(10) Ifr² = x² +y² + z², then Vxr is (а) 1 (b) о (c) 3 (d) None of these.

Q: -11sin (z)dz -

A:

Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: xdx 3 (5–4x-x2) Z

A: We have to evaluate the integral

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: consider a discrete random variable Y with the following probability table. -2 3 9. 12 p(y) 0.21…

A:

Q: (5) If z = xf (2) +g (2), then the value of Z. + 2xy- + y?. is Əxdy (а) -1 (b) 0 (c) 2 (d) 3г

A:

Q: 2. If y = x2 + 2 and u = 2x – 1, then du II

A:

Q: 4 1+ w ? + jw6

A:

Q: 1. (2u). (2v) = 2 (u.v) 2. (7x+3y). (6x + 4y) = Note: u. (vw) = u(v + (−1)w) =u.v+u.(-1)w =u.v +…

A:

Q: 21 (D² +6D² + 12D+8)) = 0 [AD: y = (C₁+C₂K+ (3²²) ²24

A: Given differential equation D3+6D2+12D+8y=0. The objective is to solve the differential equation.

Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Find a, b, c, d for P(x) : = ax3 + bx? + cx + d if P(1) = 11, b = 3d, a = 2c and P(x) = Q(x) + x+1'

A: Polynomial and remainder

Q: If z=x2sinh 4 then 02z дхду

A: Explanation of the answer is as follows

Q: For u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b)…

A:

Q: Find Re(z) if z(2 + i) = z+(16 + 20i)

A: Given that, z2+i=z¯+16+20i. The objective is to find Rez.       For any complex number z=a+ib, its…

Q: 2. Show that if 8=(AB)- then - > N - - (AB)² + (aß)² – (αB)² – (AB)² = [(A) − (α)] [(B) − (ß)] +…

A:

Q: why does z go from x2+y2 to 1?

A: Sketch the region E.

Q: d) (О. R)(x) — e) (О. R)(-1) 3

A: Given,Qx=7x3+xandRx=6x-7x2then,(Q.R)x=7x3+x6x-7x2=42x4-49x5+6x2-7x3=-49x5+42x4-7x3+6x2

Q: If у %3D x(x2 — 5)2, A. 60(x2 + 1) then y у " is В. 60 (х2 — 1) С. — 60(х2 — 1) D. – 60(x2 + 1)

A:

Q: In 2 (In 2)2-y2 evx2+y² dxdy 0.

A:

Q: Assume that n(U)=70n(U)=70, n(A)=20n(A)=20, and n(B)=15n(B)=15. Then n((A∪B)′)=

A: The given details are                n(U) = 70                n(A) = 20                n(B) = 15

Q: 1 [(3x)2-1]2

A: We will use partial fraction to solve the integral

Q: Find the center and radius of each circle.

A: Center is (-1,-6) with radius 4

Q: Show that if u(x) = el p(2)d then u(z) [1/4 + p(x)y] = — [U(x) y)

A:

Q: If x(z) = 2z + 5z¬1+ 6z¬3 – z4 find x(n).

A: Given,  xz = 2z+5z-1+6z-3-z4  We have to find xn.

Q: 2. If Ā = ê + ŷ, B = 2â – 3ŷ + 2 and C = 4ŷ – 32, determine %3D (a) (Ã × B) × Č (b) Ã× (B × Č)…

A: