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Take 10 figure logarithm to base 10 from x = 300 to x = 310 by unit increment. Calculate
the first derivative of log10 x when x = 310
the first derivative of log10 x when x = 310
Math
A solid of revolution is formed by rotating about the x-axis the area bounded between
x = ,0 x = 1 and the curve given by the table
x- f(x)
0 - 1.0
0.25 - 0.98965
0.5 - 0.9587
0.75 - 0.9089
1.0- 0.841
Find the volume of the solid so formed using
i) Trapezodial rule ii) Simpson’s rule
x = ,0 x = 1 and the curve given by the table
x- f(x)
0 - 1.0
0.25 - 0.98965
0.5 - 0.9587
0.75 - 0.9089
1.0- 0.841
Find the volume of the solid so formed using
i) Trapezodial rule ii) Simpson’s rule
Math
Consider the following data
x - f(x)
1.0 - 0.7651977
1.3 - 0.6200860
1.6 - 0.4554022
1.9 - 0.2818186
2.2- 0.1103623
Use Stirling’s formula to approximate f(1.5) with x0 = 1.6
x - f(x)
1.0 - 0.7651977
1.3 - 0.6200860
1.6 - 0.4554022
1.9 - 0.2818186
2.2- 0.1103623
Use Stirling’s formula to approximate f(1.5) with x0 = 1.6
The annual inventory cost of C for a manufacturer is given by
C = (2 000 000)/x + 500x
where x is the number of items that are ordered each item. Find C(200) and C ‘ (200), and interpret the result.
C = (2 000 000)/x + 500x
where x is the number of items that are ordered each item. Find C(200) and C ‘ (200), and interpret the result.
Find the coordinates of the foot of the perpendicular from (3, − 2) on the line
4x + 5y −1 = 0 .
4x + 5y −1 = 0 .
Math
Solve the following linear programming problem graphically:
Max x1 + 3x2
Subject to
-3x1 + 7x2 ≤ 21
3x1 - 3x2 ≤ 3
-2x1 + 2x2 ≤ 4
x1, x2 ≥ 0
Max x1 + 3x2
Subject to
-3x1 + 7x2 ≤ 21
3x1 - 3x2 ≤ 3
-2x1 + 2x2 ≤ 4
x1, x2 ≥ 0
A grocery shop sell milk packets containing half a litre of milk. It makes bulk purchase of the same from the nearby city. Every time a purchase is made, it incurs a cost of Rs.50 towards transportation. The daily demand of packets is about 250. The holding cost is Rs. 0.10 for a packet per day to preserve it in a refrigerator. Determine the optimum quantity of a bulk purchase and the cycle time.
Math
Let A = 5i − j + k, B = j − 5k, C = −15i + 3 j − 3k be three vectors. Which pair of
vectors are
i) perpendicular? ii) parallel?
vectors are
i) perpendicular? ii) parallel?
Let G be a group of order n ≥ 2 , with only two subgroups -{e} and itself. Find a
minimal generating set for G . Also, find out whether n is a prime or a composite
number, or can be either.
minimal generating set for G . Also, find out whether n is a prime or a composite
number, or can be either.
Explicitly give the elements and structure of the group Sn/An, n≥5.
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#340153 on Dec 2023
#340153 on Dec 2023