PART - 2 CH - 12 Limits and Derivatives — MATHS STD 11 Science — Question

The sum of terms equidistant from the beginning and end in an A.P. is equal to _____.

Fill in the blanks:
The x-axis and y-axis taken together determine a plane known as_______.

A point moves so that square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 3. The equation of its locus is ____.

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______________.

Fill in the Blank.
The number of six-digit numbers, all digits of which are odd is ______.

A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.
[Hint: At least 3 men and 2 women: The number of ways = ¹⁰C₃ × ⁷C₃ + ¹⁰C₄ × ⁷C₂ . For 2 particular women to be always there: the number of ways = ¹⁰C4 + ¹⁰C₃ × ⁵C₁ . The total number of committees when two particular women are never together = Total – together.]

¹⁵C₈ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ = ______.