The problem asks us to identify the odd one out from a given set of words. We need to find a common characteristic among three words and then identify the word that does not share that characteristic.
Correct Option: D) Chop is the odd one out because it is a method of cutting or preparing food, whereas Boil, Bake, and Fry are all methods of cooking food using heat.
The problem asks us to identify the odd one out from a given list of words. This is a classification-based reasoning question where we need to find a common characteristic shared by three words and identify the one that does not share that characteristic.
Correct Option: C) Stomach is the odd one out because it is an internal organ primarily involved in digestion, whereas Nose, Tongue, and Ears are external sensory organs.
Solve the following.
\(\frac{4+3\times3-2}{4-3\times(3-2)}\) = ?
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). We will evaluate the numerator and the denominator separately and then perform the division.
The numerator is \(4+3\times3-2\).
The denominator is \(4-3\times(3-2)\).
Now, divide the numerator by the denominator:
\[ \frac{\text{Numerator}}{\text{Denominator}} = \frac{11}{1} = 11 \]C) 11. The calculation shows that the expression simplifies to 11.
This problem involves understanding how basic statistical measures like mean and median are affected by a uniform change (subtraction) applied to each observation in a dataset. We will use the properties of mean and median under such transformations.
C) 9 and 8. This matches our calculated new mean and new median.
The question asks for the full form of the acronym REDD, a program run by the United Nations since 2008, focusing on forests, carbon emissions, and low-carbon development. This is a factual recall question related to international environmental initiatives.
Correct Option: B) Reducing Emissions from Deforestation and Forest Degradation
The question asks to identify the polymer commonly used for manufacturing water pipes. This requires knowledge of common polymers and their applications based on their properties.
D) PVC (Polyvinyl Chloride) is extensively used for manufacturing water pipes due to its durability, chemical resistance, non-corrosive nature, and cost-effectiveness.
The problem involves ratios and algebraic manipulation. We are given a ratio involving \((x+y)\) and \((x-y)\), and we need to find another ratio involving \((x^2+y^2)\) and \((x^2-y^2)\). The key is to first find the ratio of \(x\) to \(y\) from the given information, and then substitute these values (or a common multiple) into the expression we need to evaluate.
Set up the initial ratio:
Given that \((x + y) : (x - y) = 7 : 3\), we can write this as a fraction:
Cross-multiply to eliminate fractions:
\[ 3(x + y) = 7(x - y) \]Distribute the terms:
\[ 3x + 3y = 7x - 7y \]Group like terms (x terms on one side, y terms on the other):
Subtract \(3x\) from both sides:
Add \(7y\) to both sides:
\[ 10y = 4x \]Find the ratio of \(x\) to \(y\):
Divide both sides by \(4y\):
Simplify the ratio:
\[ \frac{x}{y} = \frac{5}{2} \]This means \(x = 5k\) and \(y = 2k\) for some constant \(k\). For simplicity, we can assume \(x=5\) and \(y=2\) for calculating the ratio, as the constant \(k\) will cancel out.
Calculate \(x^2\) and \(y^2\):
If \(x = 5\) and \(y = 2\), then:
Calculate \((x^2 + y^2)\) and \((x^2 - y^2)\):
\[ x^2 + y^2 = 25 + 4 = 29 \]\[ x^2 - y^2 = 25 - 4 = 21 \]Form the final ratio:
\[ (x^2 + y^2) : (x^2 - y^2) = 29 : 21 \]C) 29 : 21
The question asks to identify the Viceroy of India who declared India's entry into World War II alongside Britain in 1939. This requires knowledge of the timeline of Viceroys and significant historical events during their tenure.
C) Lord Linlithgow was the Viceroy of India from 1936 to 1943. It was he who, on September 3, 1939, unilaterally declared that India had entered World War II alongside Britain, without consulting any Indian political parties or leaders. This decision led to widespread protests and the resignation of Congress ministries in the provinces.
The value of sin1° sin2° sin3°…sin180°…sin196° is:
\( \frac{1}{4} \)
\( \frac{1}{2} \)
0
\( \frac{1}{3} \)
The problem asks for the value of a product of sine functions: \(\sin 1^\circ \sin 2^\circ \sin 3^\circ \dots \sin 180^\circ \dots \sin 196^\circ\). To solve this, we need to identify if any term in the product evaluates to zero, as multiplying by zero will make the entire product zero.
The given expression is a product of sine values:
\[ P = \sin 1^\circ \cdot \sin 2^\circ \cdot \sin 3^\circ \cdot \dots \cdot \sin 180^\circ \cdot \dots \cdot \sin 196^\circ \]We need to examine the terms in the product. The angles range from \(1^\circ\) to \(196^\circ\).
Recall the values of the sine function for standard angles. Specifically, we know that \(\sin n^\circ = 0\) when \(n\) is a multiple of \(180\).
In the given product, one of the terms is \(\sin 180^\circ\).
The value of \(\sin 180^\circ\) is \(0\).
Since \(\sin 180^\circ = 0\) is one of the terms in the product, the entire product will evaluate to zero, regardless of the values of the other terms.
Therefore,
\[ P = \sin 1^\circ \cdot \sin 2^\circ \cdot \dots \cdot \sin 180^\circ \cdot \dots \cdot \sin 196^\circ = 0 \]C) 0. The product includes \(\sin 180^\circ\), which is equal to 0. Any product that contains a zero term will result in zero.
What is the common name of the compound NaHCO3?
Washing soda
Bleaching powder
Caustic soda
Baking soda
The question asks for the common name of the chemical compound with the formula NaHCO₃. This requires knowledge of common chemical names and their corresponding formulas.
Correct Option: D) Baking soda
Sodium bicarbonate (\( \text{NaHCO}_3 \)) is widely known as baking soda. It is a white crystalline powder that is commonly used as a leavening agent in baking due to its ability to release carbon dioxide gas when heated or when it reacts with an acid.