Description : The equation m(d 2 x/ dt 2 ) + c (dx/dt) + Kx = F 0 sin ωt is a second order differential equation. The solution of this linear equation is given as A. complementary function B. particular function C. sum of complementary and particular function D. difference of complementary and particular function
Last Answer : C. sum of complementary and particular function
Description : According to D' Alembert's principle, m (d 2 x/ dt 2 ) + c (dx/dt) + Kx =0 is the differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is ... Φ) C x = (A - Bt) e - ωt D x = X e - ξωt (cos ω d t + Φ)
Last Answer : A x = (A + Bt) e – ωt
Description : According to D' Alembert's principle, m (d 2 x/ dt 2 ) + c (dx/dt) + Kx =0 is the differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is ... ) C. x = (A - Bt) e - ωt D. x = X e - ξωt (cos ω d t + Φ
Last Answer : A. x = (A + Bt) e – ωt
Description : According to D' Alembert's principle, m (d 2 x/ dt 2 ) + c (dx/dt) + Kx =0 is the A differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is ... (C)x = (A - Bt) e - ωt ( D )x = X e - ξωt (cos ω d t + Φ
Last Answer : ( A ) x = (A + Bt) e – ωt
Description : According to D' Alembert's principle, m (d 2 x/ dt 2 ) + c (dx/dt) + Kx =0 is the differential equati damped free vibrations having single degree of freedom. What will be the solution to this differ equation if the system is critically ... c. x = (A - Bt) e - ωt d. x = X e - ξωt (cos ω d t + Φ)
Last Answer : a. x = (A + Bt) e – ωt
Description : `" if " f(x) ={ underset( 5x" "2 le x le 3) (3x+ 4,0 le x le 2),` then `int_(0)^(3) f(x) dx=?`
Last Answer : `" if " f(x) ={ underset( 5x" "2 le x le 3) (3x+ 4,0 le x le 2),` then `int_(0)^(3) f(x) dx=?` A. `(53)/(2)` B. `(55)/(2)` C. `(57)/(2)` D.
Description : `"if "f(x) ={ underset(5x, 1,2 le x le 3)(3x+4, 0 le x le 2}},` then evaluate `int_(0)^(3) f(x) dx.`
Last Answer : `"if "f(x) ={ underset(5x, 1,2 le x le 3)(3x+4, 0 le x le 2}},` then evaluate `int_(0)^(3) f(x) dx.`
Description : The order of reaction is the number of moles whose concentrations determine the rate of a reaction at a given temperature Give the integrated equation for first order reaction. K = (2.303 / t) * log (a ... a' is the initial concentration of reactants x' is the amount reacted in time t seconds
Last Answer : What is Threshold energy ?
Description : Gibbs-Helmholtz equation is (A) ∆F = ∆H + T [∂(∆F)/∂T]P (B) ΔF = ΔH - TΔT (C) d(E - TS) T, V < 0 (D) dP/dT = ∆Hvap/T.∆Vvap
Last Answer : (A) ∆F = ∆H + T [∂(∆F)/∂T]P
Description : A second order liquid phase reaction, A → B, is carried out in a mixed flow reactor operated in semi batch mode (no exit stream). The reactant A at concentration CAF is fed to the reactor at a volumetric flow rate of F. The volume ... 2V (C) d(VCA )/dt = -FCA - kCA 2V (D) d(VCA )/dt = FCAF - kCA 2V
Last Answer : (D) d(VCA )/dt = FCAF - kCA 2V
Description : `"If "f(x) ={underset(x^(2)+1.2 le x le 3)(2x+1.1 le x le 2),` then evaluate `int_(1)^(3) f(x) dx.`
Last Answer : `"If "f(x) ={underset(x^(2)+1.2 le x le 3)(2x+1.1 le x le 2),` then evaluate `int_(1)^(3) f(x) dx.`
Description : `int(1)/(tsqrt(t^(2) -1))dt`
Last Answer : `int(1)/(tsqrt(t^(2) -1))dt`
Description : The 'E' curve for a non-ideal reactor defines the fraction of fluid having age between t and t + dt (A) At the inlet (B) At the outlet (C) In the reactor (D) Averaged over the inlet and outlet
Last Answer : (B) At the outlet
Description : If Cv is the coefficient of consolidation, is the time and is drainage path of one dimensional consolidation of soil, the time factor Tv, is given by (A) Tv = d²/Cv t (B) Tv = t²/d²Cv (C) Tv = Cv3 /d²t (D) Tv = Cv t/dt
Last Answer : Answer: Option D
Description : Pick out the Clausius-Clapeyron equation from the following: (A) dP/dT = ∆H/T∆V (B) ln P = - (∆H/RT) + constant (C) ∆F = ∆H + T [∂(∆F)/∂T]P (D) None of these
Last Answer : B) ln P = - (∆H/RT) + constant
Description : The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + s/m X x = 0 If the roots of this equation are real, then the system will be A. over damped B. under damped C. critically damped D. none of the mentioned
Last Answer : A. over damped
Description : The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + k/m X x = 0 If the roots of this equation are real, then the system will be a) over damped b) under damped c) critically damped d) none of the mentioned Ans:a
Last Answer : a) over damped
Description : A DT signal x(n) is defined as
Last Answer : x(n)= {2,3,4,5,6} � x(-n)={6,5,4,3, 2} � x(-n+4)={6,5,4,3,2} �
Description : When electric potential is null, then the electric field intensity will be a) 0 b) 1 c) dA/dt d) –dA/dt
Last Answer : d) –dA/dt
Description : The exit age distribution of a fluid leaving a vessel (denoted by E) is used to study the extent of non-ideal flow in the vessel. The value of ∫∞ 0 E.dt is (A) 0 (B) 1 (C) ∞ (D) √2π
Last Answer : (B) 1
Description : The first order gas phase reaction as shown in the bellow figure is conducted isothermally in batch mode. The rate of change of conversion with time is given by (A) dXA /dt = k1 (1 - XA ) 2 (1 + 2XA ) (B) dXA /dt = k1 (1 - XA ... 5XA ) (C) dXA /dt = k1 (1 - XA ) (D) dXA /dt = k1 (1 - XA )/(1 + XA )
Last Answer : (C) dXA /dt = k1 (1 - XA
Description : In an irreversible process (A) Tds = dE - dW = 0 (B) dE - dW - Tds = 0 (C) Tds - dE + dW < 0 (D) Tds - dT + dW < 0
Last Answer : (C) Tds - dE + dW < 0
Description : Calculate the recoverable waste heat (Q, in kCal/hour) from flue gases using the followingparameters: V (flow rate of the substance) 2000 m3/hr r (density of the flue gas): 0.9 kg/m3 Cp (specific heat ... (temperature difference): 120 oC h (recovery factor): 50% a. 21600 b. 43200 c. 25600 d. 34000
Last Answer : 21600
Description : `int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?`
Last Answer : `int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?` A. `-log 3` B. `-2 log 3` C. `2 log 3` D.
