PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if

The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is

The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are

The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is  

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

8 ____ A

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

0 ____ A

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

4 _____ A

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

2 _____ A

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

10 _____ A

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a function from A to B

Justify your answer in case.

The following example is the null set example or not?

Set of odd natural numbers divisible by 2

Which of the following are examples of empty set? 

Set of all even natural numbers divisible by 5

Which of the following are examples of empty set? 

Set of all even prime numbers

Which of the following are examples of empty set? 

 {x : x² −2 = 0 and x is rational}

Which of the following are examples of empty set? 

{x : x is a natural number, x < 8 and simultaneously x > 12};

Which of the following are examples of empty set? 

 {x : x is a point common to any two parallel lines}.

If P (n) is the statement "n(n + 1) is even", then what is P(3)?

If P (n) is the statement "n3 + n is divisible by 3", prove that P (3) is true but P (4) is not true.