The question asks to identify the Indian badminton player who secured a silver medal at the 2016 Rio Olympics. This requires knowledge of major sporting achievements by Indian athletes.
Correct Option: B) PV Sindhu is the correct answer. She created history by becoming the first Indian woman to win a silver medal in badminton at the Olympics, specifically at the 2016 Rio Games.
To find the water:squash ratio in the final blend, we need to calculate the total amount of water and total amount of squash from both mixtures, considering their respective ratios and the blending ratio. We will first determine the proportion of water and squash in each individual mixture. Then, we will use the blending ratio to find the weighted average of water and squash.
Analyze the first mixture:
The water-to-squash ratio is 4 : 1.
This means for every 5 parts of the mixture, 4 parts are water and 1 part is squash.
Analyze the second mixture:
The water-to-squash ratio is 3 : 1.
This means for every 4 parts of the mixture, 3 parts are water and 1 part is squash.
Consider the blending ratio:
The two mixtures are blended in the ratio 1 : 2. This means for every 1 part of the first mixture, there are 2 parts of the second mixture.
Let's assume we take 1 unit of the first mixture and 2 units of the second mixture.
Calculate total water in the blend:
To add these fractions, find a common denominator, which is 10:
\[ \text{Total Water} = \frac{4 \times 2}{5 \times 2} + \frac{3 \times 5}{2 \times 5} = \frac{8}{10} + \frac{15}{10} = \frac{23}{10} \]Calculate total squash in the blend:
To add these fractions, find a common denominator, which is 10:
\[ \text{Total Squash} = \frac{1 \times 2}{5 \times 2} + \frac{1 \times 5}{2 \times 5} = \frac{2}{10} + \frac{5}{10} = \frac{7}{10} \]Determine the final water : squash ratio:
The ratio of water to squash in the blend is:
\[ \text{Water} : \text{Squash} = \frac{23}{10} : \frac{7}{10} \]\[ \text{Water} : \text{Squash} = 23 : 7 \]B) 23 : 7
This question asks about the maximum number of electrons that can be accommodated in a specific electron shell, the M shell. This can be determined using the formula for the maximum number of electrons in a shell, which is \(2n^2\), where \(n\) is the principal quantum number corresponding to the shell.
Therefore, the M shell can accommodate a maximum of 18 electrons.
Correct Option: A) 18
The question asks for the definition of the principal focus of a spherical mirror. We need to recall the standard definitions of key terms related to spherical mirrors from optics.
Correct Option: B) It is the point on the principal axis through which rays of light parallel to the principal axis pass after reflection or appear to be arising from this point on the principal axis.
This option accurately describes the principal focus for both concave (rays pass through) and convex (rays appear to arise from) spherical mirrors.
This is a syllogism problem that can be solved using Venn diagrams or by analyzing the logical relationships between the statements. We need to assume the given statements are true, regardless of real-world facts, and determine which conclusions logically follow.
D) Only (2) conclusion follows
Based on our analysis, only the second conclusion, "Some of the tigers are rats," logically follows from the given statements.
This problem involves properties of tangents to a circle. We will use the facts that the radius is perpendicular to the tangent at the point of contact, and that the line joining the external point to the center bisects the angle between the tangents and the angle subtended by the points of contact at the center.
Let O be the center of the circle and P be the external point from which tangents PA and PB are drawn to the circle.
We are given that the angle between the tangents, \(\angle APB\), is 110°.
A key property of tangents from an external point to a circle is that the line segment OP (joining the external point to the center) bisects the angle between the tangents. Therefore, \(\angle APO = \angle BPO\).
Since OP bisects \(\angle APB\), we have:
\[ \angle APO = \frac{1}{2} \times \angle APB \]\[ \angle APO = \frac{1}{2} \times 110^\circ \]\[ \angle APO = 55^\circ \]Another property is that the radius to the point of tangency is perpendicular to the tangent. So, OA is perpendicular to PA, which means \(\angle OAP = 90^\circ\).
Now consider the triangle \(\triangle OAP\). The sum of angles in a triangle is 180°.
\[ \angle POA + \angle OAP + \angle APO = 180^\circ \]Substitute the known values:
\[ \angle POA + 90^\circ + 55^\circ = 180^\circ \]\[ \angle POA + 145^\circ = 180^\circ \]Solve for \(\angle POA\):
\[ \angle POA = 180^\circ - 145^\circ \]\[ \angle POA = 35^\circ \]C) 35° is the correct answer, as calculated from the properties of tangents and triangles.
The question asks which of Newton's laws of motion or gravitation provides the definition of force. We need to recall the core concept introduced by each law.
The first law is often called the 'Law of Inertia' and fundamentally establishes force as the agent that alters an object's state of motion or rest. Therefore, it provides the most basic definition of force.
Correct Option: B) Newton's first law of motion is considered to provide the fundamental definition of force, as it describes force as the external agent required to change an object's state of motion or rest (overcoming inertia).
This problem involves tracking directional changes based on turns (clockwise and anticlockwise) from an initial direction. We will calculate the net angular displacement by summing up the clockwise and anticlockwise turns separately and then finding the difference. Finally, we apply this net displacement to the initial direction.
Let's calculate the total clockwise and anticlockwise turns:
Now, let's find the net turn:
\[ \text{Net Turn} = \text{Total Anticlockwise Turn} - \text{Total Clockwise Turn} \]\[ \text{Net Turn} = 180^\circ - 90^\circ = 90^\circ \]Since the total anticlockwise turn is greater, the net turn is \(90^\circ\) anticlockwise.
Starting from East, a \(90^\circ\) anticlockwise turn will lead to North.
C) North
The problem requires simplifying a trigonometric expression using complementary angle identities. We will use the identities for sine and cosine of complementary angles to transform the expression into a simpler form.
Recall the complementary angle identities:
Substitute these identities into the given expression:
The given expression is: \(\sin \theta \cos(90^\circ - \theta) + \cos \theta \sin(90^\circ - \theta)\)
Using the identities, we replace \(\cos(90^\circ - \theta)\) with \(\sin \theta\) and \(\sin(90^\circ - \theta)\) with \(\cos \theta\).
So, the expression becomes:
\[ \sin \theta (\sin \theta) + \cos \theta (\cos \theta) \]Simplify the expression:
This simplifies to:
\[ \sin^2 \theta + \cos^2 \theta \]Apply the fundamental trigonometric identity:
Recall the fundamental trigonometric identity:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]Therefore, the simplified value of the given expression is 1.
A) 1 — By applying the complementary angle identities \(\cos(90^\circ - \theta) = \sin \theta\) and \(\sin(90^\circ - \theta) = \cos \theta\), the expression transforms into \(\sin^2 \theta + \cos^2 \theta\), which is equal to 1 based on the fundamental trigonometric identity.
To sum decimal numbers, it is crucial to align the decimal points vertically. This ensures that digits of the same place value (ones, tens, tenths, hundredths, etc.) are added together correctly. After aligning, perform standard addition from right to left, carrying over when necessary.
0.196 1.960 19.600 196.000 -------
A) 217.756 is the correct sum obtained by aligning the decimal points and adding the numbers.