Question - If sin y = x sin (a + y), prove that ---------
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Question - Sand is pouring from a pipe at the rate of 12 cm^3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the sand cone increasing when the height is 4 cm?
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Question - manufacturer produces nuts and bolts. It takes 1 hours of work on machine A and 3 hours on machine B to product a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7 per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operates his machines for at the most 12 hours a day? Form the above as a linear programming problem and solve it graphically.
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Question - Solve the following differential equation: ---------
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Question - Solve the following differential equation: -------------
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Question - Evaluate: -------
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Question - How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?
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Question - Evaluate: -----
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Question - Evaluate: -----
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Question - If x = a(---- - sin ---), y = a (1 + cos--), find
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Question - Find the equation of the plane determined by the point A(3, - 1, 2), B(5, 2, 4) and C(-1, - 1, 6) and hence find the distance between the plane and the point P(6, 5, 9).
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Question - Evaluate: -------- | x | | x 2| | x 4|dx
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Question - Differentiate the following function with respect to x: --------------
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Question - Using properties of determinants, prove that
------------
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Question - Using elementary transformations, find the inverse of the matrix -------
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Question - Show that the function -------- is continuous but not differentiable at x = 3.
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Question - Using elementary operations, find the inverse of the following matrix: -------
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Question - Using matrix method, solve the following system of equations: ---------
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Question - Find the equation of the line passing through the point (-1, 3, -2) and perpendicular to the lines -------
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Question - Find the points on the curve x^2 + y^2 – 2x – 3= 0 at which the tangents are parallel to x-axis.
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