Tag: maths

Questions Related to maths

What will be the Remainder when $3x^{3} - 2x^{2} - 7x + 6$ is divided by $x + 1$?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $4$

  2. $5$

  3. $8$

  4. $0$

Show answer
Correct Option: C
Explanation:

Let $f(x)=3x^3-2x^2-7x+6$

To find out reminder when equation is divided by $x+1$ we should calculate $f(-1)$
$f(-1)=3(-1)^3-2(-1)^3-7(-1)+6$
            $=13-5=8$

A body falling from rest under gravity passes a certain point $P$.It was a distance of $400m$ from P and $4$ sec prior to passage through $P$ If $g=10m/sec^2$,then the height above the point $"P"$ from where the body began to fall is ?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $900m$

  2. $320m$

  3. $680m$

  4. $720m$

Show answer
Correct Option: B
Explanation:
Distance travelled $=400\ m$.
Time$=4\ sec$
$B=10m/s^{2}$
$s=ut+1/2 at^{2}$
$400=4u-1/2\times 10\times 16\times 5$
$400=4u-80$
$4u=480$
$u=120$
At highest point
$V=0$
${u}^{2}=2\times g\times h$
$120\times 120=2\times 10\times h$
$h=720$
This height is from $400\ mtr$ below $P$ 
So height above $P$ is $720-400=320\ mtrs$

The remainder when $x^3 + 4x^2 - 7x + 6$ is divided by $(x - 1)$ is

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $4$

  2. $0$

  3. $-4$

  4. $3$

Show answer
Correct Option: A
Explanation:

Let $f\left( x \right) =x^{ 3 }+4x^{ 2 }-7x+6$
As $f\left( x \right) $ is divided by $x-1$, substituting $x=1$ in $f\left( x \right) $ we get
$f\left( 1 \right) =1^{ 3 }+4\cdot1^{ 2 }-7\cdot1+6=4$
Hence, $4$ is the remainder.

What will be the Quotient when $4x^{3} - 8x^{2} - x + 5$ is divided by $2x - 1$?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $2x^{2} - 3x - 2$

  2. $3x^{2} - 6x - 2$

  3. $4x^{2} - 6x +4$

  4. $2x^{2} - 6x - 2$

Show answer
Correct Option: A
Explanation:

Given: equation $4x^3-8x^2-x+5$

To find the quotient when divided by $2x-1$
Sol: $2x-1)\overline{4x^3-8x^2-x+5}(2x^2-3x-2)\\quad\quad \quad 4x^3-2x^2\\quad\quad\quad \overline{\quad \quad -6x^2-x}\\quad\quad\quad\quad\quad- 6x^2+3x\\quad\quad\quad\overline{\quad\quad\quad\quad \quad -4x+5}\\quad\quad\quad\quad\quad\quad \quad \quad- 4x+2\\quad\quad\quad\quad\overline {\quad\quad\quad\quad\quad\quad\quad 3} $

The rational number is not lying between $\dfrac {5}{16}$ and $\dfrac {1}{2}$ is _________.

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. $\dfrac {3}{8}$

  2. $\dfrac {7}{16}$

  3. $\dfrac {1}{4}$

  4. $\dfrac {13}{32}$

Show answer
Correct Option: C

Find 9 rational numbers between  $2$ and $3$

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. $2 < 2.1 < 2.2 < 3.3 < 2.4 < ... < 2.9 < 3$

  2. $2 < 4.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

  3. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

  4. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 0.9 < 3$

Show answer
Correct Option: C
Explanation:

$2 < 2.1=(2+0.1) < 2.2=(2.1+0.1) < 2.3=(2.2+0.1) < 2.4=(2.3+0.1) < ... < 2.9=(2.8+0.1) < 3=(2.9+0.1)$


$2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

Write two rational numbers between $\displaystyle \sqrt{2}$ and $\displaystyle \sqrt{3}.$

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. $1.5,\ 1.6$

  2. $1.4,\ 1.6$

  3. $1.5,\ 1.8$

  4. none of the above

Show answer
Correct Option: A
Explanation:

We know that, $ \sqrt {2} = 1.414

$ and $ \sqrt {3} = 1.732 $

Hence two rational numbers between $ 1.414 $ and $ 1.732

$  can be $ 1.5 (= \frac {3}{2}) $ and $ 1.6 (= \frac {16}{10}= \frac {8}{5}) $

Write three rational numbers between $\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{5}$.

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. 1.8,2 and 2.2

  2. 1.6,2 and 2.2

  3. 1.8,2.2 and 2.4

  4. none of the above

Show answer
Correct Option: A
Explanation:

We know that, $ \sqrt {3} = 1.732$ and $ \sqrt {5} = 2.236 $

Hence three rational numbers between $ 1.732 $ and $ 2.236$  can be $ 1.8 \left(= \dfrac {18}{10}\right)  $ , $ 2 $ and $ 2.2 \left(= \dfrac {22}{10}\right) $.

Which one of the following is the rational number lying between $\displaystyle \frac{6}{7} \ and \ \frac{7}{8}?$

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. $\displaystyle \frac{3}{4}$

  2. $\displaystyle \frac{99}{122}$

  3. $\displaystyle \frac{95}{112}$

  4. $\displaystyle \frac{97}{112}$

Show answer
Correct Option: D
Explanation:

Required rational number $\displaystyle =\frac{1}{2}\left ( \frac{6}{7}+\frac{7}{8} \right )=\frac{1}{2}\left ( \frac{48+49}{56} \right )=\frac{97}{112}$
Hence option (d) is correct

The number of integers between $\displaystyle -\sqrt{8}: and: \sqrt{32} $ is

maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

  1. 5

  2. 6

  3. 7

  4. 8

Show answer
Correct Option: D
Explanation:
We will find the number of integers as follows,
√8 = 2.8 ( approximately )
- √8 = - 2.8
√32 = 5.6 ( approximately )
Now integers between -2.8 and 5.6 are
-2, -1, 0, 1, 2, 3, 4, 5
and a total of 8 numbers
Option D is the correct answer.