Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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") =` ____________.

`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.

`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.

`"cos" (2  "tan"^-1 1/7) - "sin" (4  "sin"^-1 1/3) =` ____________.

The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.