The question asks to identify a metal from the given options. To answer this, we need to recall the classification of elements into metals, non-metals, and metalloids based on their properties and position in the periodic table.
Correct Option: B) Sodium is an alkali metal, characterized by its metallic properties such as good conductivity, malleability, and tendency to form positive ions.
This problem involves the relationship between the ratio of corresponding sides of similar triangles and the ratio of their areas. A fundamental theorem in geometry states that if two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
A) 25 : 36 is the correct answer because the ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Given the side ratio of 5:6, the area ratio is \(5^2 : 6^2 = 25 : 36\).
Rohit started on his bicycle from his home and travelled a distance of 5 km in the south direction. He then turned towards the right and travelled a distance of 2.5 km, and again took a turn towards the right and travelled a distance of 5 km. Finally, after taking a left turn, he travelled a distance of 5 km. What is the shortest distance between his present location and his home? (All turns are 90-degree turns only.)
This problem involves calculating the shortest distance between two points, which can be visualized as a displacement problem. We need to track Rohit's movements in a coordinate system or by drawing a path, then use the Pythagorean theorem or simple addition/subtraction of distances along perpendicular axes to find the final displacement.
B) 7.5 km is the shortest distance between Rohit's present location and his home, as calculated by tracking his movements.
The question asks to identify the Indian state where the Bushu Jiba festival is celebrated. This requires knowledge of Indian festivals and their regional associations.
Correct Option: D) Nagaland
The Bushu Jiba festival is a significant post-harvest festival celebrated by the Dimasa Kachari tribe. This tribe is one of the oldest inhabitants of the North Eastern region of India, with a substantial population residing in Nagaland, particularly in the Dimapur district, and also in parts of Assam. The festival is a celebration of a good harvest and includes traditional dances, songs, and feasts.
The pH of a salt solution depends on the nature of the acid and base from which the salt is formed. A pH greater than 7 indicates a basic solution. We need to identify the salt that, upon dissolving in water, undergoes hydrolysis to produce a basic solution.
C) K₂CO₃ is a salt formed from a strong base (KOH) and a weak acid (carbonic acid, H₂CO₃). When dissolved in water, the carbonate ion (CO₃²⁻) hydrolyzes, reacting with water to produce hydroxide ions (OH⁻), which increases the pH of the solution above 7, making it basic.
If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘+’, what will come in place of the question mark (?) in the following equation?
44 ÷ 120 × 5 − 2 + 10 × 2 =?
This problem requires us to substitute the given new meanings for mathematical operators into the given equation and then solve it using the BODMAS/PEMDAS rule (Order of Operations).
The original equation is: \(44 \div 120 \times 5 \minus 2 + 10 \times 2 = ?\)
Applying the changes:
So, the new equation is:
\[ 44 + 120 \div 5 \times 2 \minus 10 \div 2 = ? \]BODMAS/PEMDAS stands for Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction. We perform operations from left to right for Division/Multiplication and then for Addition/Subtraction.
First, perform divisions:
\[ 44 + (120 \div 5) \times 2 \minus 10 \div 2 \]\[ 44 + 24 \times 2 \minus (10 \div 2) \]\[ 44 + 24 \times 2 \minus 5 \]Next, perform multiplication:
\[ 44 + (24 \times 2) \minus 5 \]\[ 44 + 48 \minus 5 \]Finally, perform addition and subtraction from left to right:
\[ (44 + 48) \minus 5 \]\[ 92 \minus 5 \]\[ 87 \]C) 87
The question asks to identify the mountain range where Doddabetta peak, the highest peak, is located. This requires knowledge of the major hill ranges in South India and their prominent peaks.
Correct Option: D) Doddabetta peak is the highest mountain peak in the Nilgiri Hills. It is located in the Nilgiris district of Tamil Nadu, India, and is a popular tourist destination.
This question tests fundamental knowledge of spherical mirrors and their associated terminology. Understanding the definitions of key points and distances related to spherical mirrors is crucial.
B) centre of curvature and pole — The radius of curvature is defined as the distance between the centre of curvature (C) and the pole (P) of the spherical mirror. This is the standard definition in optics.
The problem asks us to calculate the total cost of 3 pens and 2 pencils, given the relationship between the cost of a pen and a pencil, and the cost of one pencil. We will first determine the cost of one pen and then calculate the total cost.
The problem states that the cost of a pencil is Rs 1.
\[ \text{Cost of 1 pencil} = \text{Rs } 1 \]The problem states that the cost of a pen is twice the cost of a pencil.
\[ \text{Cost of 1 pen} = 2 \times \text{Cost of 1 pencil} \]\[ \text{Cost of 1 pen} = 2 \times \text{Rs } 1 = \text{Rs } 2 \]Now, we find the total cost for 3 pens.
\[ \text{Cost of 3 pens} = 3 \times \text{Cost of 1 pen} \]\[ \text{Cost of 3 pens} = 3 \times \text{Rs } 2 = \text{Rs } 6 \]Next, we find the total cost for 2 pencils.
\[ \text{Cost of 2 pencils} = 2 \times \text{Cost of 1 pencil} \]\[ \text{Cost of 2 pencils} = 2 \times \text{Rs } 1 = \text{Rs } 2 \]Finally, we add the cost of 3 pens and 2 pencils to get the total cost.
\[ \text{Total Cost} = \text{Cost of 3 pens} + \text{Cost of 2 pencils} \]\[ \text{Total Cost} = \text{Rs } 6 + \text{Rs } 2 = \text{Rs } 8 \]Correct Option: D) Rs 8