Subject

Mathematics

Class

CBSE Class 12

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

Download the PDF Sample Papers Free for off line practice and view the Solutions online.
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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.


The probability of solving the problem independently by  A  and  B  are given as  12  and   13  respectively.

i.e.  P ( A ) = 12,  P ( B ) = 13. P  A  B  = P  A  . P  B 

[ Since the events corresponding to  A  and  B  are independent ]

= 12 x 13 = 16

( i ) Probability that the problem is solved 

= P  A  B  = P  A  + P  B  - P  A  B = 12 + 13 - 16= 3 + 2 - 16= 46= 23Thus, the probability that hte problem is solved is  23.

( ii ) Probability that exactly one of them solves the problem

= P  A - B  + P  B - A =  P ( A ) - P ( A  B ) +  P ( B ) - P ( A  B )  =  12 - 16  +  13 - 16 = 3 - 1 + 2 - 16= 36= 12Thus, the probability that exactly one of them solves the problem is 12.


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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.


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