The differential equation ( ydy + xdx = 0 ) represents family of ……….. , A ) circle , B ) Parabola , C ) Ellipse , D ) All of these ,

1 )   The differential equation ( ydy + xdx = 0 ) represents family of ……….. , 

A ) circle  ,                                       B ) Parabola  ,

C ) Ellipse ,                                      D ) All of these ,

Correct Answer : -   A ) circle  ,

 

2 )  Find the value of n , if 

A ) 18  ,                                            B ) 20 ,

C )  22 ,                                           D ) None of these ,

Correct Answer : -  B ) 20 ,

Solution : -

Formula : -

As we know a simple formula : -  

 So ,

  

So , We can also write it like this : -

Ø  n – 8 = 12 ,

Ø  n = 20  ,  Answer .

 

3 ) An enclosed figure have 5 sides . So no. of diagonals ?

A ) 5 ,                                               B ) 6 ,

C ) 7 ,                                              D ) None of these ,

Correct Answer : -  A ) 5 ,

Solution : -

Formula : -

To find no. of diagonals of a closed shape , we have simple trick or formula : -

No. of diagonals = (1/2)(n)(n-3) ,

n = no. of sides ,

So ,

Ø  No. of diagonals = (1/2)(n)(n-3) ,

Ø  No. of diagonals = (1/2)(5)(5-3) ,

Ø   No. of diagonals = (1/2)(5)(2) ,

Ø   No. of diagonals = 5   ,      Answer .

 

4 ) If (3,5) is mid-point of (5,a) and (b,6). Then value of  a and b? 

 A ) a = 1 , b = 8 ,                              B ) a = 8 , b = 1 ,

C ) a = 4 , b = 1 ,                             D ) a = 1 , b = 6 ,

Correct Answer : -  C ) a = 4 , b = 1 ,

Solution : -

Given data : -

·        X = 3 , Y =5 ,

·        X₁ = 5  , Y₁ = a ,

·        X₂ = b ,  Y₂ = 6 ,

·        a = ?   , b = ?

Formulas : -

For mid – points we have formulas ,

X = ( X₁ + X₂ ) / 2  ,

·        3 = ( 5 + b ) / 2  ,

·        6 = 5 + b  ,

·        b = 1 ,  Answer .

Y = ( Y₁ + Y₂ ) / 2  ,

·        5 = ( a + 6 ) / 2 ,

·        10 = a + 6  ,

·        a = 4 ,  Answer .

 

5 )   tan(70) = cot(?) ,

A ) 20 ,                                             B ) 50 ,

C ) 70 ,                                            D ) None of these ,

Correct Answer : -  A ) 20 ,

Formulas : -

tan (90-x) = cot(x)   and (tanx)(cotx)=1 .

e.g  tan(50) = cot(40).

 

6 )  Polar form of complex number  x+iy = ?

A ) rcos(theta) + irsin(theta).                                  

B ) rsin(theta) + ircos(theta).

C ) Both of these ,                                          

D ) None of these ,

Correct Answer : -  A ) rcos(theta) + irsin(theta).

 

7 )  The period of cot(x/3) ?

A ) 2π ,                                            B ) 2π/3 ,

C ) 3π ,                                            D ) None of these ,

Correct Answer : -  C ) 3π ,

Soution : -

Formula : -

For ( sin , cos , cosec , sec ) , we add 2π .

But for ( tan , cot ) , we add only π .

So ,

Ø   cot (x/3)  ,

Ø   cot ( x/3 + π )  ,     so multiply by 3 ,

Ø   3cot ( x + 3π )  ,

Ø    So period is 3π ,  Answer .

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