Tag: maths

Questions Related to maths

The quotient when  $1 + x ^ { 2 } + x ^ { 4 } + x ^ { 6 } + \dots + x ^ { 34 }$  is divided by  $1 + x + x ^ { 2 } + x ^ { 3 } + \dots + x ^ { 17 }$  is

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $x ^ { 17 } - x ^ { 15 } + x ^ { 13 } - x ^ { 11 } + \dots + x$

  2. $x ^ { 17 } + x ^ { 15 } + x ^ { 13 } + x ^ { 11 } + \dots + x$

  3. $x ^ { 17 } + x ^ { 16 } + x ^ { 15 } + x ^ { 14 } + \dots + 1$

  4. $x ^ { 17 } - x ^ { 16 } + x ^ { 15 } - x ^ { 14 } + \dots - 1$

Show answer
Correct Option: D
Explanation:
$1+x^2+x^4+\cdots+x^{34}=\dfrac{1-x^{36}}{1-x^2}$

$1+x+x^2+x^3+\cdots+x^{17}=\dfrac{1-x^{18}}{1-x}$

$\implies \dfrac{1+x^2+x^4+x^6+\cdots +x^{34}}{1+x+x^2+\cdots+x^{17}}=\dfrac{1-x^{36}}{1-x^{18}}\times \dfrac{1-x}{1-x^2}=\dfrac{1+x^{18}}{1+x}=x^{17}-x^{16}+x^{15}+\cdots-1$

What should be multiplied by $-23$ to get $575$?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $15$

  2. $25$

  3. $-25$

  4. $35$

Show answer
Correct Option: C
Explanation:

Let $x $ be multiplied by $-23$ to get $575$


$x (-23) = 575$


$x = \dfrac{575}{-23}$

$\therefore x = -25$

The number of positive n in the range $12\le n\le 40$ such that the product (n -1) (n -2).... 3.2.1 is not divisible by n is :

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 5

  2. 7

  3. 13

  4. 14

Show answer
Correct Option: B

The value of $4 \times 378 \times 25$ is 

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 37800

  2. 3780

  3. 9450

  4. 30078

Show answer
Correct Option: A
Explanation:

$4 \times 378 \times 25$


$=378 \times 4 \times 25$


$=378 \times 100$

$=37800$

The value of $47 \times 99$ is:

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 4635

  2. 4653

  3. 4563

  4. 6453

Show answer
Correct Option: B
Explanation:

Now,

$47\times 99$
$=47\times (100-1)$
$=4700-47$
$=4653$

Mark the correct alternative of the following.
The product of a whole number(other than zero) and its successor is?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. An even number

  2. An odd number

  3. Divisible by $4$

  4. Divisible by $3$

Show answer
Correct Option: A
Explanation:

Consider whole number is $a$


Case-I

$a$ is odd
So $a=2n+1$
Successor $a\neq 1$
                  $=2n+1+1$
                  $=2n+2$
product $=(2n+1)(2n+2)$ 
              $=2(2n+1)(n+1)$
              $=2r\rightarrow Even$

Case - II
$a$ is even
So $a=2n$
Successor $=2n+1$
Product $=2n(2n+1)$
              $=2r\rightarrow\,even$

So, The product of a whole number(other than zero) and its successor is an even number.

Mark the correct alternative of the following.
The product of the predecessor and successor of an odd natural number is always divisible by?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $2$

  2. $4$

  3. $6$

  4. $8$

Show answer
Correct Option: A,B
Explanation:

odd Natural Number

$2n+1$

Predecessor $=2n+1-1$
                      $=2n$

Successor     $=2n+1+1$
                      $=2n+2$


Product $=2n.(2n+2)$
              $=2n.2(n+1)$
              $=4.n(n+1)$
             $=4r$
                   $\downarrow$
          divisible by $4,2$

The product of the predecessor and successor of an odd natural number is always divisible by $4,2$.

6(7 x 3) = (6 x 7) x 3 is an example of

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. Associative property

  2. Closure property

  3. Commutative property

  4. Distributive property

Show answer
Correct Option: A
Explanation:

a(b x c ) = (a x b) x c is an example of associative property.

(98 + 14) x 0 is ________

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 112

  2. 1

  3. 0

  4. 0 + 98 + 14

Show answer
Correct Option: C
Explanation:

We know that for any number $n$ multiplied by $0$ is always $0$ that is $n\times 0=0$.


Now, let us consider the given expression $(98+14)\times 0$ and solve as follows:

$(98+14)\times 0=112\times 0=0$

Hence, $(98+14)\times 0=0$

What number should replaced M in This multiplication problem ? 

 3 M 4
$\displaystyle \frac{4}{\underline {1\, 2\, 1\, 6}}$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 0

  2. 5

  3. 7

  4. 8

Show answer
Correct Option: A
Explanation:

$0$ should be replaced M because
$304\times 4 = 1216$