61. Study showed the percentage of occurrence of an activity as 50%. The number of observation for 95% confidence level and an accuracy of ±2% is
(a) 1500
(b) 2000
(c) 2500
(d) 3000
62. 1 m^3 of air at a pressure of 10 kg/cm^2 is allowed to expand freely to a volume 10 m^3. The work done will be
(a) +ve (b) -ve
(c) zero (d) $10^5$ kg m
63. Suppose that a particle moves on a coordinate line so that its velocity at time is v(t) = t^2 -2t m/s. The displacement of the particle during time interval 0 < t < 3 is
(a) 4 m (b) 0 m
(c) 8/3 m (d) 3/8 m
64. Approach of cooling tower means
(a) difference in temperature of hot water entering the cold water leaving
(b) difference in temperature of cold water and atmospheric temperature
(c) difference in temperature of the cold water leaving the cold tower and the wet bulb temperature of surrounding air
(d) amount of heat thrown away by the cooling tower in kcal/hr
65. Which of the following is not the intensive property?
(a) pressure (b) heat
(c) density (d) temperature
66. A Carnot cycle consist of
(a) two constant pressure and two adiabatic processes
(b) two isothermal and two adiabatic processes
(c) two constant volume and two adiabatic processes
(d) one constant pressure, one constant volume and two adiabatic processes
67. Two loads P act at right angles to one another at the free end of a cantilever beam having square cross-section dxd and length l on the vertical and horizontal faces. Maximum bending stress in the beam will be equal to
(a) 6 $Pl/d^3$ (b) 24 $Pl/d^3$
(c) 12 $Pl/d^3$ (d) 18 $Pl/d^3$
68. The head loss due to sudden expansion assuming incompressible flow is exposed by
(a) $\frac{V_1^2-V_2^2}{2}$ (b) $\frac{V_2^2-V_1^3}{2}$
(c) $\frac{(V_1-V_2)^2}{g}$ (d) 5$\frac{(V_1-V_2)^2}{2g}$
69. PERT has the following time estimate
(a) one time estimate (b) two time estimate
(c) three time estimate (d) four time estimate
70. Two plane slabs of equal areas and conductivities in the ratio 1:2 are held together and temperature in between surface ends are t1 and t2. If junction temperature in between two surfaces is desired to be $\frac{t_1 +T_2}{2}$, then their thickness should be in the ratio of
(a) 2:1 (b)1:2
(c) 1:1 (d) 3:1
71. 300 kJ/s of heat is supplied at constant temperature of 500 K to a heat engine. The heat rejection takes place at 300 K. The following results are obtained (a) 210 kJ (b) 180 kJ (c) 150 kJ. Identify whether result is a reversible cycle, irreversible cycle or impossible cycle respectively
(a) reversible/irreversible/impossible respectively
(b) irreversible/reversible/impossible respectively
(c) irreversible/impossible/reversible respectively
(d) none of the above
72. If cube root of unity are 1, w, w^2 then the roots og the equation $(x-1)^3 + 8=0$
(a) -1, -1+2w, -1-2$w^2$ (b) -1, -1, -1
(c) -1, 1- 2w, 1-2$w^2$ (d) -1, -1+2w, 1+2$w^2$
73. If 1, w, $w^2$ ar cube roots of unity, then the value of
\(\det{\begin{vmatrix}1&w&w^{2n}\\ w^n&w^{2n}&1\\w^{2n}&1&w^n\end{vmatrix}}\)
(a) 1 (b) 0
(c) w (d) $w^2$
74. Three houses are available in a localoty. Three person apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
(a) 2/9 (b) 1/9
(c) 8/9 (d)7/9
75. The rank of the matrix
\(\begin{bmatrix}-2&4&2\\3&-4&-1\\4&-3&1\end{bmatrix}\) is
(a) 0 (b) 1
(c) 2 (d) 3
76.If $3e^x tany dx + (1-e^x)sec^2 ydy =0$, then y is
(a) $tany = c(1+e^x)^3$ (b) $y = c(1-e^x)^3$
(c) $log y = c(1+e^x)^3$ (d) $tan y = c(1-e^x)^3$
77. Which of the following represents a wave equation?
(a) $\bigtriangledown^2V =0$
(b) $\frac{\partial^2V}{\partial t^2} = c^2\bigtriangledown^2V$
(c) $\frac{\partial V}{\partial t} = k \bigtriangledown^2V$
(d) none of the above
78. $1+ x^2/2! + x^4/4! + x^6/6!+ ..... stands for
(a) sinh x (b) cosh x
(c) cos x (d) sin x
79. $\int sec x dx$ is
(a) log(sec x + tan x) + c (b) tan x + c
(c) sec x + tan x + c (d) sec x *tan x) + c
80. Inverse Laplace transformation of $\frac{s}{s^2+a^2}$ is
(a) cos at (b) sin at
(c) cosh at (d) sinh at
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