Subject

Mathematics

Class

CBSE Class 12

Pre Boards

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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. 


Consider the equation, y = mx, where m is the parameter.
Thus, the above equation represents the family of lines which pass through the origin.
y = mx    ....(1)
 rightwards double arrow space space straight y over straight x space equals space straight m space... left parenthesis 2 right parenthesis 
Differentiating the above equation (1) which respect to x,
   straight y space equals space mx
dy over dx space equals space straight m space cross times space 1
space space rightwards double arrow space space dy over dx equals straight m
space space space rightwards double arrow space dy over dx space equals space straight y over straight x space left square bracket because space from space equation space left parenthesis 2 right parenthesis right square bracket
space space space space rightwards double arrow dy over dx minus space straight y over straight x space equals space 0

space
Thus we have eliminated the constant, m.
The required differential equation is
dy over dx minus straight y over straight x space equals 0

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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%?

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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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