What is the main use of index numbers in economics?

Important Questions on Complex Numbers and Quadratic Equations

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The mean and variance for seven observations are $8$ and $16$ respectively. If $5$ of the observations are $2,4,10,12,14,$ then the product of the remaining two observations is

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If $\sum _{i=1}^9\left(x_i-5\right)=9$ and $\sum _{i=1}^9{\left(x_i-5\right)}^2=45$, then the standard deviation of the $9$ items $x_1, x_2,\dots .,x_9$ is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If the standard deviation of the numbers $-\mathrm{1,} 0, 1, k$ is $\sqrt{5}$ where $k>0,$ then $k$ is equal to

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Time $\left(T\right)$, velocity $\left(C\right)$ and angular momentum $\left(h\right)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3,4$ and $4$; then the absolute value of the difference of the other two observations, is :

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If the data $x_1,x_2,\dots x_{10}$ is such that the mean of first four of these is $11,$ the mean of the remaining six is $16$ and the sum of squares of all of these is $2000$, then the standard deviation of this data is:

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

A student scores the following marks in five tests: $\mathrm{45,54,41,57,43}$. His score is not known for the sixth test. If the mean score is $48$ in the six tests, then the standard deviation of the marks in six tests is

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

An urn contains $5$ red, $2$ white and $3$ black balls. Three balls are drawn, one-by-one, at random without replacement. Find the probability distribution of the number of white balls. Also, find the mean and the variance of the number of white balls drawn.

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

For all complex numbers $z$ of the form $1+i\alpha , \alpha \in R,$ if $z^2=x+iy,$ then 

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The variance of the first $50$ even natural numbers is :

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The mean of five observations is $5$ and their variance is $9.20.$ If three of the given five observations are $\mathrm{1,} 3$ and $8,$ then a ratio of other two observations is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If the mean and standard deviation of $5$ observations $x_1, x_2, x_3, x_4, x_5$ are $10$ and $3,$ respectively, then the variance of $6$ observations $x_1, x_2, \dots , x_5$ and $-50$ is equal to

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum $\sum _{n=1}^{13}\left(i^n+i^{n+1}\right), \text{where} i=\sqrt{-1},$equals

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

For positive integers $n_1, n_2$ the value of the expression ${\left(1+i\right)}^{n_1}+{\left(1+i^3\right)}^{n_1}+{\left(1+i^5\right)}^{n_2}+{\left(1+i^7\right)}^{n_2}, i=\sqrt{-1}$ is a real number if and only if

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If $\left|\frac{1-iz}{z-i}\right|=1,$ then $z$ lies on

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The maximum value of $\left|z\right|$where $z$satisfies the condition $\left|z+\frac{2}{z}\right|=2$, is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum $\sum _{n=1}^{13}(i^n+i^{n+1})$, where $i=\sqrt{-1}$, equals

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If the complex number $z$ satisfy the equation $\left(i-z\right)\left(1+2i\right)+\left(1-iz\right)\left(3-4i\right)=1+7i,$ then $z+\overline{z}+z\overline{z}$ is equal to -

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The equation, whose roots are $i,\frac{1+i}{\sqrt{2}},\frac{i-1}{\sqrt{2}},$ their conjugates, $-1 \mathrm{and}\mathrm{ }1$ is