To find the molar mass of a compound, we need to sum the atomic masses of all the atoms present in its chemical formula. The chemical formula for ethyne is C₂H₂. We will use the standard atomic masses for Carbon (C) and Hydrogen (H).
Correct Option: D) 26 u
To determine the type of triangle, we first need to find the actual measures of its angles. We are given the ratio of the angles. We know that the sum of the angles in any triangle is 180 degrees. Using this information, we can calculate each angle and then classify the triangle based on its angle measures.
Represent the angles:
Let the angles of the triangle be \(5x\), \(6x\), and \(7x\), where \(x\) is a common multiplier.
Use the angle sum property of a triangle:
The sum of the angles in a triangle is \(180^\circ\).
\[ 5x + 6x + 7x = 180^\circ \]Solve for \(x\):
\[ 18x = 180^\circ \] \[ x = \frac{180^\circ}{18} \] \[ x = 10^\circ \]Calculate the measure of each angle:
Classify the triangle:
A triangle is classified based on its angles:
In our case, the angles are \(50^\circ\), \(60^\circ\), and \(70^\circ\). All these angles are less than \(90^\circ\).
B) acute triangle — Since all three angles (\(50^\circ\), \(60^\circ\), \(70^\circ\)) are less than \(90^\circ\), the triangle is an acute triangle.
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing word.
C) Debate — Debate is a formal, structured, and often argumentative form of spoken communication, which stands in contrast to the informal and spontaneous nature of a conversation. This mirrors the relationship between prose (straightforward written form) and poetry (structured, artistic written form).
The question asks for the location of the 'Shri Shiv Chhatrapati Sports Complex', also known as Balewadi Stadium. This requires general knowledge about prominent sports facilities in India.
C) Pune — The 'Shri Shiv Chhatrapati Sports Complex', commonly known as Balewadi Stadium, is indeed located in Balewadi, Pune, Maharashtra. It is a significant sports venue in the state.
To find the coordinates of a point that divides a line segment internally in a given ratio, we use the section formula. The section formula provides a direct method to calculate the coordinates of such a point.
Identify the given points and ratio:
Let the two given points be \(A = (x_1, y_1) = (-3, 7)\) and \(B = (x_2, y_2) = (9, -1)\).
The ratio in which the point divides the line segment internally is \(m : n = 3 : 1\).
Recall the section formula:
If a point \(P(x, y)\) divides the line segment joining \(A(x_1, y_1)\) and \(B(x_2, y_2)\) internally in the ratio \(m : n\), its coordinates are given by:
\[ x = \frac{m x_2 + n x_1}{m + n} \]\[ y = \frac{m y_2 + n y_1}{m + n} \]Substitute the values into the formula to find the x-coordinate:
\[ x = \frac{(3)(9) + (1)(-3)}{3 + 1} \]\[ x = \frac{27 - 3}{4} \]\[ x = \frac{24}{4} \]\[ x = 6 \]Substitute the values into the formula to find the y-coordinate:
\[ y = \frac{(3)(-1) + (1)(7)}{3 + 1} \]\[ y = \frac{-3 + 7}{4} \]\[ y = \frac{4}{4} \]\[ y = 1 \]State the coordinates of the point:
The coordinates of the point are \((6, 1)\).
Correct Option: B) (6, 1) is the correct answer, as calculated using the section formula.
To find the smallest number that leaves a remainder of 3 when divided by 4, 6, 10, and 15, we first need to find the Least Common Multiple (LCM) of these divisors. The number we are looking for will be 3 more than this LCM.
We can use the prime factorization method.
To find the LCM, we take the highest power of all prime factors present in these numbers:
\[ \text{LCM}(4, 6, 10, 15) = 2^2 \times 3^1 \times 5^1 \]\[ \text{LCM} = 4 \times 3 \times 5 \]\[ \text{LCM} = 12 \times 5 \]\[ \text{LCM} = 60 \]The problem states that the number should leave a remainder of 3 each time. So, the required number is the LCM plus 3.
\[ \text{Required Number} = \text{LCM} + 3 \]\[ \text{Required Number} = 60 + 3 \]\[ \text{Required Number} = 63 \]The number 63 satisfies all the conditions.
D) 63 is the smallest number that leaves a remainder of 3 when divided by 4, 6, 10, and 15.
Select the different figure from the given figures.
To solve this problem, we need to identify which figure is different from the others based on a specific characteristic. Observing the shapes and their accompanying smaller shapes will help us determine the odd one out.
Correct Option: C) Option C is different because the smaller shape is filled and matches the main shape, unlike Option D where the smaller shape is not filled.
The question asks to identify the recipient of the 'Indira Gandhi Prize for Peace, Disarmament and Development' in 2017. This requires knowledge of significant awards and their recipients in a specific year, which is a common type of general knowledge question in competitive exams.
Correct Option: D) Manmohan Singh was awarded the 'Indira Gandhi Prize for Peace, Disarmament and Development' in 2017 for his contributions as a statesman and economist.
The question asks for the resistivity of copper. Resistivity is an intrinsic property of a material that quantifies how strongly it resists electrical current. It is a fundamental constant for a given material at a specific temperature. For competitive exams, it's often expected to know the approximate values of resistivity for common conductors like copper.
Correct Option: B) 1.69 \(\times\) 10 \( dash\)8 \(\Omega\)-m
This option correctly states the resistivity of copper, which is a very low value, indicating its excellent conductivity. The unit for resistivity is Ohm-meter (\(\Omega\)-m).
The question asks to identify the correct title of the autobiography of Indian tennis champion Sania Mirza from the given options. This is a factual recall question related to sports and literature.
Correct Option: C) Ace Against Odds is the autobiography of tennis champion Sania Mirza. It was launched in 2016 and chronicles her journey to becoming a world-class tennis player.