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Multiple choice maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

The base and the corresponding altitude of a parallelogram are $10: cm$ and $3.5: cm$, respectively. The area of the parallelogram is

  1. $30\: cm^2$
  2. $35\: cm^2$
  3. $70\: cm^2$
  4. $ 17.5\:cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of the parallelogram is base $\times$ height $cm^2$

Area of the parallelogram$=(10)(3.5)=35:cm^2$.

Multiple choice maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

A parallelogram has sides $30 m, 70 m$ and one of its diagonals is $80 m$ long. Its area will be

  1. $600\displaystyle m^{2}$
  2. $\displaystyle 1200\sqrt{3}m^{2}$
  3. $1200\displaystyle m^{2}$
  4. $\displaystyle 600\sqrt{3} m^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The diagonal of parallelogram divides it into two congruent triangles. 
$\therefore $ Area (parallelogram $ABCD) = 2 \times$ Area $ \left (\Delta ABC  \right ) $
In $ \Delta ABC$,
$ s=\cfrac{80m+ 30m+70m}{2}=\cfrac{180m}{2}=90m$
$ \therefore Area=\sqrt{90\left ( 90-80 \right )(90-30)(90-70)}m^{2}$
$ =\sqrt{90\times10\times60\times20m^{2} }$
$= 600\sqrt{3} m^{2}$

$ \therefore $ Area of parallelogram $ABCD =$$ 2\times 600\sqrt{3}m^{2}$ $ =1200\sqrt{3}m^{2}$
Multiple choice maths application of derivatives - iii second derivative test maxima and minima application of derivatives

The value of $a$ for which the function $f(x)=a\ \sin x+\dfrac{1}{3}\sin 3x$ has an extremum at $x=\dfrac{\pi}{3}$ is

  1. $1$
  2. $-1$
  3. $0$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$f\left( x \right) = a\sin x + \dfrac{1}{3}\sin 3x$
$ \Rightarrow f'\left( x \right) = a\cos x + \dfrac{1}{3}\cos 3x \times 3$
$ \Rightarrow f'\left( x \right) = a\cos x + \cos 3x$
For extremum at ${\dfrac{\pi }{3}}$
$f'\left( {\dfrac{\pi }{3}} \right) = 0$
$ \Rightarrow a\cos \left( {\dfrac{\pi }{3}} \right) + \cos 3\left( {\dfrac{\pi }{3}} \right) = 0$
$ \Rightarrow \dfrac{a}{2} - 1 = 0$
$\Rightarrow a = 2$