If y (in 2)2, then O 2eln 2 0 O 2 In 2 1 (in 2)2 O eln 2

Q: 1. If N = 12, k = 8, and n = 5. Find P(2). %3D

A: X follows a hypergeometric distribution with N=12, K=8 and n=5 and k=2 We will use the formula:…

Q: If z| =5 and w =- z+5 then Re(w) is equal to

A: Introduction :

Q: If A = then 3A-2 = 4 -1 0 0 5 27 0 0 0 48 0 0 0 75 None of the above -27 0 0 0 - 48 0 0 75 27 0 -27…

A:

Q: in+2S n-1 {(-1)" 7+1} n=1 O None {7 1 n+ 2

A: Strictly decreasing function is : 1/(n+2)    Therefore, answer is fourth.

Q: Evaluate fc 713 where C : |z| = 2. Ans. fc z+1)3 Ti ( – 4). 1 z² (z+1)³

A:

Q: IfΣ ( a+ bk) 4n_ and n+1 k-1 E(ar – br) +, then Ear n n+2 k=1 k-1 2 O None 2 2

A:

Q: If Z-N(0, 1). then P(Z>1) = 0.8413 O True False

A: Given that Z~N(0,1)So, mean=0 and standard deviation=1=1

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: 2. If P (n) : "2.4z + 3""" is divisible by k for all ne N" is true, then the value of k is

A: The solution is given below:

Q: -2 1 and P=. 7. If Q= then QP: 21 O Does not exist. 4 L13 41 -2 07 2. O L21 41 -2 1 7. 25J

A:

Q: If In z + In(x – 6) = In(5x), then r

A:

Q: 2 7e" + dy -5 In 2 – In 5 7 7(금) +2 In2- In5 7-) + 2(n 2 – In 5)

A: We have to find given integral.

Q: In 7 9 6. 6 5 is equal to A In r + Blns where A = and where B

A:

Q: 4. If 2 3 -1 1 A %3D 1 Then det(A) -34 -26 34 26 O 5 3

A:

Q: Cas If A-[? ] and 8: [ ). (AB)'= é' Ā! 2 3 Show that B A

A:

Q: IfΣ (aε+ b:) - 2n and n+1 k-1 8. (ak- br) 1, then Ear = - n+2 k=1 k=1 2. 2. O None 21 2.

A:

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: – 4 a (a) In 6-4c-1 (b) In Vb°c'a…

A:

Q: If 3 5 A = then det(A") = 9 Select one: O True O False

A: Topic = Matrix True

Q: n IfΣ (a +b:) 2n and n+1 k=1 n (ar – br) = -, then Ea n+2 k-1 k=1 O 7 O None 5. 2 2 2

A:

Q: Let I = 2xdxdy. Then I is equal to O None of these O 2 O 1 Оо O 4

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 2n if 1sn< 457 | Зп +1 b) {a,} where a, ={ne"* if 457 <n< 2100 4n –1 if n22100 5n+7

A:

Q: Let z-2 z-2 n st pC& >0.5)20.9 and y:bin (n,o.38), find or

A: Y~Binomialn, 0.38 Compute the mean and the standard deviation of Y using the formulae: Y=np…

Q: 6 - En küçük kareler yönten katsayısı aşağıdakilerden O a) 0.776 O B) 0.556

A: We have to fit the curve of the form  y=aebx Take logarithms to both sides of the above equation, we…

Q: If X ~N (6.7,25), then 1) u = ; 2) o² = ; o = 3) P(8<X<14) = .

A: Reviewing information, Given, X~N(6.7 , 25)

Q: 3 2 3. Vxydydx = Vxdx Vydy Select one: O True O False

A: This question is related to double integral , we will solve it using given information.

Q: #Resl Zerex 2 *Ral Za 1 O There is no correct answer.

A: Option C will be the right answer.

