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

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))`

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

Prove that: `sin^2  pi/6 + cos^2  pi/3 - tan^2  pi/4 = -1/2`

Prove that  `2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2`

Prove that  `cot^2  pi/6 + cosec  (5pi)/6 + 3 tan^2  pi/6 = 6`

Prove that: `2 sin^2  (3pi)/4 + 2 cos^2  pi/4  + 2 sec^2  pi/3 = 10`

Find the value of: sin 75°