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After the tremendous success of our last year Important Question Bank for Uttar Pradesh class 12th HSC Board Exam 2016 and 2017 we have also created a list of **Most Important Question Bank for Uttar Pradesh Intermediate class XII (HSC) Board Exam 2019** which are likely to appear in HSC Board Exams this year.

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- There are 5 cards numbered 1 to 5 , one number on one card. Two cards drawn at random without replacement. Let X denote the sum of the number on two cards drawn. Find the mean and variance of X.
- Evaluate
- Write a unit vector perpendicular to both the vectors and
- solve by logarithmic differentiation.
- Find the area of the region bounded by x^2=4y, y=2, y=4 and the y-axis in the first quadrant.
- Find all the points of discontinuity of f, where f is defined by

f(x)= - In a dice game, a player pays a stake of Re.1 for each throw of a die. She receives Rs.5 if the die shows a 3 , Rs.2 if the die shows a 1 or 6 and nothing otherwise. What is the player’s expected profit per throw over a long series of throws?
- Maximize Z=3x+2y+7

Subject to the constraints: x+y<9, x>0 , y>0. - If, then find the value of y

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