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

If tan\(\theta\) + cot \(\theta\) = 5 then tan³ \(\theta\) + cot³ \(\theta\) is equal to ______.

If first and last terms ofanAP. are 3 and 18 and the sum of its terms is 84, then number of terms will be ______.

In the parabola y2 = 4ax,the length of the chord passing through the vertex and inclined to the axis at π/4 is ________.

State which of the following sets are finite and which are infinite?
B = {x : x \(\in\) Z and x² is even}

Find equation of the circle with centre (5,-2) and radius 3.

Evaluate the following limit \(\lim_ { x\rightarrow \pi /2 }{ lim } \frac { { cos }^{ 2 }x }{ 1-sin x } \)

A and B are mutually exclusive events of an experiment. If P(not A)=0.65, \(P(A\cup B)=0.65\) and P(B) = p, then find the value of p.

Let R be a relation of N defined by R={(a,b):a,b\(\epsilon \)N and a=b²} Are the following true?
(a,a)\(\epsilon \)R for all a\(\epsilon \)N

If \(cos\theta =\frac { cos\alpha -cos\beta }{ 1-cos\alpha cos\beta } ,\) then prove that \(tan\frac { \theta }{ 2 } =\pm tan\frac { \alpha }{ 2 } cot\frac { \beta }{ 2 } .\)

If z₁ = 3+2i and z₂ = 2-4i, then verify that \({ \left| { z }_{ 1 }+{ z }_{ 2 } \right| }^{ 2 }+ { \left| { z }_{ 1 }-{ z }_{ 2 } \right| }^{ 2 }=2({ \left| { z }_{ 1 } \right| }^{ 2 }+{ \left| { z }_{ 2 } \right| }^{ 2 })\)

In how many different ways, the letters of the word 'ALGEBRA' can be arranged in a row, if  the two A's are together?

How many terms of GP\(3,\frac { 3 }{ 2 } ,\frac { 3 }{ 4 } \),...are needed to give the sum \(\frac { 3069 }{ 512 } \)?

Find the equation of an ellipse, if it satisfies the condition b = 3, c = 4, centre at the origin, foci on the X-axis.

Find the derivative of \(\frac{x^{n}-a^{n}}{x-a}\) for some constant a.

If X = {a,b,c,d} and Y = {f,b,d,g}, then find 
\(X\cap Y\)

In a \(\Delta\)ABC prove that,
\(\cfrac { co{ s }^{ 2 }(\cfrac { B-C }{ 2 } ) }{ (b+c{ ) }^{ 2 } } +\cfrac { si{ n }^{ 2 }(\cfrac { B-C }{ 2 } ) }{ (b-c{ ) }^{ 2 } } ={ a }^{ -2 }\)

If x and y are any two distinct integers, then prove by mathematical induction that \(\left( { x }^{ n }-{ y }^{ n } \right) \) is divisible by (x-y), for all \(n\in N\)

If a line passes through (2,2) and is perpendicular to the line 3x + y = 3, then find its y-intercept.

By giving a counter example, shows that the following statement is not true.
p: If all the angles of a triangle are equal, than the triangle is an obtuse angled triangle.

From a well-shuffled deck of 52 cards is drawn at random. Find the probability of getting a face card.