SOME QUESTIONS ON DIFFERENTIABILITY

• Find the point on the curve y = 2x² – 6x – 4 at which the tangent is parallel to the x – axis
• Find the slope of tangent for y = tan x + sec x at x = π/4
• For the curve y = 3x² + 4x, find the slope of the tangent to the curve at the point x = -2.
• Find a point on the curve y = x² – 4x -32 at which tangent is parallel to x-axis.
• Find a, for which f(x) = a(x+sinx)+a is increasing .
• The side of a square is increasing at 4 cm/minute. At what rate is the area increasing when the side is 8 cm long?
• Find the point on the curve y =x²-7x+12, where the tangent is parallel to x-axis.

CBSE SAMPLE PAPERS 2012

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MATHS: PROBABILITY

A few questions in probability....


Q. 1. Two dice are rolled once. Find the probability that:
1. the numbers on two dice are different
2. the total of numbers on the two dice is at least 4
Q. 2. A pair of dice is tossed twice. If the random variable X is defined as the number of doublets, find the probability distribution of X.


Q. 3. In a factory, which manufactures nuts, machines A, B and C manufacture respectively 25%, 35% and 40% of nuts. Of their output 5, 4 and 2 per cent respectively are defective nuts. A nut is drawn at random from the product and is found to be defective. Find the probability that it is manufactured by machine B.


Q. 4. If the mean and variance of the binomial distribution are respectively 9 and 6, find the distribution.


Q. 5.8% of people in a group are left handed. What is the probability that 2 or more of a random sample of 25 from the group are left handed?