Tag: maths

Questions Related to maths

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?

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

  1. $-7$

  2. $-4$

  3. $7$

  4. $1.75$

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Correct Option: A
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 $=-2\times 3.5=-7$

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

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

  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

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Correct Option: A,B
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.

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

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

  1. $0$

  2. $(a+b)^{3}$

  3. $a^{3}-b^{3}$

  4. $(a^{2}+b^{2})$

Show answer
Correct Option: B
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.


If $(\vec{a}\times\vec{b})^{2}+(\vec{a}.\vec{b})^{2}=144$ and $|\vec{a}|=4,\ |\vec{b}|=$

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

  1. $16$

  2. $8$

  3. $3$

  4. $5$

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Correct Option: C

One of the following is not a vector

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

  1. displacement

  2. work

  3. centrifugal force

  4. gravitational field

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Correct Option: B
Explanation:

Displacement,Centrifugal force and Gravitation are vectors.
Work $W=\overrightarrow { F } \cdot \overrightarrow { S } $ a scalar.
Hence, option B.

Which one of the following is not a scalar quantity?

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

  1. Temperature

  2. Density

  3. Mass

  4. Weight

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Correct Option: D
Explanation:

Temperature,Density,Mass are clearly scalars.
Whereas in case of weight, it acts always downwards beacuse of
accelration due to gravity.
Hence, option D.

If a be an unit vector then

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

  1. direction of a is constant

  2. magnitude of a is constant

  3. direction and magnitude of a is constant

  4. any one of direction or magnitude is constant.

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Correct Option: C
Explanation:

For a given unit vector , Magnitude and direction are constant (fixed).
since, a vector cannot have two directions.
Hence, option C.

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

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

  1. Co-initial vectors

  2. Colinear vectors

  3. Equal Vectors

  4. Unit Vector

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Correct Option: C
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.

A line PQ is symbolically written as

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

  1. PQ

  2. $\overrightarrow{PQ}$

  3. $\overleftrightarrow{PQ}$

  4. None of these

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Correct Option: C
Explanation:

We know that the symbolically is  $\leftrightarrow$

now,  option $C$ is correct.

A ray has ................ end point/points.

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

  1. 1

  2. 2

  3. 3

  4. no

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Correct Option: A
Explanation:

In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and taken to be at infinity.