Given that the determinant of the matrix \(\begin{bmatrix} 1 & 3 &0 \\ 2 &6 &4 \\ -1 &0 &2 \end{bmatrix}\) is – 12, the determinant of the matrix \(\begin{bmatrix} 2 & 6 &0 \\ 4 &12 &8 \\ -2 &0 &4 \end{bmatrix}\) is___________ .
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Solution
Match the correct pairs
Numerical Order of
Interation Scheme Fitting polynormal
P.Simpson’s Rule 1.First
Q.Trapezoidal Rule 2.Second
R.Simpson’s Rule 3.Third
The integral \(\oint\)f(z)dz, evaluated around the unit circle on the complex plane for f(z) = \(\frac{cos\: z}{z}\) is
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Solution
The inverse transform of the function F(s) =\(\frac{1}{S(S+1)}\) is given by
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Solution
Given function is f(x) =x–\(\frac{X^{3}}{3!}+\frac{X^{5}}{5!}-\frac{X^{7}}{7!}\)+………., if limit of the series as x approaches π⁄2, then the value of \(\lim_{X\rightarrow \frac{\pi }{2}}\) f(x) is _____.
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Solution
A system to forces acting on a lamina shown in figure.The resultant of force system will meet AB at:
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Solution
tan α = \(\frac{5}{10}\) = 1⁄2 ⇒ α = tan–1(1/2)
So, we can say that resultant of forces must at C.
If the volume of moist air with 50% relative humidity is isothermally reduced to half its original volume, then relative humidity of moist air will be…………….
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Solution
Nodular grey cast iron is obtained from the grey cast iron by adding a small amount of
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Solution
Nodular grey cast iron is produced from grey cast iron by adding a small amount of magnesium.
A 4 kw, 20 L water heater is switched on for 10 min. The heat capacity for water in 4 kJ/kgK. Assuming all the electrical energy has gone into heating the water. The increase of the water temperature will be ________
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Solution
30°C: Heat capacity (cp) = 4 kJ/kg K, time (t) = 10 min
Mass (m) = 20 L, Load (p) = 4 kw
Using the following equation :
Heat (Q) = mcpδT = 4 × 10 × 6020 × 4 × δT = 4 × 10 × 60
δT= 30°C
A composite wall of a furnace has 3 layers of equal thickness having thermal condutivities in the ratio of 1 :2 : 4. What will be the temperature drop ratio across the three respective layers?
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Solution