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 QuestionsShort Answer Type

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11.

Differentiate the function (sin x)x + sin–1 √xwith respect to x.


straight y space equals space left parenthesis sin space straight x right parenthesis to the power of straight x space plus sin to the power of negative 1 end exponent space square root of straight x
straight y space equals space straight u plus straight v
rightwards double arrow space dy over dx space equals space du over dx space plus dv over dx
straight u space equals space left parenthesis sin space straight x right parenthesis to the power of straight x
rightwards double arrow space log space straight u space equals space straight x space log space sin space straight x
rightwards double arrow du over dx space equals space left parenthesis sin space straight x right parenthesis to the power of straight x left square bracket space straight x space cot space straight x space plus space log space sin space straight x right square bracket

straight v equals space sin to the power of negative 1 end exponent square root of straight x space
rightwards double arrow space dv over dx space equals space fraction numerator 1 over denominator 2 square root of straight x minus straight x squared end root end fraction
therefore dy over dx space equals space left parenthesis sin space straight x right parenthesis to the power of straight x space left square bracket straight x space cot space straight x space plus space log space sin space straight x right square bracket space plus fraction numerator 1 over denominator 2 square root of straight x minus straight x squared end root end fraction
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12.

If xm yn = (x + y)m + n, prove that fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 0

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13.

Evaluate: integral subscript 2 superscript 3 space 3 to the power of straight x space dx.

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14.

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

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15.

Prove that if E and F are independent events, then the events E and F' are also independent.

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16.

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

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17. Find space integral fraction numerator dx over denominator straight x squared space plus 4 straight x space plus 8 end fraction
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18.

Find integral fraction numerator 2 straight x over denominator left parenthesis straight x squared plus 1 right parenthesis left parenthesis straight x squared plus 2 right parenthesis squared end fraction dx

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19.

Evaluate: integral subscript 0 superscript straight pi fraction numerator straight x space sin space straight x over denominator 1 plus cos squared x end fraction dx

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20.

Evaluate:integral subscript 0 superscript 3 divided by 2 end superscript vertical line space straight x space sin space πx vertical line space dx

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