Tag: maths

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Questions Related to maths

Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

If the standard deviation of $x _1, x _2, .., x _n$ is $3.5$, then the standard deviation of $-2x _1-3, -2x _2-3$,....., -2x_n-3$ is?

  1. $-7$
  2. $-4$
  3. $7$
  4. $1.75$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The Standard Deviation of a set remains unchanged if each data is increased or decreased by a constant however changes similarly when data is multiplied or divided by a constant.
$\therefore $ The SD for the new data set will be $=-2\times 3.5=-7$
Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

Consider the following statements.Which of these is/are correct?

  1. Mode can be computed from histogram

  2. Median is not independent of change of scale

  3. Variance is independent of change of origin and scale

  4. none of these
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

If we change scale by using x + h then median increases by h.
so median is not independent of change of scale.
From histogram we can see highest frequency so made.
Hence, options 'A' and 'B' are correct.

Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

In a square matrix $A$ of order $3$ the elements, $a _{i\ i}s^{'}$ are the sum of the roots of the equation $x^{2}-(a+b)x+ab=0;\ a _{1,\ i+1}s^{'}$ are the product of the roots, $a _{1,\ i-i}s^{'}$ are all unity and the rest of the elements all zero. The value of the det. $(A)$ is equal to

  1. $0$
  2. $(a+b)^{3}$
  3. $a^{3}-b^{3}$
  4. $(a^{2}+b^{2})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given, square matrix $A$ of order $3$ with $a _{ii}= (a+b) $ (sum of roots)

$a _{1 i+1}=a _{12}=ab$  (product of roots)

$a _{1i-1}= a _{10}=1$

$|A|= \begin{vmatrix} (a+b) & 0 & 0 \\ 1 & (a+b) & ab \\ 0 & 0 & (a+b) \end{vmatrix}= (a+b)[(a+b)(a+b)-0]$

$=(a+b)^{3}$

$\therefore $ Option $B$ is correct.


Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

If two vectors have the same magnitude and direction regardless of the positions of their initial points, then they are

  1. Co-initial vectors

  2. Colinear vectors

  3. Equal Vectors

  4. Unit Vector
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 A quantity that has magnitude as well as direction is called a vector.  

or we can say ,
Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.