Tag: maths

Questions Related to maths

The straight line joining the mid-points of the opposite sides of a parallelogram divides it into two parallelogram of equal area  

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. True

  2. False

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Correct Option: A

In a $\triangle DEF$; $A,B$ and $C$ are the mid-points of $EF,FD$ and $DE$ respectively. If the area of $\triangle DEF$ is $14.4{ cm }^{ 2 }$, then find the area of $\triangle {ABC}$.

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. $1.75$cm

  2. $2.54$cm

  3. $3.2$cm

  4. $3.6$cm

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Correct Option: D
Explanation:

Fact: Using mid-point theorem $\dfrac{\Delta{DEF}}{\Delta{ABC}}=4$


Here $\Delta{DEF}=14.4$ cm$^2$ is given 
Hence are of triangle $ABC $ is given by $ \dfrac{14.4}{4}=3.6$ cm$^2$ 

In a $\triangle ABC$, if $D, E, F$ are the midpoints of the sides $BC, CA, AB$ respectively then $\overline {AD} + \overline {BE} + \overline {CF} =$

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. $\overline {0}$

  2. $\overline {AE}$

  3. $\overline {BD}$

  4. $\overline {CE}$

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Correct Option: A

A cross section at the midpoint of the middle piece of a human sperm will show

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. Centriole, mitochondria and 9 +2 arrangement of microtubules.

  2. Centriole and mitochondria

  3. Mitochondria and 9+2 arrangement of microtubules.

  4. 9+2 arrangement of microtubules only.

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Correct Option: C
Explanation:

The middle piece is the tubular structure in which mitochondria are spirally arranged and it also has the beginning part of the flagellum. The sperm tail or the flagellum is based upon unique 9+2 arrangement. This arrangement refers to the nine peripheral, symmetrically arranged microtubule doublets.
Thus, the cross-section of the middle piece of sperm will show mitochondria and 9+2 arrangement of microtubules.
Hence, the correct answer is option (C), 'Mitochondria and 9+2 arrangement of microtubules'.

Factorise ${\left( {3 - 4y - 7{y^2}} \right)^2} - {\left( {4y + 1} \right)^2}$ 

maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. $\left( {4 - 7{y^2}} \right)\left( {2 - 8y - 7{y^2}} \right)$

  2. $\left( {7{y^2} - 4} \right)\left( {2 - 8y - 7{y^2}} \right)$

  3. $\left( {4 - 7{y^2}} \right)\left( {7{y^2} + 8y - 2} \right)$

  4. $\left( {7{y^2} - 4} \right)\left( {7{y^2} - 8y - 2} \right)$

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Correct Option: A
Explanation:

We have,

${\left( {3 - 4y - 7{y^2}} \right)^2} - {\left( {4y + 1} \right)^2}$ 

We know that
$a^2-b^2=(a+b)(a-b)$

Therefore,
$\Rightarrow (3 - 4y - 7y^2+4y + 1)(3-4y-7y^2-4y-1) $ 

$\Rightarrow (4 - 7y^2)(2-8y-7y^2) $ 

Hence, this is the answer.

Factorise :

$4x+12$

maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. $4(x+2)$

  2. $4(x+3)$

  3. $3(x+4)$

  4. none of these

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Correct Option: B
Explanation:

$4x+12=4(x+3)$

Factorize : $y^2 + 100y$
maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. $y(y+100)$

  2. $y^2(y+100)$

  3. $y(y^2+100)$

  4. none of these

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Correct Option: A
Explanation:

We need to find value of $y^2+100y$

Taking $y$ common, we get $y(y+100)$.
Hence, option A is correct.

If (x+1) is a factor of $\displaystyle x^{3}+11x^{2}+15x+a$ then the value of 'a' is

maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. 2

  2. 3

  3. 5

  4. 4

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Correct Option: C
Explanation:

$x+1\div x^{3}+11x^{2}+15x+a\setminus x^{2}+10x+5$

                $x^{3}+x^{2}$ ( subtracted)
               ..............................................................
                               $10x^{2}+15x+a$
                               $10x^{2}+10x$ ( subtracted)
                            ....................................................................
                                          $5x+a$
                                          $5x+5$  ( subtracted)
.....................................................................................................
                                             a-5
If x+1 is the factor of $x^{3}+11x^{2}+15x+a$
Then a-5=0 or a=5

Factorization is the  ......... process of multiplication.

maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. equal

  2. same

  3. inverse

  4. common

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Correct Option: C
Explanation:

Factorization is the inverse process of multiplication.

________ is a method of writing numbers as the product of their factors or divisors.

maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

  1. Polynomial

  2. Factorisation

  3. Division algorithm

  4. Quadratic equation

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Correct Option: B
Explanation:

Factorisation is a method of writing numbers as the product of their factors or divisors.
Example: $4x^2+2x$ is a factor $2x(2x+1)$
By multiplying the factor we get the original number.