Check whether the following sets are disjoint where p = {x : x is a prime < 15} and Q = {x : x is a multiple of 2 and x < 16}

If A⊂B then find A⋂B and A\B (using venn diagram)

Show that the relation R on the set A = {1, 2, 3} given by R = {(1, 1) (2, 2) (3, 3) (1, 2) (2, 3)} is reflexive but neither symmetric nor transitive.

Show that the function f : N➝N given by f(x) = 2x is one-one but not onto.

Let S = {1, 2, 3,....,10}. Define 'm is related to n' if m divides n.

Let P denote the set of all straight lines in a plane. Let R be the relation defined on P as lR m if I is parallel to m

If  \(f(x)=\frac { x-1 }{ x+1 } \), then show that \(f\left( \frac { 1 }{ x } \right) =-f(x)\)

Find the domain and range of the function f(x) = \(\frac { { x }^{ 2 }-9 }{ x-3 } \).

Solve |3x - 4| = |x-2|

Solve \(\frac{1}{|3x-2|}<2\) and express using interval notching.

Find the domain and range of the real valued function f(x) = \(\frac{5-x}{x-5}\).

Solve: (x - 2)(x + 3)²< 0

Prove that 2\(cos\left( \frac { \pi }{ 13 } \right) cos\left( \frac { 9\pi }{ 13 } \right) +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } \) = 0

Prove that \(\frac { 1+sinx-cosx }{ 1+sinx+cosx } =tan\frac { x }{ 2 } \) .

Let p(n) be the statement "7 divides 2³ⁿ-1" What is p(n+1) =?

If ⁵P_r = ⁷P_r-1 find r.

Find the greatest term in (1 + 2x)⁸ when x = 2.

Write down the series whose r^th  term is \(\frac{1}{3}r\). Is it an arithmetic series?

Transform the equation 3x + 4y + 12 = 0 in to normal form.

Solve\(\left[ \begin{matrix} { x }^{ 2 } \\ { y }^{ 2 } \end{matrix} \right] -3\left[ \begin{matrix} x \\ 2y \end{matrix} \right] =\left[ \begin{matrix} -2 \\ 9 \end{matrix} \right] \)

Prove that \(\left| \begin{matrix} 1 & 1+p & 1+p+q \\ 2 & 3+2p & 4+4p+2q \\ 3 & 6+3p & 10+6p+3q \end{matrix} \right| =1\)

Prove that \(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{matrix} \right| =xy\)

Evaluate\(\lim _{ x\rightarrow 0 }{ \frac { { x }^{ \frac { 2 }{ 3 } }-9 }{ x-27 } } \)

\(If\lim _{ x\rightarrow 2 }{ \frac { { x }^{ n }-{ 2 }^{ n } }{ x-2 } } =80\quad and\quad n\in N,\quad find\quad n.\)

Show that the function is \(f\left( x \right) =\begin{cases} \frac { \sin { x } }{ x } +\cos { x,\quad x\neq 0 } \\ 2,\quad \quad \quad x=0 \end{cases}\) continuous at x =0.