For the differential equation \(\frac{d^{2}x}{dt^{2}}+6\frac{dx}{dt}+8x=0\) with initial conditions x(0) = 1 and \(\frac{dx}{dt}\mid _{t=0}=0\), the solution is
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Solution
A fair coin is tossed three times in succession. If the first toss produce a head, then the probability of getting exactly two heads in three tosses is _______.
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Solution
For a given matrix \(A=\begin{bmatrix} 2\, -2\, 3 & & \\ -2\, -1\, 6 & & \\ 1\, 2\, 0 & & \end{bmatrix}\), one of the eigen value is 3. The other two eigen values are
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Solution
Consider an ordinary differential equation dx⁄dt = 4t + 4. If x= x0. at t = 0, the increment in x calculated using Runge-kutta fourth order multi-step method with a step size of Dt = 0.2 is________.
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Solution
If \(\underset{F}{\rightarrow}=(2X^{2}-3z)\hat{i}-2xy\hat{j}-4x\hat{k}\), then evaluate \(\underset{V}{\int \int \int}\underset{\bigtriangledown }{\rightarrow}\underset{F}{\rightarrow}dV\),where V is the region bounded by the planes x= 0, y= 0, z =0 and 2x + 2y + z = 4
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Solution
The equation of motion of a body is given as:a = t3– 3t2 + 6. If velocity is 4 m/s at t = 1 sec. Then, velocity at 10 seconds will be __________.
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Solution
Which one of the following is the steady flow energy equation for a boiler?
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Solution
Stead flow energy equation for a boiler is given as: Q = h2 + h1
A 320 cm high vertical pipe at 150°C wall temperature is in a room with still air at 10°C. This pipe supplies heat at the rate of 8 kw into the room air by natural convection. Assuming laminar flow, the height of pipe needed to supply 1kw only will be ________.
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Solution
Given: Height of pipe (H1) = 320 cm
Temperature difference (ΔT) = 140°C
Rate of Heat transfer (Q1) = 8 kw
Rate of Heat transfer haded (Q2) = 1 kw
Q = HdAΔT (According to Newton’s Law of colling)
Match List-I with List-II
List-I List-II
A.Gas to liquid 1.Compact
B.Space vehicle 2.shell and tube
C.Condenser 3.Finned tube
D.Air pre-heater 4.Regenerative
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Solution
Gas to liquid = Finned tube
Space vehicle = compact
condensor = shell and tube
Air-preheater = Regenerative
A Bell-cole-man air refrigeration cycle worker as a reversed:
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Solution
A Bell-coleman air refriguration cycle worker as a reverse Brayton cycle which is driven in reverse direction through net work input and air is used and working fluid.