Write the following in roster form {x\(\in \)N : 4x + 9 < 52}

Write the following in roster form.
\(\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\} \)

Discuss the following relations for reflexivity, symmetricity and transitivity :
On the set of natural numbers, the relation R is defined by "xRy if x + 2y = 1".

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it 
(i) reflexive
(ii) symmetric
(iii) transitive
(iv) equivalence

Solve for x \(\left| x \right| -10<-3\)

Represent the following inequalities in the interval notation:
\(x\ge -1\) and \(x<4\)

Express each of the following angles in radian measure
135⁰

Find the degree measure corresponding to the following radian measure; \(\frac { 2\pi }{ 5 } \)

Express each of the following as a product.
cos 65^o + cos 15^o

Find the principal value of tan^-1 \(({-1\over\sqrt{3}})\)

If (-2, -3) is a point on the terminal side of \(\theta\). Find all the trigonometrical ratios.

Evaluate \(\frac { n! }{ r!(n-r)! } \) when n = 10, r = 3

Evaluate: ⁸P₄.

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them 2018

Find the equation of the line through (1, 2) and which is perpendicular to the line joining (2, -3) (-1, 5)..

Show that x² - y² + x - 3y - 2 = 0 represents a pair of straight lines. Find also angle between the lines.

Give your own examples of matrices satisfying the following conditions in each case:
(i) A and B such that AB \(\neq\) BA.
(ii) A and B such that \(A B=O=B A, A \neq O \text {and } B \neq O \text {. }\)
(iii) A and B such that \(A B=O \text {and } B A \neq O\)

Find the direction cosines and direction ratios for the following vectors. 5\(\hat{i}\) - 3\(\hat{j}\) - 48\(\hat{k}\)

Find the direction cosines and direction ratios for the following vectors. \(\hat{i}\) - \(\hat{k}\)

Complete the table using calculator and use the result to estimate the limit.
\(lim_{x\rightarrow{2}}{x-2\over x^2-4}\)

x	1.9	1.99	1.999	2.001	2.01	2.1
f(x)	0.25641	0.25062	0.250062	0.24993	0.24937	0.24390

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow3}(4-x)\).

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow3}{1\over x-3}\)

Calculate \(lim_{x \rightarrow \infty}{1-x^3\over 3x+2}\)

Integrate the following with respect to x : x¹¹

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
\(P(\overline { A } \cup \overline { B } )\)