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.
Advertisement

 Multiple Choice QuestionsLong Answer Type

11.

(i) Is the binary operation *, defined on set N, given by  a * b = a + b2  for all a,b N, commutative?


(ii) Is the above binary operation * associative?


12.

Prove the following:

tan-113 + tan-115 + tan-117 + tan-118


13.

Let A= 325413067. Express A as sum of two matrices such that one is symmetric and the other is skew symmetric.


14.

If A = 1 2 2212221, verify that A2 – 4A – 5I = 0.


Advertisement
15.

For what value of k is the following function continuous at x = 2?

f ( x )  =2x + 1     ;   x<2    k            ;   x = 2        3x - 1  ;   x>1       


Advertisement

16.

Find the equation of tangent to the curve x = sin 3t, y = cos 2t, at t = π4


X = sin3t    dxdt = 3 cos3t   xt = π4 = sin3π4 = 12y = coc2t dydt = -2 sin2t  yt = π4 = cos2t = cos2π4 = 0 dydx =  dydt. dtdx             = -2sin2t13cos3t              = -23sin2tcos3t

 

dydxt = π4 = -23sin2 x π4cos3 x π4                        =  -23sinπ2cos3π4 = 223Therefore, the equation of the tangent at the point 12,0 isy - 0 = 223 x - 12 y = 223 x  - 233y - 22x + 2 = 0


Advertisement
17.

Using properties of determinants, prove the following:

αβγα2β2γ2β + γ     γ + α     α + β = α - β β - γ  γ - α α + β + γ


18.

Show that the rectangle of maximum area that can be inscribed in a circle is a square.


Advertisement
19.

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is 13h.


20.

Differentiate the following with respect of x:

y = tan-1 1 + x - 1 - x1 + x + 1 - x 


Advertisement