To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we should evaluate Brackets/Parentheses first, then Orders/Exponents, then Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right). The term "of" in mathematics implies multiplication.
First, evaluate the innermost brackets:
\[ -2 - 8 - 4 = -14 \]Next, evaluate the expression inside the curly braces:
\[ \{5 + (-2)(-1)\} \]\[ \{5 + 2\} \]\[ \{7\} \]Now, substitute these values back into the original expression:
\[ 63 - (-3)(-14) \div 3 \text{ of } 7 \]Evaluate the "of" operation (multiplication):
\[ 3 \text{ of } 7 = 3 \times 7 = 21 \]The expression becomes:
\[ 63 - (-3)(-14) \div 21 \]Perform the multiplication:
\[ (-3)(-14) = 42 \]The expression is now:
\[ 63 - 42 \div 21 \]Perform the division:
\[ 42 \div 21 = 2 \]Finally, perform the subtraction:
\[ 63 - 2 = 61 \]D) 61 is the correct answer after following the BODMAS rule systematically.
The question asks to identify the item that does not belong to the group. This is a classification question where we need to find a common characteristic among most items and identify the outlier.
C) D (Sugar) — Lemon, Tamarind, and Raw Mango are all known for their sour taste, primarily due to the presence of acids. Sugar, however, is known for its sweet taste. Therefore, Sugar does not belong to the group of sour-tasting food items.
The question asks about the relationship described by the second equation of motion. We need to recall the standard kinematic equations for uniformly accelerated motion and identify which one is the second equation and what variables it relates.
A) position-time: The second equation of motion, \(s = ut + \frac{1}{2}at^2\), directly relates the displacement (\(s\), which is a change in position) to time (\(t\)).
The question asks to identify the sector for which the Union government launched the "SAMPADA Scheme". This requires knowledge of major government schemes and their objectives.
The SAMPADA Scheme was later renamed to Pradhan Mantri Kisan SAMPADA Yojana (PMKSY). Its primary aim is to boost the growth of the food processing sector in India.
C) Food processing — The SAMPADA (Scheme for Agro-Marine Processing and Development of Agro-Processing Clusters) scheme, later renamed Pradhan Mantri Kisan SAMPADA Yojana (PMKSY), was launched by the Ministry of Food Processing Industries. Its objective is to supplement agriculture, modernize processing, and decrease agri-waste, thereby boosting the food processing sector.
The question asks to identify the non-metal that exists in a liquid state at room temperature. This requires knowledge of the physical states of common elements, particularly non-metals, at standard room temperature.
A) Bromine
Bromine (\(\text{Br}\)) is a halogen and the only non-metallic element that is a liquid at standard room temperature and pressure. It is a reddish-brown volatile liquid with a strong, unpleasant odor.
If tanθ = \( \frac{4}{3} \), what is the value of sinθ + cosθ?
\( \frac{4}{5} \)
\( \frac{1}{3} \)
\( \frac{7}{5} \)
\( \frac{6}{5} \)
We are given the value of \(\tan\theta\) and need to find the value of \(\sin\theta + \cos\theta\). We can use the relationship between trigonometric ratios in a right-angled triangle or trigonometric identities to find the values of \(\sin\theta\) and \(\cos\theta\) individually and then sum them up.
Understand the given information:
We are given \(\tan\theta = \frac{4}{3}\). In a right-angled triangle, \(\tan\theta\) is defined as the ratio of the length of the side opposite to angle \(\theta\) to the length of the side adjacent to angle \(\theta\).
Determine the sides of the right-angled triangle:
Let the opposite side be \(4k\) and the adjacent side be \(3k\) for some positive constant \(k\).
Calculate the hypotenuse using the Pythagorean theorem:
For a right-angled triangle, \((\text{Hypotenuse})^2 = (\text{Opposite})^2 + (\text{Adjacent})^2\).
Find the values of \(\sin\theta\) and \(\cos\theta\):
\(\sin\theta\) is the ratio of the opposite side to the hypotenuse.
Calculate \(\sin\theta + \cos\theta\):
\[ \sin\theta + \cos\theta = \frac{4}{5} + \frac{3}{5} \]\[ \sin\theta + \cos\theta = \frac{4+3}{5} \]\[ \sin\theta + \cos\theta = \frac{7}{5} \]C) The calculated value of \(\sin\theta + \cos\theta\) is \(\frac{7}{5}\), which matches option C.
The question asks to identify the company founded and chaired by Sunil Bharti Mittal, a well-known Indian billionaire entrepreneur and philanthropist. This requires knowledge of prominent Indian business leaders and their associated companies.
Correct Option: A) Bharti Enterprises
The question asks about the primary source of revenue for Indian Railways. To answer this, one needs to understand the different revenue streams of Indian Railways and their relative contributions.
C) freight — Freight transportation, which involves carrying goods like coal, cement, food grains, petroleum products, etc., across the country, is by far the largest revenue generator for Indian Railways. It accounts for a significant majority of the total earnings, often exceeding 60-70% of the total revenue.
The question asks about the type of reflection that occurs when light strikes a polished surface. Understanding the characteristics of different types of surfaces and how they interact with light is key to answering this question.
Correct Option: A) regular — When light is incident on a polished surface, the surface is very smooth, and all parallel incident rays reflect as parallel rays in a single direction. This phenomenon is known as regular or specular reflection.
\( \frac{0.3}{1000} \) is equal to:
The problem asks us to express the fraction \( \frac{0.3}{1000} \) in scientific notation. This involves converting the decimal to a fraction, simplifying the fraction, and then expressing the result as a number multiplied by a power of 10.
The numerator is \(0.3\). This can be written as \( \frac{3}{10} \).
The expression becomes:
\[ \frac{0.3}{1000} = \frac{\frac{3}{10}}{1000} \]To simplify, multiply the numerator by the reciprocal of the denominator:
\[ \frac{\frac{3}{10}}{1000} = \frac{3}{10} \times \frac{1}{1000} = \frac{3}{10 \times 1000} = \frac{3}{10000} \]The denominator \(10000\) can be written as \(10^4\).
So, the expression is:
\[ \frac{3}{10^4} \]Using the rule \( \frac{1}{a^n} = a^{-n} \), we can write \( \frac{3}{10^4} \) as \( 3 \times 10^{-4} \).
Correct Option: A) \( 3 \times 10^{-4} \)