The question asks for the full form of the acronym NASSCOM. This is a factual recall question related to organizations in the Indian IT sector.
B) NATIONAL ASSOCIATION OF SOFTWARE AND SERVICES COMPANIES
NASSCOM is indeed the acronym for the National Association of Software and Services Companies. It is a non-profit trade association and advocacy group of the Indian information technology (IT) and Business Process Outsourcing (BPO) industry.
The question asks to identify the founder of India's first newspaper, the Bengal Gazette, which was established in 1780. This requires knowledge of key figures in the history of Indian journalism.
D) J.K. Hicky was the founder of the Bengal Gazette, which began publication in 1780. It was the first newspaper printed in Asia.
The question asks to identify the state that announced legislation for the 'right to water', ensuring a minimum of 55 litres of water per person per day. This requires knowledge of recent policy announcements by Indian states regarding water rights and access.
Correct Option: C) Madhya Pradesh has announced its plan to enact legislation for the 'right to water', aiming to guarantee a minimum of 55 litres of water per person per day. This was a significant policy announcement by the state government.
If cot3θcot6θ = 1, then the value of tan15θ will be:
-\(\sqrt{3}\)
0
\(-\frac{1}{\sqrt{3}}\)
3\(\sqrt{3}\)
The problem provides an equation involving cotangent functions and asks for the value of a tangent function. We will use trigonometric identities, specifically the complementary angle identity \(\cot \theta = \tan (90^\circ - \theta)\), to simplify the given equation and find the value of \(\theta\). Once \(\theta\) is found, we can calculate the value of \(\tan 15\theta\).
The given equation is \(\cot 3\theta \cot 6\theta = 1\).
We know that \(\cot \theta = \frac{1}{\tan \theta}\). So, we can rewrite the equation as:
\[ \frac{1}{\tan 3\theta} \cdot \cot 6\theta = 1 \]\[ \cot 6\theta = \tan 3\theta \]We know that \(\tan \alpha = \cot (90^\circ - \alpha)\) or \(\cot \alpha = \tan (90^\circ - \alpha)\). Using this identity, we can write \(\tan 3\theta\) as \(\cot (90^\circ - 3\theta)\). So the equation becomes:
\[ \cot 6\theta = \cot (90^\circ - 3\theta) \]If \(\cot A = \cot B\), then \(A = B + n \cdot 180^\circ\) for integer \(n\). For the simplest case, we can equate the angles:
\[ 6\theta = 90^\circ - 3\theta \]\[ 6\theta + 3\theta = 90^\circ \]\[ 9\theta = 90^\circ \]\[ \theta = \frac{90^\circ}{9} \]\[ \theta = 10^\circ \]We need to find the value of \(\tan 15\theta\). Substitute \(\theta = 10^\circ\) into the expression:
\[ \tan 15\theta = \tan (15 \times 10^\circ) \]\[ \tan 15\theta = \tan 150^\circ \]The angle \(150^\circ\) is in the second quadrant. In the second quadrant, the tangent function is negative. We can write \(150^\circ\) as \(180^\circ - 30^\circ\).
\[ \tan 150^\circ = \tan (180^\circ - 30^\circ) \]\[ \tan (180^\circ - A) = -\tan A \]\[ \tan 150^\circ = -\tan 30^\circ \]We know that \(\tan 30^\circ = \frac{1}{\sqrt{3}}\).
\[ -\tan 30^\circ = -\frac{1}{\sqrt{3}} \]Thus, the value of \(\tan 15\theta\) is \(-\frac{1}{\sqrt{3}}\).
Correct Option: C) \(-\frac{1}{\sqrt{3}}\) is the correct value derived from the calculations.
This question deals with the concept of logical negation and the Square of Opposition in traditional logic. We are given that a universal affirmative proposition is false, and we need to determine which other proposition must, therefore, be true.
Let's represent the propositions:
Given: A is False.
Contradictory relationship: A and O are contradictories. If A is False, then O must be True.
Therefore, "Some men are not rich" must be true.
A) Some men are not rich. This is the contradictory of "All men are rich". If "All men are rich" is false, then its contradictory, "Some men are not rich", must be true.
The question asks to identify the relationship between the first two terms and apply the same relationship to find the missing term for the third term. This is a classic analogy question, often found in reasoning sections of competitive exams. The relationship here is between a state and its capital city.
A) Bhopal is the capital city of Madhya Pradesh. This fits the established state-capital relationship.
To find the ratio of the cost price to the selling price when an article is sold at a certain profit percentage, we first define the relationship between cost price, selling price, and profit. Profit percentage is calculated based on the cost price. We will assume a cost price and then calculate the selling price based on the given profit percentage.
Correct Option: A) 2 : 5
The problem asks us to find the number of sides of a regular polygon given the ratio of its interior angle to its exterior angle. We will use the formulas for the interior and exterior angles of a regular polygon in terms of the number of sides, and then use the given ratio to solve for the number of sides.
Let \(n\) be the number of sides of the regular polygon.
The formula for the measure of an interior angle of a regular polygon with \(n\) sides is:
\[ \text{Interior Angle} = \frac{(n-2) \times 180^{\circ}}{n} \]The formula for the measure of an exterior angle of a regular polygon with \(n\) sides is:
\[ \text{Exterior Angle} = \frac{360^{\circ}}{n} \]We are given that the ratio of the interior angle to the exterior angle is 4 : 1. So, we can write the equation:
\[ \frac{\text{Interior Angle}}{\text{Exterior Angle}} = \frac{4}{1} \]Substitute the formulas for the interior and exterior angles into the ratio:
\[ \frac{\frac{(n-2) \times 180^{\circ}}{n}}{\frac{360^{\circ}}{n}} = 4 \]Simplify the equation. The \(n\) in the denominator of both numerator and denominator cancels out:
\[ \frac{(n-2) \times 180^{\circ}}{360^{\circ}} = 4 \]Further simplify by dividing 180 by 360:
\[ \frac{n-2}{2} = 4 \]Multiply both sides by 2:
\[ n-2 = 4 \times 2 \]\[ n-2 = 8 \]Add 2 to both sides to solve for \(n\):
\[ n = 8 + 2 \]\[ n = 10 \]Thus, the number of sides of the polygon is 10.
B) 10 is the correct answer. The calculations show that a regular polygon with 10 sides satisfies the given ratio of interior to exterior angle.
The question asks to identify the state government that banned e-cigarettes in May 2019. This is a factual question related to current affairs and government policies in India.
C) Rajasthan announced its decision to ban the production, distribution, advertisement, and sale of e-cigarettes within its territory in May 2019. This made Rajasthan the third state in India, after Punjab and Maharashtra, to take such a step.
The problem involves finding the present age of Anil given the ratio of present ages of Alok and Anil, and Alok's age 20 years from now. We will use the information about Alok's future age to find his present age, and then use the ratio to find Anil's present age.
C) 56 years — Based on the calculations, Anil's present age is 56 years.