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: 3 a (a) In 64cl (b) In V/bªc²a! 2

A: Given that: lna=2, lnb=3, lnc=5.(a)lna3b4c1(b)lnb4c2a(c)ln(a3b4)ln(bc)1       NOTE: As per our…

Q: a. Neither CNF b. CNF, but no

A: Given as, x+y+z¯uw

Q: if (n+5)! = 56 (n+ 3)!, then (n+ 4)! = 5040 true O false

A:

Q: (-1)" In(nº) Σ 20. 4n n=2

A:

Q: 3y = In(Cr - 2) O 3ry/ = 1-2ey O 3ry =1+ 2e-3y O zy = 1- 3ey O 2ry = 1- 3e 2v

A: This question from differential equations.

Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

A:

Q: 3 Let A = 4 1 Write 5A. Is det 5A = 5 det A?

A:

Q: 니ut-4) (r-3'- 16 3')] = L. | %3D 8le ( (r-In 3) (r-In 3)2 ( * 2. 64e-3 (r-In 4) 6. (r-In 4)2 2 (-4)…

A: Lapalace transform satisfies linearity property, La·ft+b·gt=a·Lft+b·Lgt By laplace transform table…

Q: If then |A|=1 O JA|=-1 O |Al=0 O

A: Follow next step

Q: -5y + 8 = -7 -3 -1/5 C. 1/5 O e Answer not given O O O O O

A: Given: -5y+8=-7 For finding solution of given equation, we do transportation then simplify it

Q: 16. If an+2 = 5an+1 - 6an and ao = 0, a1 = 1, then a10 = %3D 59,125 O 58,025 O 56,425 O 59,700

A:

Q: FAYUL is unformy onlinos on adikset ard f lon) Caueby then f Cauly sauun in R 8 andR and Seruene Cou…

A: Let f be a uniformly continuous function on A of . We have to show that if (xn) is Cauchy, then…

Q: In (x + 2)- In (x + 4x + 4) + In(e*+2) =? O x+2 O 2ln(x+2) O In(x+2) O 4ln(x+2)

A:

Q: 120 If A=0 3 1 R3 B, then det(B) = %3D 0 0 4

A:

Q: In P2 , if B = {1,1+x+x², x + 2} and D = {x²,x, 1} , then Pp-B = 1 2 0 1 1 1 1 0 1 0 1 1 1 1 2

A:

Q: that d | n + 5 and d | n2 + 7, then d | 32. , then n + 5 and n2 + 7 are coprime.

A: For part (a) We have to prove that d is an integer such that dn+5 and dn2+7, then d32. It is given…

Q: If n∈Z, then 5n^2+3n+7 is odd. (Try Cases)

A: Given: 5n2+3n + 7 is odd for n∈Z

Q: If det A 3, then det(2A) 6. O TRUE O FALSE

A:

Q: 14. If an+1 = 2a, + 2 and ao = 2, then an O 2n + 1 O 2n + n + 1 2n+2 - 2 O 3(2") - 1

A: a0 = 2 an+1 = 2an +2 We need to find an. The solution is given below.

Q: dr 1.10. / de A. InlV구+9+피+C C. In 3 3. B. In lV+9+피-In3+ C D. In 3.

A: Given integral is ∫dxx2+9dx. Substitute x=3tanu ⇒dx=3sec2udu Hence,…

Q: O Findl az au if ऊ (1,2)

A: Given: z=x2y+y2x+xyx=u-v y=2u+3v And, u,v=1,2 The objective is to find ∂z∂u. So, at u,v=1,2, the…

Q: If y = C1e + C2e and y(0) =e and y'(0) = 0 then C1 None of These 1 O 26 12

A:

Q: If In a = 2, In b = 3, and In c = 5, evaluate the following: a4 (a) In 62c-2 (b) In vbc-a In(a-b-4)…

A:

Q: 4°c2, 4°c3 Let S = 1+4³c+ 2! 412c4 + 4! 3! If In S = 1216, then find c.

A: Here we use exponential series.