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

The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is 

If a, b, c are in G.P. and a^1/x = b^1/y = c^1/z, then xyz are in

In the following, state whether A = B or not:

A = {a, b, c, d}; B = {d, c, b, a}

In the following, state whether A = B or not:

A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

In the following, state whether A = B or not:

A = {2, 4, 6, 8, 10}; B = {x : x is positive even integer and x ≤ 10}

In the following, state whether A = B or not:

A = {x : x is a multiple of 10}; B = {10, 15, 20, 25, 30, ...}

Are the following pair of sets equal? Give reasons.

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

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))`