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SY CE/CSE ISE even 2026

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Suppose that the characteristic polynomial of some matrix

A is found to be 

p(λ) = (λ − 1)(λ − 3)^2

(λ − 4)^3

. What is

the size of A?

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A manufacturer of sports equipment has developed a new synthetic fishing line that

the company claims has a mean breaking strength of 8 kilograms with a standard

deviation of 0.5 kilogram. Test the hypothesis that μ = 8 kilograms against the

alternative that μ is not equal to 8 kilograms if a random sample of 50 lines is tested and found

to have a mean breaking strength of 7.8 kilograms. Use a 0.01 level of significance. What is critical region

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Consider product of three matrices M subscript 1M1​,M subscript 2M2​ and M subscript 3M3​ having w rows and x columns, x rows and y columns, and y rows and z columns. Under what condition will it take less time to compute the product as left parenthesis M subscript 1 M subscript 2 right parenthesis M subscript 3(M1​M2​)M3​ than to compute M subscript 1 left parenthesis M subscript 2 M subscript 3 right parenthesisM1​(M2​M3​) ?

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What will be theCombination of Space and  time complexity  of Fibonacci series solving with Dp using bottom up approach.

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