Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a is less than 6 and a ∈ Y

Suppose A₁, A₂, ..., A₃₀ are thirty sets each having 5 elements and B₁, B₂, ..., Bn are n sets each with 3 elements, let \[\bigcup\limits_{i=1}^{30} A_{i} = \bigcup\limits_{j=1}^{n} B_{j}\] = and each element of S belongs to exactly 10 of the A_i’s and exactly 9 of the B,’S. then n is equal to ______.

If X = {8ⁿ – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.

State True or False for the following statement.

If A is any set, then A ⊂ A.

State True or False for the following statement.

Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.

State True or False for the following statement.

The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.

State True or False for the following statement.

Q ∪ Z = Q, where Q is the set of rational numbers and Z is the set of integers.

Find x and y if: (4x + 3, y) = (3x + 5, – 2)

Find x and y if: (x – y, x + y) = (6, 10)

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

f(3) + g(– 5)

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

`f(1/2) xx g(14)`

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

f(– 2) + g(– 1)

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

f(t) – f(– 2)

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

`(f(t) - f(5))/(t - 5)`, if t ≠ 5

Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) = g(x)?

Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) < g(x)?

If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x² + 1, then find fg

If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x² + 1, then find `f/g`

Find the values of x for which the functions f(x) = 3x² – 1 and g(x) = 3 + x are equal.

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g(x) = αx + β, then what values should be assigned to α and β?