development Council is the correct full form of NDC as a government agency in India. It was established in 1952 to secure cooperation of states in the execution of the Five-Year Plans. Though its role has diminished since the abolition of the Planning Commission and the establishment of NITI Aayog, it remains a historically significant body.
The quality of coal is primarily determined by its carbon content and moisture content. Higher carbon content and lower moisture content generally indicate higher quality coal. We need to identify the coal types that represent the highest and lowest quality based on these criteria.
C) Anthracite, lignite — Anthracite is the highest quality coal due to its high carbon content and low moisture. Lignite is the lowest quality coal due to its low carbon content and high moisture.
The question asks to identify the individual credited with starting the first newspaper in India. This is a factual question related to the history of journalism in India.
B) James A Hickey — James Augustus Hicky started "The Bengal Gazette" in 1780, which is widely recognized as the first newspaper published in India. It was an English-language weekly newspaper published in Kolkata (then Calcutta).
tan 100° + tan 125° + tan 100° tan 125° is equal to:
This problem can be solved using the tangent addition formula. The key is to recognize that the sum of the two angles \(100^\circ\) and \(125^\circ\) is \(225^\circ\), which is a special angle. We can then use the identity for \(\tan(A+B)\) to simplify the given expression.
Let the given expression be \(E\):
\[ E = \tan 100^\circ + \tan 125^\circ + \tan 100^\circ \tan 125^\circ \]Recall the tangent addition formula:
\[ \tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]Rearrange the formula to express \( \tan A + \tan B \):
\[ \tan A + \tan B = \tan(A+B)(1 - \tan A \tan B) \]\[ \tan A + \tan B = \tan(A+B) - \tan(A+B) \tan A \tan B \]Now, substitute \(A = 100^\circ\) and \(B = 125^\circ\). Then \(A+B = 100^\circ + 125^\circ = 225^\circ\).
Substitute these values into the rearranged formula:
\[ \tan 100^\circ + \tan 125^\circ = \tan(225^\circ) - \tan(225^\circ) \tan 100^\circ \tan 125^\circ \]We know that \( \tan(225^\circ) = \tan(180^\circ + 45^\circ) = \tan(45^\circ) = 1 \).
Substitute the value of \( \tan(225^\circ) \) into the equation:
\[ \tan 100^\circ + \tan 125^\circ = 1 - (1) \tan 100^\circ \tan 125^\circ \]\[ \tan 100^\circ + \tan 125^\circ = 1 - \tan 100^\circ \tan 125^\circ \]Rearrange the terms to match the given expression:
\[ \tan 100^\circ + \tan 125^\circ + \tan 100^\circ \tan 125^\circ = 1 \]Thus, the value of the given expression is 1.
B) 1 is the correct answer, as derived from the tangent addition formula.
The question asks for the location of the Space Application Centre (SAC). This requires knowledge of the major centres of the Indian Space Research Organisation (ISRO) and their respective locations.
Correct Option: A) Ahmedabad is the correct answer because the Space Application Centre (SAC), a major research and development centre of ISRO, is located there. SAC is responsible for the design, development, and realisation of space-borne instruments for satellites and the development and operationalisation of applications of space technology.
On which date was the first World Cleanup Day held?
The question asks for the date on which the first World Cleanup Day was held. This is a factual question related to environmental awareness events. To answer correctly, one needs to recall the specific date of this global initiative's inception.
Correct Option: A) September 15
If cosecθ - cotθ = a, then the value of cosecθ is:
\(\frac{1}{2}\left(a+\frac{1}{a}\right)\)
\(\frac{1}{2}\left(a-\frac{1}{a}\right)\)
\(\frac{1}{4}\left(a-\frac{1}{a}\right)\)
\(\left(a+\frac{1}{a}\right)\)
This problem involves trigonometric identities. We are given an equation relating cosec\(\theta\) and cot\(\theta\), and we need to find the value of cosec\(\theta\). The key identity to use here is \( \text{cosec}^2\theta - \text{cot}^2\theta = 1 \).
We are given the equation:
\[ \text{cosec}\theta - \text{cot}\theta = a \quad \text{(Equation 1)} \]Recall the fundamental trigonometric identity:
\[ \text{cosec}^2\theta - \text{cot}^2\theta = 1 \]This identity can be factored using the difference of squares formula \((x^2 - y^2 = (x-y)(x+y))\):
\[ (\text{cosec}\theta - \text{cot}\theta)(\text{cosec}\theta + \text{cot}\theta) = 1 \]Substitute the value of \( (\text{cosec}\theta - \text{cot}\theta) \) from Equation 1 into the factored identity:
\[ a(\text{cosec}\theta + \text{cot}\theta) = 1 \]From this, we can find the value of \( (\text{cosec}\theta + \text{cot}\theta) \):
\[ \text{cosec}\theta + \text{cot}\theta = \frac{1}{a} \quad \text{(Equation 2)} \]Now we have a system of two linear equations with two variables (cosec\(\theta\) and cot\(\theta\)):
Equation 1: \( \text{cosec}\theta - \text{cot}\theta = a \)
Equation 2: \( \text{cosec}\theta + \text{cot}\theta = \frac{1}{a} \)
To find cosec\(\theta\), add Equation 1 and Equation 2:
\[ (\text{cosec}\theta - \text{cot}\theta) + (\text{cosec}\theta + \text{cot}\theta) = a + \frac{1}{a} \]\[ 2\text{cosec}\theta = a + \frac{1}{a} \]Finally, solve for cosec\(\theta\):
\[ \text{cosec}\theta = \frac{1}{2}\left(a + \frac{1}{a}\right) \]A) \[\frac{1}{2}\left(a+\frac{1}{a}\right)\] is the correct expression for cosec\(\theta\), as derived from the trigonometric identity and the given equation.
The following figure is a combination of 4 figures, A, B, C and D. Figure A and B represent students who are enrolled in science club and debate club respectively. Figure C and D represent students who have joined drama club and sports club respectively. The numbers inside the figures represent the number of students in that particular region. How many students have joined more than two clubs?
To find the number of students who have joined more than two clubs, we need to identify the regions in the Venn diagram where three or more figures overlap.
Correct Option: D) 3
The question asks for the continent where Mount Vinson is located. This requires knowledge of world geography, specifically the location of major mountain peaks.
Correct Option: B) Antarctica — Mount Vinson (Vinson Massif) is the highest mountain in Antarctica, located in the Ellsworth Mountains.
Which company became 2nd Indian firm to cross ₹6 lakh crore market value in 2018?
The question asks to identify the second Indian company to achieve a market capitalization of ₹6 lakh crore in 2018. This requires knowledge of major Indian companies' market valuations and historical milestones.
Correct Option: D) TCS
In 2018, Tata Consultancy Services (TCS) became the second Indian company to cross a market capitalization of ₹6 lakh crore. The first company to achieve this milestone was Reliance Industries Limited (RIL).