This is a blood relation question. We need to establish the relationships between the individuals mentioned and then determine how B is related to U. We can use a family tree or symbolic representation to solve this.
B) Father-in-law - As established, B is the father of A, and U is married to A. Thus, B is the father-in-law of U.
The question asks about the winner of the FIFA U-17 World Cup final held in Kolkata on October 28, 2017, where Spain was the losing finalist. This is a factual question related to major international sporting events, which are often covered in current affairs sections of competitive exams.
Correct Option: A) England defeated Spain in the final of the FIFA U-17 World Cup 2017 held in Kolkata.
The area of the circumcircle of a right-angled triangle whose sides are given as 2 cm, 2\(\sqrt{3}\) cm and 4 cm is given by:
To find the area of the circumcircle of a right-angled triangle, we first need to determine the radius of the circumcircle. For a right-angled triangle, the hypotenuse is the diameter of its circumcircle. Once the diameter is known, the radius can be calculated, and subsequently, the area of the circle using the formula \(A = \pi r^2\).
Identify the sides of the triangle: The given sides are 2 cm, \(2\sqrt{3}\) cm, and 4 cm.
Verify if it's a right-angled triangle: We can use the Pythagorean theorem (\(a^2 + b^2 = c^2\)) to check if the triangle is right-angled. The longest side must be the hypotenuse. Here, the longest side is 4 cm.
Let \(a = 2\) cm and \(b = 2\sqrt{3}\) cm. Let \(c = 4\) cm.
\[ a^2 + b^2 = (2)^2 + (2\sqrt{3})^2 \]\[ = 4 + (4 \times 3) \]\[ = 4 + 12 \]\[ = 16 \]\[ c^2 = (4)^2 = 16 \]Since \(a^2 + b^2 = c^2\), the triangle is indeed a right-angled triangle.
Determine the diameter of the circumcircle: For a right-angled triangle, the hypotenuse is the diameter of its circumcircle. Therefore, the diameter \(D = 4\) cm.
Calculate the radius of the circumcircle: The radius \(r\) is half of the diameter.
\[ r = \frac{D}{2} = \frac{4}{2} = 2 \text{ cm} \]So, the radius of the circumcircle is 2 cm.
Calculate the area of the circumcircle: The area \(A\) of a circle is given by the formula \(A = \pi r^2\).
\[ A = \pi (2)^2 \]\[ A = 4\pi \text{ cm}^2 \]Correct Option: D) 4π cm 2
This question requires us to analyze a given statement and determine which of the provided conclusions logically follow from it. We need to evaluate each conclusion based on the information explicitly stated or strongly implied by the statement, without introducing external assumptions.
Correct Option: D) Both the conclusions follow.
The given series is an alternating series where two different patterns are interleaved. We need to identify these two patterns to find the next term.
Sub-series 1 (Odd positions): 3, 9, 15, ...
Sub-series 2 (Even positions): 2, 8, 14, ...
The terms are 3, 9, 15.
This is an arithmetic progression with a common difference of 6.
The terms are 2, 8, 14.
This is also an arithmetic progression with a common difference of 6.
The last term in Sub-series 1 is 15. To find the next term in this sub-series, we add the common difference:
\[ 15 + 6 = 21 \]Correct Option: C) 21
To find the momentum of an object, we use the fundamental formula that defines momentum as the product of its mass and velocity. We will substitute the given values for mass and velocity into this formula and calculate the result, paying close attention to the units.
Identify the given values:
Recall the formula for momentum:
Momentum (\(p\)) is defined as the product of mass (\(m\)) and velocity (\(v\)).
\[ p = m \times v \]Substitute the values into the formula:
\[ p = 80 \text{ kg} \times 60 \text{ ms}^{-1} \]Calculate the product:
\[ p = 4800 \text{ kgms}^{-1} \]Determine the units:
The unit of mass is kilograms (kg) and the unit of velocity is meters per second (ms\(^{-1}\)). Therefore, the unit of momentum is kgms\(^{-1}\).
Correct Option: B) 4800 kgms\(^{-1}\)
The nature of the image formed by a mirror depends on the type of mirror and the position of the object. For a convex mirror, its diverging nature dictates specific characteristics for all images formed, regardless of the object's position.
Correct Option: D) virtual and diminished
India celebrates its National Sports Day on:
The question asks for the date on which India celebrates its National Sports Day. This is a factual question related to important days and events in India, often covered in general knowledge sections of competitive exams.
Correct Option: C) 29th August is celebrated as National Sports Day in India. This day marks the birth anniversary of the legendary Indian hockey player, Major Dhyan Chand, who was born on August 29, 1905. The day is dedicated to promoting sports and games in the country and honoring the achievements of Indian athletes.
This problem involves relative speed. When a train crosses a person walking in the same direction, the effective speed is the difference between the train's speed and the person's speed. The distance covered by the train in both cases is its own length. We can set up equations based on the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) and solve for the train's speed.
Correct Option: C) 36
The problem asks us to determine which combination of statements is sufficient to establish the complete order of seven balls (green, yellow, blue, orange, red, pink, black) from largest to smallest. We need to analyze each statement and see how it helps in creating a definitive sequence.
Let's denote the balls by their first letters: G, Y, B, O, R, P, K (for black).
Let's combine the information from all statements:
Combining these, we have a partial order: B > ... > R > G > Y > (O, K) > P.
The complete sequence needs to be determined for all seven balls. We know B is the largest and P is the smallest. We also know R > G > Y. And Y is larger than O and K. However, the relative order of O and K is not given. We only know Y > O and Y > K, but we don't know if O > K or K > O, or if they are equal (though the problem states balls are of different sizes, so they must be unequal).
Even with all five statements, we cannot determine the exact order of O and K. For example, two possible orders could be:
Since we cannot definitively place O and K relative to each other, no combination of these statements is sufficient to answer the question, which asks for the *order* of the balls from largest to smallest.
A) Neither statement is sufficient - As shown above, even with all five statements, the relative order of the orange and black balls cannot be determined. Therefore, no subset or all of these statements can provide a complete order.