Skip to main content

ISRO Mechanical Engineering Mathematics Questions, Answers and Explanation

ISRO Mechanical Engineering Mathematics Questions, Answers and Explanation

Linear Algebra

2017.2.36. A point P moves along the path y = x2 -4. What is the displacement when the point moves from x =1 to x = 3.
a) 8.24, @ tan-1 (4)
b) 2,  @ tan-1 (1)
c) 11.3, @ tan-1 (4)
d) 11.3,  @ tan-1 (1)

Answer
a) 8.24, @ tan-1 (4)

Explanation
when x = 1, y = 1-4 = -3
when x = 3, y = 9-4 = 5
distance between the 2 points = √ (22+82) = √ (68), which is just greater than 8. So other options are eliminated.

2017.2.47. A cubic B-spline curve requires minimum ......... control points
a) 3
b) 4
c) 5
d) 6

Answer
b) 4

Explanation
A line (linear curve) requires minimum 2 control points
A quadratic curve requires minimum 3 control points
In general a curve of degree n requires minimum n+1 control points

Derivatives

2017.2.80.  A point moves according to the relation x = 8t2 cos ω t , y = -4t3 sin ωt, where x and y are in meters and t in seconds. If angular velocity ω = 8 π rad/s, velocity vector of the point at t = 0.5s is given by
a) 8 + j4π
b) 6 + j20π
c) 8 - j4π
d) -20π -j6

Answer
c) 8 - j4π

Explanation
x = 8t2 cos ω t
y = -4t3 sin ωt
u = dx/dt = 16t cos ω t - 8ωt2 sin ω t
v = dy/dt = -12t2 sin ωt - -4ωt3 cos ωt
velocity vector = u + jv
 = 16t cos ω t - 8ωt2 sin ω t + j(-12t2 sin ωt - 4ωt3 cos ωt)
Substituting ω = 8 π rad/s and t = 0.5s,
velocity vector = 16*0.5 cos 8 π *0.5 - 8*8 π*0.52 sin 8 π *0.5 + j(-12*0.52 sin 8 π*0.5 -4*8 π*0.53 cos 8 π*0.5)
 = 8 cos 4 π  - 2 sin 4 π + j(-3 sin 4 π -4 πcos 4 π)
 = 8 - j4 π

Laplace Transforms

2006. Laplace transform of t2 + 2t + 3 is
a) - 2 ⁄ s3 - 2 ⁄ s2  - 3 ⁄ s
b) 2 ⁄ s3 + 2 ⁄ s2 - 3 ⁄ s
c) 2 ⁄ s3 + 2 ⁄ s2+3 ⁄ s
d) - 2 ⁄ s3 + 2 ⁄ s2 - 3 ⁄ s

2007. Laplace transform of sin3 3t is
a) 24 ⁄ (s2+4)(s2+36)
b) 1 ⁄ (s2+4)(s2+64)
c) 48 ⁄ (s2+4)(s2+36)
d) 64 ⁄ (s2+4)(s2+36)

2017_1. Laplace transform of t cos (at) is
a) s2+a2 ⁄ (s2-a2)
b) s ⁄ (s2-a2)
c) s2-a2 ⁄ (s2+a2)
d) s ⁄ (s2+a2)

2017.2.4 If f(t) = eat, its Laplace transform (for s > a) is given by
a) a⁄s2 + (s-a)
b) √π⁄2(s-a)
c) 1⁄(s-a)
d) Does not exist

Answer
c) 1⁄(s-a)

Explanation
If L{f(t)}=F(s), then L{eatf(t)}=F(s-a)
In the problem f(t) = 1, L(1) =  F(s) = 1/s
Therefore, L(eat1) = F(s-a) = 1/(s-a)

Probability

2017.2.23. A man draws 3 balls from a jug containing 5 white balls and 7 black balls. He gets Rs. 20 for each white ball and Rs. 10 for each black ball. What is his expectation?
a) Rs. 21.25
b) Rs 42.50
c) Rs 31.50
d) Rs 45.21

