PART - 1 CH - 2 Relations and Functions — MATHS STD 11 Science — Question

The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.

To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is ⁵C₃ × ²⁰C₉ .
In each if the Exercises from 60 to 64 match each item given under the column C1 to its correct answer given under the column C₂ .

The following stetements are true? Given reason to support your answer.
Every set has a proper subset.

If the sum of n terms of a sequence is quadratic expression, then it always represents an A.P.

State True or False for the following:
Multiplication of a non zero complex number by -i rotates the point about origin through a right angle in the anti-clockwise direction.

State Whether the statements are True or False. Justify.
The line x + 3y = 0 is a diameter of the circle x² + y² + 6x + 2y = 0.

For any complex number z the minimum value of |z| + | z - 1| is 1.

State True or False for the following statement:
If some or all of n objects are taken at a time, the number of combinations is 2^n–1.