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For all even integral value of n, lim (x+1)^-n


n to ∞


Exist or not


True or false with full explanation



if two varieties are tested in 5 different locations for their yeld proformance in (q/ha) with the follo results.Find out which variety which is more consistent over the location by comparing their CV value?


Variety A -12,8,10,11,14


Variety B - 15,9,7,12,12

From a population of 700 plants, 500 plants are healthy, rest are unhealthy. For a sample size of 10 plants, calculate the probabilities that—(a) Exactly 3 are unhealthy (b) at least 3 plants are unhealthy (c) at most 3 plants are unhealthy (d) Exactly 3 are healthy (e) None healthy?

Calculate the mean and the variance of the discrete random variable X which can take only values 1, 2, and 3, given that P(1) = 10/33, P(2) = 1/3, and P(3) = 12/33.




P(X) X-P(X) X²P(X)


























Solve for the mean and the variance of the discrete random variable X which can take only the values 2, 4, 5 and 9, given that P(2) = 9/20, P(4) = 1/20, P(5) = 1/5 and P(9) = 3/10.



X P(X) X∙P(X) X2∙P(X)




























Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not

Analyse the following transactions for Surprise Ltd. using the concept of Accounting Equation comprising of Assets, Liabilities and Equity 1.Commenced business with cash of ₹ 5,00,000. Purchased equipment for cash ₹ 2,00,000. 3. Purchased furniture worth ₹50,000 on credit from IndiMart. 4. Purchased raw materials for ₹25,000 against cash from XYZ Suppliers. 5. Deposited cash of ₹ 1,25,000 in the current account. 6. Sold goods for ₹75,000 and received a cheque against the same


12 students have appeared in the exam in which the top four will get a prize. How many possible ways are there to get the prize winners?

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.


If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.


Find the bitwise OR, bitwise AND, and bitwise XOR of each of these pairs of bit strings. a) 101 1110, 010 0001


b) 1111 0000, 1010 1010


pc) 00 0111 0001, 10 0100 1000


d) 11 1111 1111, 00 0000 0000

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