Tag: maths

Questions Related to maths

The sum of  first eight odd numbers is 

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. 64

  2. 74

  3. 80

  4. 95

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Correct Option: A
Explanation:

The sum of the first odd numbers is,


$1+3+5+7+9+11+13+15= 64$

So option A is the correct answer

$121$ can also be represented as ?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $40+41$

  2. $11^2$

  3. $120+3$

  4. All of these

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Correct Option: B
Explanation:

$11 \times 11= 121$ 

$= 11^2$
Thus option $B$ is correct

$5^2=?$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $25$

  2. $15$

  3. $14$

  4. $12+13$

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Correct Option: A,D
Explanation:

52 = 5  × 5 = 25 = 12 + 13

The value of $3^2$ is

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $9$

  2. $4+5$

  3. $8$

  4. None of these

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Correct Option: A,B
Explanation:

$3^2$ means taking square of $3$, i.e. $3\times 3=9$

$9$ can be written as addition of $9=4+5$.
Hence, options A and B are correct.

$24+25=?$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $49$

  2. $34$

  3. $7^2$

  4. $36$

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Correct Option: A,C
Explanation:

24 + 25 = 49 = 72

Which of the following option matches with $361$?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $360+1$

  2. $19^2$

  3. $180+181$

  4. None of these

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Correct Option: A,B,C
Explanation:

361 = 19 × 19 = 192
361 = 360 + 1 = 180 + 181

Evaluate: $220+221$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $437$

  2. $441$

  3. $21^2$

  4. None of these

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Correct Option: B,C
Explanation:

220 + 221 = 441 = 21  × 21 = 212

The expression $(x + 1)(x + 2)(x + 3)(x + 4) + 1$ is a 

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. perfect square

  2. cube

  3. quartic polynomial

  4. none of the above

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Correct Option: A
Explanation:

Solving

$(x+1)(x+2)(x+3)(x+4)+1$
$Multiplying\ first\ bracket\ with\ last\ and\ second\ to\ the\ third\ one$
$(x^2+5x+4)(x^2+5x+6)+1$
$Replacing\ x^2+5x+4\ by\ 'B'$
$(B)(B+2)+1$
$B^2+2B+1$
$(B+1)^2=(x^2+5x+5)^2$
Hence $L.H.S.$ is the $Perfect\ Square$ of $(x^2+5x+5)$



$\cfrac { { \left( 963+476 \right)  }^{ 2 }+{ \left( 963-476 \right)  }^{ 2 } }{ \left( 973\times 963+476\times 476 \right)  } =$?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $1449$

  2. $497$

  3. $2$

  4. $4$

  5. None of these

Show answer
Correct Option: C
Explanation:

Given Exp.$=\cfrac { { \left( a+b \right)  }^{ 2 }+{ \left( a-b \right)  }^{ 2 } }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right)  } =\cfrac { 2\left( { a }^{ 2 }+{ b }^{ 2 } \right)  }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right)  } =2$

By what least number $21600$ must be multiplied to make it a perfect cube?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $6$

  2. $10$

  3. $30$

  4. $60$

Show answer
Correct Option: B
Explanation:

$21600 $ can be factorized as $6\times 6\times 6\times 10\times 10$

To make it perfect cube, it must be multiplied by $10$.