Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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 ?

  1. $900m$
  2. $320m$
  3. $680m$
  4. $720m$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $720-400=320\ mtrs$

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

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

  1. $4$
  2. $0$
  3. $-4$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $2x^{2} - 3x - 2$
  2. $3x^{2} - 6x - 2$
  3. $4x^{2} - 6x +4$
  4. $2x^{2} - 6x - 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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} $

Multiple choice 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

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

  1. $\dfrac {3}{8}$
  2. $\dfrac {7}{16}$
  3. $\dfrac {1}{4}$
  4. $\dfrac {13}{32}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

5/16 = 0.3125 and 1/2 = 0.5. Comparing options: 3/8 = 0.375 (in range), 7/16 = 0.4375 (in range), 1/4 = 0.25 (not in range), 13/32 = 0.40625 (in range).

Multiple choice 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

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

  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. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 0.9 < 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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


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

Multiple choice 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

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

  1. $1.5,\ 1.6$
  2. $1.4,\ 1.6$
  3. $1.5,\ 1.8$

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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}) $

Multiple choice 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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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) $.

Multiple choice 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

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

  1. $\displaystyle \frac{3}{4}$
  2. $\displaystyle \frac{99}{122}$
  3. $\displaystyle \frac{95}{112}$
  4. $\displaystyle \frac{97}{112}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

Multiple choice 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

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

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
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.