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}

• Three friends F₁, F₂, and F₃ exercised their voting right in general election-2019, then which of the following is true?

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 functions from A to B. How many number of functions 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.

• Ravi wants to know among those relations, how many functions can be formed from B to G?

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 → G be defined by R = { (b₁,g₁), (b₂,g₂),(b₃,g₁)}, 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 wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?

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.

• The function f: R → R defined by f(x) = x − 4 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 f: R → R be defined by f(x) = x − 4. Then the range of f(x) is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x².

Answer the following questions using the above information.

• Let f: R → R be defined by f(x) = x² is:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x².

Answer the following questions using the above information.

• Let f: N → N be defined by f(x) = x² is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x².

Answer the following questions using the above information.

• Let f: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x² is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x².

Answer the following questions using the above information.

• Let : N → R be defined by f(x) = x². Range of the function among the following is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x².

Answer the following questions using the above information.

• The function f: Z → Z defined by f(x) = x² is ____________.

If f: R → R given by f(x) =(3 − x³)^1/3, find f0f(x)

Let f: R → R defined by f(x) = x⁴. Choose the correct answer

Let f: R → R defined by f(x) = 3x. Choose the correct answer

The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.

Solve for x : `"sin"^-1  2"x" + "sin"^-1  3"x" = pi/3`

The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.

If `"tan"^-1 2  "x + tan"^-1 3  "x" = pi/4`, then x is ____________.

`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.