Description : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?`
Last Answer : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?` A. `0` B. `1` C. None of the above D.
Description : `int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?`
Last Answer : `int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?` A. `(pi)/(2) +log 2` B. `(pi)/(2) -log 2` C. `-(pi)/(2) - log 2` D.
Description : `int_(0)^(pi) sin (n+(1)/(2))x. " cosec ".(x)/(2) dx=?`
Last Answer : `int_(0)^(pi) sin (n+(1)/(2))x. " cosec ".(x)/(2) dx=?` A. `(pi)/(2)` B. `pi` C. `2pi` D.
Description : `int_(0)^(pi//4) sqrt(cot x dx) =?`
Last Answer : `int_(0)^(pi//4) sqrt(cot x dx) =?` A. `(Pi sqrt(2))/(4)+(1)/(sqrt(2)) log (sqrt(2)-1)` B. `(- ... (pisqrt(2))/(4) -(1)/(sqrt(2))log (sqrt(2)-1)` D.
Description : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?`
Last Answer : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?` A. `(pi sqrt(3))/(12)+(1)/(2)` B. `(pisqrt(3))/(12)-(1)/(2)` C. `(pisqrt(3))/(12) -(1)/(2)` D.
Description : `int_(0)^(pi//4) log (1+tan x) dx =?`
Last Answer : `int_(0)^(pi//4) log (1+tan x) dx =?` A. `(pi)/(4) log 2` B. `(pi)/(6) log 2` C. `(pi)/(8) log 2` D.
Description : `int_(0)^(pi//2) x sin cos x dx=?`
Last Answer : `int_(0)^(pi//2) x sin cos x dx=?` A. `(pi)/(4)` B. `(pi)/(8)` C. `(pi)/(12)` D.
Description : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?`
Last Answer : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?` A. `sqrt(2)-1` B. `sqrt(2)` C. `-sqrt(2)` D.
Description : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?`
Last Answer : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?` A. `(pi)/(2)+1` B. `(pi)/(2) -1` C. None of these D.
Description : `int_(0)^(1) x (1 -x)^(n) dx=?`
Last Answer : `int_(0)^(1) x (1 -x)^(n) dx=?` A. `(1)/((n+1)(n+2))` B. `(1)/(n(n+2))` C. `(1)/((n+1)(n+3))` D.
Description : `int_(0)^(2) e^(x) dx`
Last Answer : `int_(0)^(2) e^(x) dx`
Description : `int_(0)^(3)(x^(2)+1)dx`
Last Answer : `int_(0)^(3)(x^(2)+1)dx`
Description : Evaluate : `int_(0)^(1) (1-x)^(3//2) dx`
Last Answer : Evaluate : `int_(0)^(1) (1-x)^(3//2) dx`
Description : `int_(0)^(pi) x sin x. cos^(2) x dx`
Last Answer : `int_(0)^(pi) x sin x. cos^(2) x dx`
Description : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Last Answer : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Description : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Last Answer : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Description : `int_(0)^(pi//2) x sin x cos x dx`
Last Answer : `int_(0)^(pi//2) x sin x cos x dx`
Description : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Last Answer : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Description : Evaluate :`int_(0)^(8) |x-5|dx`
Last Answer : Evaluate :`int_(0)^(8) |x-5|dx`
Description : Evaluate : `int_(0)^(4) x(4-x)^(3//2)dx`
Last Answer : Evaluate : `int_(0)^(4) x(4-x)^(3//2)dx`
Description : `int_(0)^(pi) x sin^(2) x dx`
Last Answer : `int_(0)^(pi) x sin^(2) x dx`
Description : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`
Last Answer : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`
Description : `int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx`
Last Answer : `int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx`
Description : `int_(0)^(pi) (1)/(5+2 cos x)dx`
Last Answer : `int_(0)^(pi) (1)/(5+2 cos x)dx`