Tag: maths

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A line joining the midpoints of opposite sides of a parallelogram is parallel to the other two sides and divides the parallelogram into two smaller parallelograms of equal area.

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

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 $\triangle {ABC}$.

  1. $1.75$cm
  2. $2.54$cm
  3. $3.2$cm
  4. $3.6$cm
Reveal answer Fill a bubble to check yourself
D Correct answer
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$^2$ 

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

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

  1. $\overline {0}$
  2. $\overline {AE}$
  3. $\overline {BD}$
  4. $\overline {CE}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The vectors AD, BE, and CF are medians of the triangle. The sum of the vectors from the vertices to the midpoints of the opposite sides is zero.

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

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

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
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'.

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

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

  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. $\left( {7{y^2} - 4} \right)\left( {7{y^2} - 8y - 2} \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. 2

  2. 3

  3. 5

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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

  1. Polynomial

  2. Factorisation

  3. Division algorithm

  4. Quadratic equation
Reveal answer Fill a bubble to check yourself
B Correct answer
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.