Let U be the universal set containing 700 elements. If A and B are sub-sets of U such that n(A) = 200, n(B) = 300 and n(A \(\cap\) B) = 100, then n(A' \(\cap\) B') =___.

If 4 sin²\(\theta=1\) then the values of \(\theta\) are ______.

The three geometric means between the numbers 1 and 81 are ______.

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is _______.

Which of the following are sets? Justify your answer.
The collection of all even integers.

Find the co-ordinates of foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

Evaluate \(\lim_{x\rightarrow 1}[\frac{1}{x^{2}+x-2}-\frac{x}{x^{3}-1}]\)

One mapping is selected at ramdom from all the mappings of the set set B = {1,2,3,.......6} into itself.Find the probability that the mapping selected is one-to-one .

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)}. Are the following true?
(i) f is a relation from A to B
(ii) f is a function from A to B
Justify your answer in each case

Find the degree measure corresponding to following radians.
6 rad

Solve the quadratic equation \(\sqrt 5 x^2+x+\sqrt 5=0\).

If ⁿP_r=ⁿP_r+1 and ⁿC_r = ⁿC_r-1, find the values of n and r.

A man accepts a position with an initial salary of Rs.5200 per month. It is understood that he will receive an automatic increase of Rs.320 in the very next month and each month thereafter.
Find his salary for the tenth month.

Find the equation of parabola when the vertex is at (0, 0) and focus is at (0, -4).
As vertex and focus lies  on Y- axis, so use the equation of parabola in the form of x² =-4axy.

Find the derivative of the following functions, \(\frac { secx+tanx }{ secx-tanx } \) First, consider the given function as f(x). Then, use quotient rule to find the required derivative.

Solve for  \(x,\frac { 4 }{ x+1 } \le 3\le \frac { 6 }{ x+1' } x>0\)

Using binomial theorem, evaluate each of the following
\(\left( 12 \right) ^{ 5 }+\left( 8 \right) ^{ 5 }\)

Which of the lines 2x - y + 3 = 0 and ax - 4y - 7 = 0, is farther from the origin?

Using the section formula, show that the points, (2, -3, 4), (-1, 2, 1) and (0, \(\frac{1}{3}\), 2) are collinear.

Verify by method of contradiction p:\(\sqrt { 11 } \) is irrational.

Three coins are tossed once.Find the probability of getting 2 heads