Prove/Disprove (informally) using any method of proof and show your step-by- step solution: ("i') = (;) + (,",). k Note that (") means n choose m, where the formula for combination is used.

Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

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Q: -3æ + 5x – 2)- 2 (a – 2æ – 1) | f the expression above is rewritten in the form ae' + bæ + c, where…

A: Given: (-3x2+5x-2)-2(x2-2x-1)

Q: Calculate the flow in the field F along the path C. F = -5 i + 4 j + 8 k; C is the curve  r(t) = 2…

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Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

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Q: Given Z1 =1+√√3i and Si Z2 = 2 e 6 Find 2 (Z2)² Z1

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Q: A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey…

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Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

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Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. 4 r(t) = (41²) ₁ +…

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Q: [10 4 -1] Q1) Find AB if A =-2 -1 and B =0 2 -3 3 20 l10 -5

A: Given Matrix A=1004-2-12-3320 and B=1-10210-5 to multiply the matrix A and B proceed as follows…

Q: 3 را (x) = 2x+7 cl if -5 ²x C1 X = 1 8 If 12X=3 7 11x-2 31 if x > 3 A) use 3-step formula B) is f…

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Q: Q1/ Given Z1 = 1 + √√3i and Z2=2e6¹ Find 2 (Z2)² Z1

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Q: 9. A person on an assembly line produces P items per day after t days of training, 400 where P(t)=…

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