Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

• The above-defined relation R is ____________.

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

• Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

• Let R ∶ B → B be defined by R = {(x, y): y is divisible by x} is ____________.

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

• Let R be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R is:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

• Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

• Let R: B → B be defined by R = {(1,1),(1,2), (2,2), (3,3), (4,4), (5,5), (6,6)}, then R is ____________.

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b₁,b₂,b₃} G={g₁,g₂} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

• Ravi wishes to form all the relations possible from B to G. How many such relations are possible?

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b₁,b₂,b₃} G={g₁,g₂} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

• Let R: B → B be defined by R = {(x, y): x and y are students of same sex}, Then this relation R is ____________.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

• Let relation R be defined by R = {(L₁, L₂): L₁║L₂ where L₁, L₂ ∈ L} then R is ____________ relation.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

• Let R = `{ ("L"_1, "L"_2) ∶ "L"_1 bot "L"_2  "where"  "L"_1, "L"_2 in "L" }` which of the following is true?

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

• Let R = {(L₁, L₂ ): L₁ is parallel to L₂ and L₁: y = x – 4} then which of the following can be taken as L₂?

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.

The relation R = {(1,1),(2,2),(3,3)} on {1,2,3} is ____________.

Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.

The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is ____________.

A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform ____________.

The rate of change of area of a circle with respect to its radius r at r = 6 cm is ____________.

Total revenue in rupees received from the sale of x units of a product is given by R(x)= 3x²+ 36x + 5. The marginal revenue, when x = 15 is ____________.

If the rate of change of the area of the circle is equal to the rate of change of its diameter then its radius is equal to ____________.

The rate of change of volume of a sphere is equal to the rate of change of the radius than its radius equal to ____________.