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Questions >> JEEMAIN and NEET >> Mathematics

Mathematics

Limit, Continuity and Differentiability

Sets, Relations and Functions

If $z$ is a complex number where $1+z+z^2=0$ , then the value of $(z+\large\frac{1}{z}$ $)^2+(z^2+\large\frac{1}{z^2}$ $)^2+(z^3+\large\frac{1}{z^3}$ $)^2+.......................(z^6+\large\frac{1}{z^6}$ $)^2$ = ?

asked Jul 5, 2013 by rvidyagovindarajan_1

1 answer

The complex number $z$ is such that $|z|=1,\:z\neq1\:and\:w=\large|\frac{z-1}{z+1}|.$ Then the real part of $w$ is ?

asked Jul 5, 2013 by rvidyagovindarajan_1

1 answer

Find the value of $\sum_{n=1}^{200}i^n$

asked Jul 4, 2013 by rvidyagovindarajan_1

1 answer

The area of the triangle with vertices $z,iz\:\:and\:\:-iz$ is ?

asked Jul 4, 2013 by rvidyagovindarajan_1

1 answer

The complex number $z$ , satisfying the equation $|\large\frac{z-5i}{z+5i}|=$ $1$ lies on?

asked Jul 4, 2013 by rvidyagovindarajan_1

1 answer

The number of complex numbers $z$ such that $|z-1|=|z+1|=|z-i|$ is ?

asked Jul 3, 2013 by rvidyagovindarajan_1

1 answer

If $\omega(\neq1)$ is a cube root of unity and $(1+\omega)^7=A+B\omega$ , then $(A,B)=?$

asked Jul 3, 2013 by rvidyagovindarajan_1

1 answer

If the conjugate of a complex number is $\large\frac{1}{i-1},$ then the complex number is?

asked Jul 3, 2013 by rvidyagovindarajan_1

1 answer

For any complex number $z$ the minimum value of $|z|+|z-1|$ is ?

asked Jul 2, 2013 by rvidyagovindarajan_1

1 answer

The number of solutions of the equation $z^2+\overline {z}=0$ is

asked Jul 2, 2013 by rvidyagovindarajan_1

1 answer

The identity element of the binary operation $\large $ defined on $Q-\{0\}$ as $a\large $ $b=\large\frac{ab}{2},$ $\forall \:a,b\:\in\:Q-\{0\}$

asked May 31, 2013 by rvidyagovindarajan_1

1 answer

If a relation $R$ on the set $\{1,2,3\}$ is defined as $R=\{(1,2)\}$ , then $R$ is

asked May 31, 2013 by rvidyagovindarajan_1

1 answer

If $f:[0,1]\rightarrow\:[0,1]$ is defined as $f(x)=\left \{\begin {array}{c,c}x &if\:x\:is\:rational\\1-x & if\:x\:is\:irrational\end {array}\right.$ then $fof(x)=?$

asked May 31, 2013 by rvidyagovindarajan_1

1 answer

The number of bijection mappings that are possible from $Set \:A$ containing 5 elements to $Set\:B$ containing 6 elements is ?

asked May 31, 2013 by rvidyagovindarajan_1

1 answer

The maximum number of equivalence relations on the set $A=\{1,2,3\}$ is?

asked May 31, 2013 by rvidyagovindarajan_1

1 answer

If $P=\{x:sinx-cosx=\sqrt2 cosx\}$ and $Q=\{x:sinx+cosx=\sqrt 2 sinx\}$ then which of the following is true ?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

Find the domain of $f(x)=\sqrt{cos(sinx)}+sin^{-1}\bigg(\large\frac{1+x^2}{2x}\bigg)$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

What type of set is "The set of poor students of a class"?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

Find the value of $\phi'$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

Find the domain of $sin(log(\large\frac{\sqrt{4-x^2}}{1-x}))$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If $n(A\times B)=8,$ then how many possible values are there for $n(A)?$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

Which of the following pairs of functions are equal ?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

What type of set is "The collection of novels written by Munshi Premchand" ?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is such that $f(x+y)=f(x).f(y)$ , then $f(0)$ = ?