Answer
b) Rs 42.50

Explanation
3 balls can be drawn in the following ways
- 3 white balls, P = 5C3/11C3 = 10/220 = 2/44
- 2 white balls and 1 black ball, P = 5C2*7C1/11C3 = 70/220 = 14/44
- 1 white ball and 2 black balls, P = 5C1*7C2/11C3 = 125/220 = 21/44
- 3 black balls, P = 7C3/11C3 = 35/220 = 7/44
Expectation = sum of the product of probability and the money he gets for each combination
= (2/44)*60 + (14/44)*50 + (21/44)*40 + (7/44)*30 = 935/22 = 85/2 = 42.50
2018.77. In a party, each person shook hands with every other person present. The total number of hand shakes was 45. The number of people in the party are
a) 12
b) 10
c) 8
d) 6

Answer
b) 10

Explanation
First person can shake the hand with n-1 persons.
The second person can shake hand with n-2 persons, because the second person has already shaken hands with the first person.
Proceeding this way the last person has no one to shake hands with. That persons handshake has been accounted previously.
So if there are n persons there are (n-1)+(n-2)+(n-3)+.....+1 hand shakes = nC2 = (n-1)n/2 = Sum of first n-1 integers.
Here (n-1)n/2 = 45
(n-1)n = 90 = 9 x 10

So n = 10 


Labels:

Popular posts from this blog

ISRO Mechanical Engineering Fluid Mechanics Questions, Answers and Explanation

ISRO Mechanical Engineering Fluid Mechanics Fluid Properties - Bulk modulus 2011. 10.  A liquid compressed in cylinder has a volume of 0.04 m 3  at 50kg/cm 2  and a volume of 0.039 m 3  at 150 kg/cm 2 . The bulk modulus of elasticity of liquid is a) 400 kg/cm 2 b) 40 x 10 6  kg/cm 2 c) 40 x 10 5  kg/cm 2 d) 4000 kg/cm 2 Answer d) 4000 kg/cm 2 Explanation The bulk elastic properties of a material determine how much it will compress under a given amount of external pressure. The ratio of the change in pressure to the fractional volume compression is called the bulk modulus of the material. The reciprocal of the bulk modulus is called the compressibility of the substance. Bulk Modulus, B = ΔP/(ΔV/V) Here ΔP = 150-50 =100 kg/cm 2 ΔV = 0.04-0.039 = 0.001m 3 V = 0.04m 3 B = (100/(0.001/0.04)) = 100x0.04/0.001 =  4000 kg/cm 2 Fluid Properties - Surface Tension 2011.13  If the surface tension of water-air interface ...
Read more

ISRO Mechanical Strength of Materials Questions, Answers and Explanation

Strength of Materials Simple Stresses and Strains 2017.2.9.  Which of the following is true for ductile materials? a) Engineering stress – strain curve cannot have negative slope b) Most applicable failure theory is maximum principal stress theory c) Ultimate strain is the strain at ultimate stress d) Strain hardening is represented by a negative slope in engineering stress strain curve Answer c)  Ultimate strain is the strain at ultimate stress Explanation  Principal stress theory is applicable for brittle materials. Elastic Constants 2017.2. 2.  For isotropic materials, the modulus of Elasticity in tension and shear (E and G) are related to the Poisson's ratio (&nu) as follows a) E = G/(2(1+ν)) b) G = E/(2(1+ν)) c) G = E/(2(1-ν)) d) E = G/(2(1-ν)) Answer b) G = E/(2(1+ν)) Explanation Derivation of relation between Modulus of elasticity in tension and shear Torsion 2017.2.76.  A 3m l...
Read more

ISRO Mechanical Engineering Heat Transfer Questions, Answers and Explanation

ISRO Mechanical Engineering Heat Transfer Questions, Answers and Explanation Conduction 2017.2.62.  The distribution of a temperature T, at a particular instant , across a large concrete wall, 1m thick, which is heated from one side is given by the equation T = 150-80x+16x 2 , where the distance x is in meters and T is in degree Celsius. Thermal conductivity of wall is 0.6W/mK, area of cross section is 10 m 2 . The heat accumulated in unit time at this instant in the concrete wall is a) 768J/sec b) 384J/sec c) 96J/sec d) 192J/sec Answer d) 192J/sec Explanation Heat accumulated = Heat conducted away - Heat conducted in Q = kA*[dT/dx] at x = 1 minus at at x = 0 = 0.6*10*(-80+32x) at x = 1 minus at x = 0 =6*32 = 192J/sec General 2017.2.29.  Which of the following is FALSE? a) Heat flow by conduction is directly proportional to the area and temperature gradient b) Heat flow by convection is directly proportional to the area and temperature differen...
Read more