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

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 Multiple Choice QuestionsShort Answer Type

11.

Find the angle between the vector straight i with hat on top minus straight j with hat on top space and space straight j with hat on top space minus space straight k with hat on top.

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12.

Find the distance of a point (2, 5, −3) from the plane straight r with rightwards arrow on top. open parentheses 6 straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top close parentheses space equals 4.

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13.

Find the differential equation of the family of lines passing through the origin. 

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14.

Find the integrating factor for the following differential equation:straight x space log space straight x dy over dx space plus space straight y space equals space 2 logx space

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15.

Evaluate: integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator sin squared straight x over denominator sinx plus cosx end fraction dx.

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16.

Evaluate integral subscript negative 1 end subscript superscript 2 left parenthesis straight e to the power of 3 straight x end exponent plus 7 straight x minus 5 right parenthesis dx

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17.

Evaluate:
integral fraction numerator straight x squared over denominator straight x to the power of 4 plus straight x squared minus 2 end fraction dx

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18.

In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides

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19.

How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?


Let  p denotes the probability of getting heads.
Let q denotes the probability of getting tails.
straight p space equals space 1 half
straight q space equals space 1 minus 1 half space equals 1 half
Suppose the coin is tossed n times.
Let X denote the number of times of getting heads in n trails. 

straight P left parenthesis straight X equals straight r right parenthesis space equals space straight C presuperscript straight n subscript straight r straight p to the power of straight r straight q to the power of straight n minus straight r end exponent space equals space straight C presuperscript straight n subscript straight r open parentheses 1 half close parentheses to the power of straight r open parentheses 1 half close parentheses to the power of straight n minus straight r end exponent space equals straight C presuperscript straight n subscript straight r open parentheses 1 half close parentheses to the power of straight n comma space space straight r space equals space 0 comma 1 comma space 2... comma straight n
straight P left parenthesis straight X greater or equal than 1 right parenthesis greater than 80 over 100
rightwards double arrow space space straight P left parenthesis straight X equals 1 right parenthesis plus straight P left parenthesis straight X equals 2 right parenthesis plus..... plus left parenthesis straight X equals straight n right parenthesis greater than 80 over 1000
rightwards double arrow space straight P left parenthesis straight X equals 1 right parenthesis plus straight P left parenthesis straight X equals 2 right parenthesis plus.... plus straight P left parenthesis straight X equals straight n right parenthesis plus straight P left parenthesis straight X equals 0 right parenthesis minus straight P left parenthesis straight X equals 0 right parenthesis greater than 80 over 100
rightwards double arrow 1 minus straight P left parenthesis straight X equals 0 right parenthesis greater than 80 over 100
rightwards double arrow straight P left parenthesis straight X equals 0 right parenthesis space less than 1 fifth
rightwards double arrow straight C presuperscript straight n subscript 0 open parentheses 1 half close parentheses to the power of straight n less than 1 fifth
rightwards double arrow open parentheses 1 half close parentheses to the power of straight n less than 1 fifth
rightwards double arrow straight n space equals space 3 comma 4 comma 5......
So the fair coin should be tossed for 3 or more times for getting the required probability.

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20.

Find x such that the four points A(4, 1, 2), B(5, x, 6) , C(5, 1, -1) and D(7, 4, 0) are coplanar.

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