Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

What is the number to be multiplied by $(-7)^{-1}$ so as to get $10^{-1}$ as the product?

  1. $\displaystyle\frac{-7}{10}$
  2. $\displaystyle\frac{7}{10}$
  3. $\displaystyle\frac{9}{10}$
  4. $\displaystyle\frac{-3}{10}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
let the number be $ x$
According to the question:
$\Rightarrow(-7)^{-1} x = 10 ^{-1}$
$\Rightarrow\dfrac{1}{-7^{1}}x = \dfrac{1}{10}$
Applying cross multiplication
$\Rightarrow x  = \dfrac{-7}{10}$


Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

Without actual multiplication, then value of $687 \times 687 - 313 \times 313$

  1. $3,50,004$
  2. $3,74,000$
  3. $5,74,000$
  4. $2,74,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$687\times687-313\times313$


$=(687)^2-(313)^2$

Using identity $(a+b)(a-b)=a²-b²$

$= (687+313)(687-313)$

$=1000\times374$

$= 3,74,000$

$\therefore \text{option B is correct}.$

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

If the solution as $\cos p\theta +\cos q\theta=0$ are in $AP$ then the common difference is

  1. $\dfrac {\pi}{p+q}$ or $\dfrac {\pi}{p-q}$
  2. $\dfrac {\pi}{p+q}$ or $\dfrac {\pi}{2(p-q)}$
  3. $\dfrac {\pi}{2(p+q)}$ or $\dfrac {\pi}{2(p-q)}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation cos(px) + cos(qx) = 0 implies 2cos((p+q)x/2)cos((p-q)x/2) = 0. Solving for x gives the roots in AP with the specified common differences.