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If function $f(x)$ is given by
$\small\left|\begin {array} {c,c,c} -cos(x+x^2) & -sin(x+x^2) & cos(x+x^2)\\sin(x^2-x) & -cos(x^2-x) & sin(x^2-x)\\sin2x &0 &sin2x^2 \end {array}\right|$ , then find $f(0)$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If $2^x+2^{f(x)}=2$ , then find the domain of $f(x)$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)$ is polynomial and $f(x).f(\large\frac{1}{x})$ $=f(x)+f(\large\frac{1}{x})$ and $f(3)=28$ then find $f(4)$

asked May 30, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=coslogx$ then $f(x^2).f(y^2)-\large\frac{1}{2}$ $(f(\large\frac{x^2}{y^2})$ $+f(x^2y^2))= ?$

asked May 29, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2\},$ then how many binary operations having 1 as identity and 2 as inverse of 2 are possible?

asked May 29, 2013 by rvidyagovindarajan_1

1 answer

If a set $A$ has 2 elements, then how many binary operations are possible in $A$ ?

asked May 29, 2013 by rvidyagovindarajan_1

1 answer

What is range of $f(x)=^{7-x}P_{x-3}$

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

If $g(x)=x^2+x-2\:\:and\:\:\large\frac{1}{2}$ $gof(x)=2x^2-5x+2$ then $f(x)= ?$

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=[x]^2+[x+1]-3$ where $[x]$ is greatest integer of $x$ , then what type of function is $f$ ?

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\left\{\begin{array}{c,c} |x| &x \leq 1 \\2-x &x>1\end{array}\right.$ , then $fof(x)=?$

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f:A\rightarrow B$ is defined as $f(x)=\sqrt 3 sinx+cosx+4$ and $f$ is invertible then find A.

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

The value of $a\:\:and\:\:b$ for which $f:R\rightarrow R$ is defined as $f(x)=ax+b$ where $a,b\in R$ is bijection with $fof$ as its identity is ?

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

Find the linear functions that maps $[-1,1]$ onto $[0,2]$ .

asked May 28, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3,4\}\:and\:B=\{3,4,7\}$ then the no. of onto functions from $A\rightarrow B$ =?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R\:\:and\:\:f(x)=|x|$ and $A=(0,1)$ , then find $f^{-1}(A)$

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f:[1,\infty )\rightarrow\:[2,\infty)$ is defined as $f(x)=x+\large\frac{1}{x}$ then find $f^{-1}(x)$ .

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f:A\rightarrow B$ is defined as $f(x)=x^2-x+1$ so that $f(x)=f^{-1}(x)$ then the solution set of $x$ is ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f(x)=x^2-x+1$ so that $f(x)=f^{-1}x$ then the solution set of $x$ is ?

asked May 27, 2013 by rvidyagovindarajan_1

0 answers

If $f(x)=x^n$ , $n\in N$ and $gof(x)=ng(x)$ , then $g(x)$ = ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f:A\rightarrow B$ , $3^{f(x)}+2^{-x}=4$ and $f(x)$ is bijection then the domain $A$ of $f(x)$ is ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f:Z\rightarrow Z$ is defined as $f(x)=x^2+ax+b$ then the values of $a$ and $b$ are ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

$If A\{x,y,z\},\:\:B=\{1,2,3\}$ and $f:A\rightarrow B\:\:is\:1-1\:$ function. Also one out of the following statements, $f(z)\neq 2,\:\:f(x)=1\:\:and\:\:f(y)\neq 1$ is true. then $f^{-1}(1)=?$

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

The Domain of $f(x)=\large^{7-x}P_{x-3}$ is ?

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:and\:x\geq 1\}$ and $f:A\rightarrow A$ is defined as $f(x)=2^{x(x-1)},$ then find $f^{-1}(x).$

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=6^x+6^{|x|}$ then what type of function is $f$ ?

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f(X)=\large\frac{kx}{1+x}$ , $x\neq1$ and $fof(x)=x$ , then find $k$ .

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

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