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Addition and subtraction - class-X

Description: addition and subtraction
Number of Questions: 23
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Tags: history of mathematics vedic mathematics maths
Attempted 0/23 Correct 0 Score 0

If $A, {A} _{1}, {A} _{2}, {A} _{3}$ be the area of the in-circle and ex-circles, then $\dfrac {1}{\sqrt {{A} _{1}}}+\dfrac {1}{\sqrt {{A} _{2}}}+\dfrac {1}{\sqrt {{A} _{3}}}$ is equal to

  1. $\dfrac {1}{\sqrt {{A}}}$

  2. $\dfrac {2}{\sqrt {{A}}}$

  3. $\dfrac {3}{\sqrt {{A}}}$

  4. $None$


Correct Option: A
Explanation:

$A _1={\pi}{r _1}^{2}=\dfrac{{\pi}{\Delta^{2}}}{(s-a)^{2}}$

$A _2={\pi}{r _2}^{2}=\dfrac{{\pi}{\Delta^{2}}}{(s-b)^{2}}$
$A _3={\pi}{r _3}^{2}=\dfrac{{\pi}{\Delta^{2}}}{(s-c)^{2}}$
$A={\pi}{r}^{2}=\dfrac{{\pi}{\Delta^{2}}}{(s)^{2}}$
$\dfrac{1}{\sqrt{A _1}}+\dfrac{1}{\sqrt{A _2}}+\dfrac{1}{\sqrt{A _3}}=\dfrac{1}{\sqrt{\pi}}\bigg[\dfrac{s-a}{\Delta}+\dfrac{s-b}{\Delta}+\dfrac{s-c}{\Delta}\bigg]=\dfrac{1}{\sqrt{\pi}\Delta}[3{s}-(a+b+c)]=\dfrac{s}{\sqrt{\pi}\Delta}=\dfrac{1}{\sqrt{A}}$

(?)$-19657-33994=9999$

  1. $63650$

  2. $53760$

  3. $59640$

  4. $61560$

  5. None of these


Correct Option: A
Explanation:

Let $x-53651=9999$
Then, $x=9999+53651=63650$

Perform the indicated operations:
$+7(-2)+(-8)+(+3)=$

  1. -17

  2. -18

  3. -19

  4. -20


Correct Option: C
Explanation:

The value of $+7(-2)+(-8)+(+3) $

$= -14-8+3 $
$= -19$

The algebraic expression for the statement: 'Product of x and a are subtracted from the product of b and y'.

  1. ax - by

  2. x + a - by

  3. by - ax

  4. xa - b - y


Correct Option: C
Explanation:

Product of x and a = xa

product of b and y = by
On subtraction: by-ax

(?)$+3699+1985-2047=31111$

  1. $34748$

  2. $27474$

  3. $30154$

  4. $27574$


Correct Option: B
Explanation:

$x+3699+1985-2047=31111$
$\Rightarrow$ $x+3699+1985=31111+2047$
$\Rightarrow$ $x+5684=33158$
$\Rightarrow$ $x=33158-5684=27474$

$(4300731)-$? $=2535618$

  1. $1865113$

  2. $1775123$

  3. $1765113$

  4. $1675123$

  5. None of these


Correct Option: C
Explanation:

Let $4300731-x=2535618$
Then, $x=4300731-2535618=1765113$

Subtract $347657$ by $238294$ using vinculum numbers.

  1. $109363$

  2. $100363$

  3. $109373$

  4. $109563$


Correct Option: A
Explanation:

1) The first thing we do is write these numbers one on top of the other.

347657
238294

2) Now we just start subtracting vertically, and whenever our number is negative we represent it as a vinculum number.

347657
238294

3) This next subtraction is 7 – 8 = -1…so we just write this as 1 and continue on.

347657
238294
1 1 443

4) The ‘1‘ and ‘4‘ here are considered as two separate groups (since theres a non-vinculum number in-between them), so each is subtracted from 10. This has the effect of reducing the “previous one” by one.

109363

In $32$ Ekanyunena Purvena of the digit $2$ is?

  1. $13$

  2. $12$

  3. $22$

  4. $10$


Correct Option: C

In $19$ Ekadhikena Purvena of digit $1$ is

  1. $120$

  2. $119$

  3. $20$

  4. $118$


Correct Option: B

In $2710$ Ekanyunena Purvena of digit $0$ is? 

  1. $2721$

  2. $2720$

  3. $2700$

  4. $2810$


Correct Option: C

$8597-$? $=7429-4358$

  1. $5246$

  2. $5706$

  3. $5526$

  4. $5476$

  5. None of these


Correct Option: C
Explanation:

  7429      Let $8597-x=3071$
-4358       Then,      $x=8597-3071$
--------                          $=5526$
3071
-------

Subtract $28375$ from $45678$ using Ekanyunena Purvena and Param mitra ank method.

  1. $17303$

  2. $19403$

  3. $13403$

  4. $15303$


Correct Option: A

Perform $79643+63405$ using Ekadhikena Purvena and Param mitra ank method.

  1. $143048$

  2. $138304$

  3. $23476$

  4. $12431$


Correct Option: A

Tarun studies for $5\dfrac{1}{4}$ hours daily. He devotes $2\dfrac{3}{4}$ hours of his time for English and Mathematics. How much time does he devote for other subjects ? 

  1. 2 hours

  2. $4\dfrac{2}{3}$ hours

  3. $2\dfrac{1}{2}$ hours

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


Correct Option: C
Explanation:

Total time period of Tarun's study

$=5\dfrac{1}{4}$ hours $=\dfrac{21}{4}$ hours
Time he devotes for English and Maths
$=2\dfrac{3}{4}$ hours $= \dfrac{11}{4}$ hours
$\therefore$ Time he devotes for other subjects
$=\left(\dfrac{10}{4}-\dfrac{11}{4}\right)$ hours
$=\dfrac{10}{4}$ hours $= \dfrac{5}{2}$ hours $=2\dfrac{1}{2}$ hours

Calculate $64769-45906$ using Ekanyunena Purvena and Param mitra ank method.

  1. $10863$

  2. $19863$

  3. $18863$

  4. $28863$


Correct Option: C

In $20$ Ekadhikena Purvena of digit $2$ is?

  1. $121$

  2. $129$

  3. $118$

  4. $120$


Correct Option: D

Subtract $48625$ from $87654$ using Ekanyunena Purvena and Param mitra and _____________.

  1. $40092$

  2. $39029$

  3. $40126$

  4. $41789$


Correct Option: B

In $325$ Ekanyunena Purvena of digit $2$ is?

  1. $225$

  2. $125$

  3. $425$

  4. $525$


Correct Option: A

Subtract $49045$ from $97005$ using Ekhadikena Purvena and Param Mitra ank

  1. $36870$

  2. $56894$

  3. $47960$

  4. $48690$


Correct Option: C

   Subtract $2536$ from $4162$ using Ekanyunena purvena and Param Mitra Ank 

  1. 1568

  2. 1126

  3. 1626

  4. 1965


Correct Option: C

Subtract $17964$ from $24892$ using Ekhadhikena Purvena and Param Mitra Ank

  1. $6982$

  2. $7982$

  3. $8982$

  4. $5682$


Correct Option: C

In $523$ Ekanyunena Purvena of digit $2$ is?

  1. $123$

  2. $323$

  3. $423$

  4. $623$


Correct Option: C

 In $47$ Ekadhikena Purvena of digit $7$ is

  1. $57$

  2. $48$

  3. $46$

  4. $37$


Correct Option: A
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