Write the following in roster form.
The set of all positive roots of the equation (x-1)(x+1)(x²-1) = 0.

State whether the following sets are finite or infinite.
{x \(\in \) N : x is an even prime number}

Justify the trueness of the statement "An element of a set can never be a subset of itself".

Discuss the following relations for reflexivity, symmetricity and transitivity :
The relation R defined on the set of all positive integers by "mRn if m divided n".

Discuss the following relations for reflexivity, symmetricity and transitivity:
Let P denote the set of all straight lines in a plane. The relation R defined by "lRm if l is perpendicular to m".

If \(f:[-2,2]\rightarrow B\) is given by f(x) = 2x³, then find B so that f is onto.

Discuss the nature of roots of -x² + 3x + 1 = 0

Identify the quadrant in which an angle of each given measure lies; 25⁰

Express each of the following angles in radian measure
150⁰

If \(\triangle ABC\) is a right triangle and if \(\angle A=\frac{\pi}{2}\), then prove that \(\sin^2B+\sin^2C=1\)

Express each of the following as a sum or difference. 2 sin 10\(\theta\) cos 2\(\theta\)

Find the principal solution of sin \(\theta =-{\sqrt{3}\over 2}\).

A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

How many chords can be drawn through 20 points on a circle?

Find the value of \(\frac { 8! }{ 5!\times 2! } \).

Show that the sum of (m + n)^th and (m - n)^th term of an A.P is equal to twice the m^th term.

Write the n^th term of the following sequences
\(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

Write the equation of the lines through the point (1,-1)
(i) parallel to x + 3y - 4 = 0
(ii) perpendicular to 3x + 4y = 6

Suppose that a matrix has 12 elements. What are the possible orders it can have? What if it has 7 elements?

If \(\overrightarrow{PO}\) +\(\overrightarrow{OQ}\) = \(\overrightarrow{QO}\) +\(\overrightarrow{OR}\), prove that the points P, Q, R are collinear.

Evaluate \(lim_{x\rightarrow 2^-}\left\lfloor x \right\rfloor \) and \(lim_{x\rightarrow 2^+}\left\lfloor x \right\rfloor \) .

Differentiate the following: y = tan 3x

Integrate the following with respect to x : \({x^2\over x^3}\)

If two coins are tossed simultaneously, then find the probability of getting (i) one head and one tail (ii) at most two tails

A single card is drawn from a pack of 52 cards. What is the probability that
The card will be 6 or smaller?