Given:

The sides AB and AC of Δ ABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 82°

Concept used:

P is the point where bisectors of the ∠ DBC and ∠ BCE meet.

As shown in the above figure,

P is the point where bisectors of the ∠ DBC and ∠ BCE meet.

The mirror image of this image is:

Hence, the correct answer is "Option (4)".

The correct answer is 68.

Key Points

• Mendeleev's periodic table
  • Mendeleev published the periodic table in 1869 but not all the elements were discovered by that time, so he left some spaces under Aluminium and Silicon.
  • He examined the relationship between atomic masses and the physical and chemical properties of elements.
  • While preparing the periodic table there were a few instances where he had to place elements with a slightly greater atomic mass before an element with a slightly lower atomic mass as he wanted to place elements with similar chemical properties together.
  • Periodic law states that "properties of elements are periodic function of their atomic masses.

Additional Information

• By his time only 63 elements were discovered.
• Mendeleev boldly predicted the existence of certain elements that had not been discovered at that time.
• He named them eka-boron, eka-aluminium, and eka-silicon as they have properties similar to that of Boron, Aluminium and Silicon.
• Later on, these names were replaced as follows:
• Eka-boron =Scandium
• Eka-aluminum = gallium
• Eka- silicon = Germanium
• Further, it was observed that the predicted atomic weights of eka-boron (scandium), eka-aluminium (gallium), and eka-silicon (germanium) are 44, 68, 72, and those of calculated weights are 43.8, 70, and 72.6 respectively.
• Eka is a Sanskrit word meaning one.

Given:

Anu can type 40 pages in 10 hours

Anu and Mohit together can type 270 pages in 54 hours

Formula Used:

Total Work = Efficiency × Time

Calculation:

According to the question,

Efficiency of Anu = 40/10 = 4 pages/hour

Efficiency of Anu and Mohit = 270/54 = 5 pages/hour

⇒ Efficiency of Mohit = 5 - 4 = 1 page/hour

For 20 pages, time taken by Mohit = 20/1 = 20 hours

∴ Mohit can type 20 pages in 20 hours.

The logic followed here is:

‘ALWAYS’ is coded as ‘AKYAXU’,

So, 'BEYOND' is coded as 'BDAOMF'.

Hence, the correct answer is "Option 3".

The Correct Answer is India and Japan.

In News

• Sahyog Kaijin: Coast Guards of India, Japan hold joint exercises on responding to distress in real-time.

Key Points

• The Indian and Japanese Coast Guards conducted a successful joint exercise, 'Sahyog Kaijin,' off the Chennai coast.
• Responding to a simulated distress call, ICGS Shaurya and JCGS Yashima swiftly rescued the crew of a distressed vessel, MT Matsyadristi, facing a fire and oil slick.
• Utilizing advanced equipment and coordinated efforts, the exercise included pollution response training, search and rescue, and maritime law enforcement.
• The collaboration, dating back to a 2006 memorandum, aims to strengthen bilateral cooperation in expertise sharing and best practices between the two coast guard agencies.

The correct option is option 4.

Key Points

Atomic Radius:

•  It is the distance from the centre of the nucleus to the outermost shell containing electrons.
• The atomic radius decreases moving from left to right in the Modern Periodic Table.
• The decrease in the atomic radius is due to an increase in the nuclear charge which pulls the electrons closer to the nucleus of the atom and reduces the size of an atom.
• When we move down the group, there is an addition of shell and hence, the atomic size increases down the group.
• For example, Sodium (Na) and Lithium (Li) belong to the same group i.e. group 1
• Lithium has 3 atomic numbers and its configuration is 2 (K), 1(L).
• While, sodium has 11 atomic numbers and its configuration is 2 (K), 8 (L), and 1 (M).
• Hence we can conclude that the Atomic size of an atom going left to right in the period of the modern periodic table decreases, and increases from top to bottom

Additional Information

• Ionization energy increases on going from left to right and from down to top.
• Electron affinity increases on going from left to right and from down to top.
• The atomic radius increases from right to left and top to bottom.

Given:

Ratio of milk and water in mixture = 3 : 2 

The initial quantity of mixture = 13 L

Quantity of mixture replaced = 3 L

Concept used:

While removing some quantity of mixture from a mixture,

The ratio of things present in the mixture remains same.

Calculation:

Mixture remaining after removal of 3 L = 13 - 3 = 10 L

So, quantity of milk = 3/5 × 10 = 6 L

And, quantity of water = 2/5 × 10 = 4 L

Now, quantity of milk after adding 3 L milk = 6 + 3 = 9 L

⇒ Milk :  Water = 9 : 4

∴ Ratio of Milk and water in newly formed mixture is 9 : 4

Given statement: Should taxes be abolished in a developing country like India?

The logic followed is:

According to the given information,

Arguments 1 1 This is implicit because if a country wants to be a developed country it needs money for development and taxes are a good source of income for the government.

Arguments 2 → This is not implicit this is not a valid reason for taxes being abolished in a developing country like India.

Hence, “Only 1 argument is strong".

The Correct Answer is ​Lionel Messi.

In News

• FIFA Best Awards 2024 Winners announced.

Key Points

• Lionel Messi clinched the 2024 FIFA Best Men's Player Award, while Aitana Bonmatí secured the women's category prize.
• Men's coach: Pep Guardiola.
• Women's coach: Sarina Wiegman.
• Men's goalkeeper: Ederson.
• Women's goalkeeper: Mary Earps.
• Puskás Award: Guilherme Madruga.
• Men's world XI: Six Manchester City players included.
• Women's world XI: England Lionesses with seven representatives.
• Fair Play: Brazil men's national team for efforts fighting racism.
• The FIFA Fan Award 2023 went to Argentinian fan Hugo Daniel “Toto” Iniguez​​.