PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(i) A × B

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically: 

(ii) B × A

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:

(iii) A × A

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:

(iv) B × B 

Which of the following sets are equal?

\[A = \left\{ 1, 2, 3 \right\};\]

Which of the following sets are equal? 

(i) \[A = \left\{ 1, 2, 3 \right\};\] 

(ii) \[B = \left\{ x \in R : x^2 - 2x + 1 = 0 \right\};\] 

(iii) \[C = \left\{ 1, 2, 2, 3 \right\};\] 

(iv) \[D = \left\{ x \in R : x^3 - 6 x^2 + 11x - 6 = 0 \right\}\]

Are the following sets equal?
A = {x : x is a letter in the word reap}:
B = {x : x is a letter in the word paper};
C = {x : x is a letter in the word rope}.

From the sets given below, pair the equivalent sets: 

\[A = \left\{ 1, 2, 3 \right\}, B = \left\{ t, p, q, r, s \right\}, C = \left\{ \alpha, \beta, \gamma \right\}, D = \left\{ a, e, i, o, u \right\} .\]

Are the following pairs of sets equal? Give reasons. 

A = {2, 3}, B = {x : x is a solution of x² + 5x + 6 = 0}

Are the following pairs of sets equal? Give reasons. 

A = {x : x is a letter of the word " WOLF"};
    B = {x : x is a letter of the word " FOLLOW"}.

From the sets given below, select equal sets and equivalent sets.
A = {0, a}, B = {1, 2, 3, 4} C = {4, 8, 12}, D = {3, 1, 2, 4},
E = {1, 0}, F = {8, 4, 12} G = {1, 5, 7, 11}, H = {a, b}. 

Which of the following sets are equal?
A = {x : x ∈ N, x, < 3},
B = {1, 2}
C = {3, 1}
D = {x : x ∈ N, x is odd, x < 5},
E = {1, 2, 1, 1} F = {1, 1, 3}. 

Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal. 

The function f is defined by

For any set A, (A')' is equal to 

The set  \[\left( A \cup B' \right)' \cup \left( B \cap C \right)\] is equal to

Let F₁ be the set of all parallelograms, F₂ the set of all rectangles, F₃ the set of all rhombuses, F₄ the set of all squares and F₅ the set of trapeziums in a plane. Then F₁may be equal to

Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40. 

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks. 

A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by\[F = \frac{9}{5}C + 32\]