For any two sets A and B, (A - B) \(\cup\) (B - A)=_____.

In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.

If the first term of an AP. is 5 and common difference is - 3 then sum of its 60 terms is equal to ______.

The latus rectum of the hyperbola \({ 16x }^{ 2 }-{ ay }^{ 2 }=144\quad is\) _______.

Write the following intervals of real numbers in the set·builder form:
(2,10)

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
x²=-18y

Evaluate the following limits \({lim}_{x\rightarrow -1}\)\(\frac{x^{10}+x^{5}+1}{x-1}\)

Two die are rolled together what is the probability that the sum of numbers on the two faces is neither divisible by 4 nor by 5?

If A={1,4}, B= {2,3,6} and C= {2,3,7}, then verify that 
\(A\times (B\cap C)=(A\times B)\cap (A\times C)\)

In a circle of diameter 44 cm, the length of chord is 22 cm. Find the length of minor arc of the chord.

Solve the equation \({ 25x }^{ 2 }-30x+11=0\) by using the general expression for the roots of a quadratic equation and show that the roots are complex conjugate.

A committee of 10 is to be formed form 8 gentleman and 9 ladies . In how many Wyas this can be done if atleat five ladies have to be included in a comittee? In how many of these committees
(i)the ladies are in majority?
(ii)the gentlement are in majority?

Express the 0.3 as rational

For some constants a and b, find the derivative of (ax²+b)².

There are 200 individuals with a skin disorder, 120 has been exposed to chemical C_1, 50 to chemical C₂ and 30 to both the chemicals C _1 ,  C ₂  . FInd  the number of individuals exposed to chemical C₁ but  not chemical C_2.

Prove that (2n+7)<(n+3)², for all natural numbers n.

If the integers r (>1), n (>2) and coefficients of (3r)th and (r + 2)nd terms in the expansion of (1 + x)²ⁿ are equal, then prove that n = 2r.

If the sum of the distance of a moving point in a plane from the axes is 1, then find the locus of the point.

Write the component statements of the following compound statement and check whether the compound statement is true or false
The sun is a star or Sun is plant

Calculate the mean deviation from the median for the following data.

Two dice are thrown simultaneously. Find the probability of getting an even number as the sum.