PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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\[F = \frac{9}{5}C + 32\]

A solution is to be kept between 30°C and 35°C. What is the range of temperature in degree Fahrenheit? 

To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four paper, find the minimum marks that she must score in the last paper to get grade 'A' in the course. 

A company manufactures cassettes and its cost and revenue functions for a week are \[C = 300 + \frac{3}{2}x \text{ and } R = 2x\] respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit? 

The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content? 

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.