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 Question 10 (a) If nPr=npr+1, and nCr=nCr-1_, then find n and r. This question has 1 answers so far. 7 (a) If and then show that x=0 or . This question has 0 answers so far. 4 (b) Everybody in a meeting shakes hand with everybody else. The total number of hand shakes is 66. Find the total number of persons in meeting  This question has 2 answers so far. 4 (a) Solve the following system of equations by Gauss Jordan Method: X+ 2y +3z=4 2x + 3y +8z = 7 x - y - 9z = 1 This question has 1 answers so far. 4 (a) The demand and supply functions under pure competition are P = 1600- x2 and P = 2x2 + 400 respectively. Find the CS and PS. This question has 0 answers so far. 3 (a)Find the value of r if (i) 10Cr=20Cr+1 (ii) 10Pr,=25Pr+2. This question has 1 answers so far. 3 (b) Find the unit vector perpendicular to the vectors and This question has 0 answers so far. 3 {b} Find the CS for the demand function x = 525 - 20p-p2 if the quantity demanded is 264 units. This question has 0 answers so far. 3 (a Use mathematical induction to prove that This question has 1 answers so far. 3 (a) let a, b, c be positive integers such that is an integer. if a, b, c geometric progression and the arithmetic meat of a , b, c is b+2, find the value of This question has 0 answers so far. 2 (b) Examine the following vector for linearly dependence and linear by independence (1,2,0), (2,3,0), (8, 13, 0).  This question has 0 answers so far. 2 (a) Find ranges of values of x for which the curve y = x4 - 6x2 + 12x2 + 5x + 7 is  concave upwards or downwards. Also determine the points of inflexion.  This question has 0 answers so far. 2 b) Prove that for any positive integer number n, divisible by 3. This question has 0 answers so far. 2 (b) Real number form an arithmetc progression. Sippose that, . Find the value of This question has 1 answers so far. 2 (a) an apartment complex has 250 apartments to rent. If they rent x- apartments then their monthly profit, in dollars, is given by . How many apartments should they rent in order to maximize their profit. This question has 1 answers so far. 1 (b) In a firm there are 20 men and 10 women. In how many can you have a committee with 3 men and 2 women? This question has 0 answers so far. 1 (b). Solve the following system of equations using Gauss elimination method. 2xy - y + 3z = 9;x + y +z = 6 and x - y + z = 2. This question has 0 answers so far. 1 (a)Find the point of inflection of the curve y= x3-3x2+6x+5. Also, find maxima and minima of y. This question has 0 answers so far. 1 (b) The demand function of a commodity is P = 15e-x/3 where P is price and x is the number of units demanded. Determine price and quantity for which revenue is maximum.  This question has 0 answers so far. 1 (a) Optimise F = x2 + y2 + z2 when x + y + z = 3a. This question has 0 answers so far. 1 (a) The elasticity of function function y = f (x) is Determine the  function if y = 6 when x = 4. This question has 0 answers so far. 1 (b) Write short note on business applications of differential equations.  This question has 0 answers so far. 1 for Using Cramer's rule scive the following This question has 0 answers so far. 1 (a) Show that the matrix satisfies the equation and hence find This question has 1 answers so far. 1 (a) If y = . prove that This question has 0 answers so far. 1 (b) if  y = This question has 0 answers so far. 1 If show that This question has 0 answers so far. 1 For the following translation matrix, find the gross output for each industry for the final demand 18 and 44 units respectively This question has 0 answers so far. 0 (a) Verify whether vectors X1=(2,2,-7), X2=(2,1,2), X3=(0,1,-3) are linearly dependent or independent. This question has 0 answers so far. 0 (b)Find the extreme values of (x, y, z) = 2x + 3y + z such that x2 +y2=5 and x+z=1.  This question has 0 answers so far. 0 (a) Solve the differential equation      (x2+4y2+xy) dx=xw dy This question has 0 answers so far. 0 (b) Solve (1-x2) (1-y) dx=xy(1+y)dy  This question has 0 answers so far. 0 Solve the following differential equations(a) = 1 + x + y + xy  This question has 0 answers so far. 0 Solve the following differential equations This question has 0 answers so far. 0 Solve the following differential equations(c) This question has 0 answers so far. 0 if a= 2i-j+2k and b=101i- 2j+7k, find the value of a axb. Also find the unit vector perpendicular to given vector.  This question has 0 answers so far. 0 If a=2i-j+3k, b-i+2j+k and c=3i+j-2k find(a) axb (b) a.b (c) (axb)(d) a x (bxc) This question has 0 answers so far. 0 (b) Find relative extreme for f(x,y) = x2-y2.  This question has 0 answers so far. 0 (a) Find the dot product of the following vector. Also find the angle between a and b This question has 0 answers so far. 0 (b) Solve (x2 + 4y2 + xy)dx - x2 dy. This question has 0 answers so far. 0 (a) Solve = (1 + x + y + xy) This question has 0 answers so far. 0 b) solve the following system of linear equations by matrix method This question has 0 answers so far. 0 (b)  Suppose you are running a factory, producing some sort of widget that requires steel as a raw material. Your costs are predominant human labour, which is \$20 per hour for your workers and the steel itself, which runs for \$170 per ton. Suppose your revenue R is loosely modelled by the following equation , where  h represents hours of Labour and represents tons of steel your budget is \$20000, what is maximum possible revenue?  This question has 0 answers so far. 0 (a) Evaluate This question has 0 answers so far. 0 b) Evaluate  This question has 0 answers so far. 0 (a)  For a certain item the demand curve is and the supply curve is. Evaluate . Five the consumer and producer surplus. This question has 0 answers so far. 0 (b) Compute the consumer' sarplus for the mille demand function Evaluate dollars per gallon, where Q  is the quantity of milk in thousands of gallons. Assumme an       quilibrium quantity of 95 thousand and an equilibrium price of \$3 per gallon This question has 0 answers so far. 0 The third and thirteenth terms of an A.P are respectively equal to -40 and 0. Find the A.P and its 20th term, This question has 1 answers so far. 0 The sum of three numbers in a G. P is 38 and their product is 1728. Find them? This question has 2 answers so far. 0 Solve the following system of equations using Cramer's Rule This question has 1 answers so far. 0 Differentiate with respect to x This question has 1 answers so far. 0 Check for maxima or minima for the function This question has 1 answers so far. 0 Find the intervals on which the following function is increasing or decreasing This question has 1 answers so far. 0 If and find  This question has 2 answers so far. 0 Differentiate sinx with respect to logx. This question has 1 answers so far. 0 find(1) (2) (3) This question has 3 answers so far. 0 If the total cost function for a commodity is given by where x is the quantity of output, show that This question has 1 answers so far. 0 Suppose that marginal cost of a product is given by and fixed cost is proven to be 55. Find the total cost and average cost functions.  This question has 1 answers so far. 0 A firm has the following total revenue and total cost functions , where x is the output. Find maximum profit. This question has 2 answers so far.