Tag: equations from statements

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Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If a $\in { 1,2,3,4 } ,$ then number of equations of the form $x ^ { 2 } + a x + 1 = 0$ having real roots is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For real roots, the discriminant D = a^2 - 4 >= 0. This implies a^2 >= 4. Given a in {1, 2, 3, 4}, the values satisfying this are a=2, 3, 4. There are 3 such values.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digit of that number ?

  1. 3

  2. 4

  3. 9

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the ten's digit be $x$ and unit's digit be $y$.

Then, $(10x + y) - (10y + x) = 36$

$9(x - y) = 36$

$x - y = 4$

Therefore, the difference between the two digit of that number is $4$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The sum of the digits of a two-digit number is 9 less then the number. Which of the following digits is at unit's place of the number ?

  1. 1

  2. 2

  3. 4

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let $x,y$ are the digits of a number. Then the number $= 10x+y$

as per condition : $10x+y-9 = x+y$

Then as per the given problem,

$x+y=10x+y-9$

or, $9x=9$

or, $x=1$

So, we can say that for any value of y from 1 to 9, the condition satisfies.

for eg: if the number is 18

18–9 = 1+8

9=9 , satisfied.


So the tenth's place digit is $1$.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Get the algebraic expression in the following cases using variables, constant and arithmetic operations.
Subtraction of $z$ from $y$.

  1. $y+z$
  2. $y-z$
  3. $z-y$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Subtraction of $z$ from $y$ implies that a number of value $z$ is to be subtracted from another number of $y$ value $y$ which means $y-z$.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Two years ago the mean age of $40$ people was $11$ years. Now a person left the group and the mean age is changed to $12$ years, then the age of the person who left the group is?

  1. $52$ years
  2. $48$ years
  3. $54$ years

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of ages 2 years ago = 40*11 = 440. Sum of ages now = 440 + 40*2 = 520. After one person leaves, 39 people have mean age 12, sum = 39*12 = 468. Age of person = 520 - 468 = 52.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Five years ago Anjali's age was twice Sarita's age. Five years hence, their ages will be $4 : 3$. Anjali's present age is 

  1. $15$ years
  2. $10$ years
  3. $12$ years
  4. $16$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A and S be current ages. (A-5) = 2(S-5) => A-2S = -5. (A+5)/(S+5) = 4/3 => 3A+15 = 4S+20 => 3A-4S = 5. Solving the system: 2A-4S = -10 and 3A-4S = 5. Subtracting gives A = 15.