Using integration find the area of the triangular region whose si

Subject

Mathematics

Class

CBSE Class 12

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 Multiple Choice QuestionsLong Answer Type

21.

Using elementary transformations, find the inverse of the matrx

 1 3  - 2- 3      0  - 121      0 


22.

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.


23.

Evaluate:  5 x + 3 x2 + 4 x + 10 dx


24.

Evaluate:  2x  x2 + 1   x2 + 3  dx


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25.

Solve the following differential equation:

ex tan y dx + ( 1 - e) sec2 y dy  = 0


26.

Solve the following differential equation:

cos2 x dydx + y = tan x


27.

Find a unit vector perpendicular to each of the vector  a + b   and   a - b , where

  a = 3 i^ + 2 j^ + 2 k^   and    b =  i^ + 2 j^ - 2 k^.


28.

Find the angle between the following pair of lines:  

- x + 2- 2 = y - 17 = z + 3- 3   and   x + 2- 1 = 2 y - 84 = z - 54

And check whether the lines are parallel or perpendicular.


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29.

Probabilities of solving problem independently by A and B are 12 and 13respectively. If both try to solve the problem independently, find the probability that

(i) the problem is solved

(ii) exactly one of them solves the problem.


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30.

Using integration find the area of the triangular region whose sides have equations  y=2x+1,  y=3x+1  and  x=4.


Equations of the lines are   y = 2 x + 1,    y = 3 x + 1     and   x = 4.

Let  y1 = 2 x + 1,   y2 = 3 x + 1 

Now area of the triangle bounded by the given lines,

=  y2 - y1 04 dx=  3 x + 1  -  2 x + 1  04 dx= x04 dx= 12  x2 04= 12  42 - 02 = 12 × 16

= 8 sq. units

Thus, the area of the required triangular region is  8 square units

       


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