Subject

Mathematics

Class

CBSE Class 12

Pre Boards

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

11.

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width. If the cost is to be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in this question?


12.

Find the magnitude of each of the two vectors a and b, having the same magnitude such that the angle between them is 60o and their scalar product is 9/2.


13.

A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.


14.

If θ is the angle between two vectors i^ - 2j^ + 3k^ and 3i^ - 2j^ + k^ find sin θ.


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15.

Find the differential equation representing the family of curves y = aebx + 5 , where a and b are arbitrary constants.


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16.

Evaluate: cos 2x + 2 sin2 x cos2 x  dx


I = cos 2 x  + 2 sin2 x cos2 x dxI = 1-2 sin2 x  + 2 sin 2xcos2 x I = sec2 x dxI = tan x + C


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17.

If y = sin (sin x), prove that d2 ydx2 + tan x dydx  + y cos2 x = 0


18.

Find the particular solution of the differential equation ex tan ydx + (2 -ex) sec2 ydy = 0, given that y  = π4 when x = 0


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19.

Find the particular solution of the differential equation dydx + 2 y tan x  = sin x, given that y = 0 when x = π3


20.

Find the shortest distance between the lines.

r = (4i^ -j^) + λ (i^ - j^ + 2k^) + μ (2i^ + 4j^-5k)^


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