PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Are the following pair of sets equal? Give reasons.

A = {x : x is a letter in the word FOLLOW};

B = {y : y is a letter in the word WOLF}

From the sets given below, select equal sets:

A = {2, 4, 8, 12},
B = {1, 2, 3, 4},
C = {4, 8, 12, 14},
D = {3, 1, 4, 2},
E = {-1, 1},
F = {0, a},
G = {1, -1},
H = {0, 1}

Assume that P (A) = P (B). Show that A = B.

Find the domain and range of the given real function:

f(x) = – |x|

Find the domain and range of the following real function:

f(x) = `sqrt(9 - x^2)`

A function f is defined by f(x) = 2x – 5. Write down the values of f(0).

The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by `t(C) = "9C"/5 + 32`

Find

(i) t(0)

(ii) t(28)

(iii) t(–10)

(iv) The value of C, when t(C) = 212.

Find the range of the following function.

f(x) = 2 – 3x, x ∈ R, x > 0.

Find the range of the following function.

f(x) = x² + 2, x, is a real number.

Find the range of the following function.

f(x) = x, x is a real number

Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`

Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from R into R. Determine the range of f.

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}.