GATE Exam tutorials: 2012

Few tips for GATE exam:
1. Believe in your capability
2. Dont take a wild guess, there is negative marking... hence it will work against you!!!
3. Try to strike out options before coming to concluding answer.
4. Many a times questions are tricky and the clue is given right in the question iteslf. Try to identify it (See Question number 9).

1. For an undamped harmonic oscillator, resonance
(A) occurs when excitation frequency is greater than undamped natural frequency
(B) occurs when excitation frequency is less than undamped natural frequency
(C) occurs when excitation frequency is equal to undamped natural frequency
(D) never occurs

Ans: option C : the resonance always occurs when excitation frequency matches undamped natural frequency. No of Natural Frequncies = No of DOF in the system. hence a continuo\us system has infinite number of natural frequencies.

2. Which of these is a solid state joining process?
(A) gas tungsten arc welding
(B) resistance spot welding
(C) friction welding
(D) submerged arc welding

Ans: Option B : all other processes involve production of heat by some means either by arc or friction so
as to melt and fuse the blanks to be welded, but in case of resistance spot welding only electric current
along with pressure is used to create the weld.

3. The force required in a blanking operation of a stel sheet is 5.0kN. the thickness of sheet is 't' and diameter is 'd'. For same material if diameter is increased to 1.5d and thickness is reduced to 0.4t the new blabking force in kN will be

(A) 3.0
(B) 4.5
(C) 5.0
(D) 8.0
Ans: Option A : pi * d * t * fs = 5.0                              Eq I
                          pi * 1.5d * 0.4t * fs = x                       Eq II
                          pi *d * t * fs * 1.5 * 0.4 = x                rearranging EqII
                          5.0 * 1.5 * 0.4 = x                              substituting Eq I in Eq II
                           x = 3.0                                               Ans

4. A Coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

(A) 1/4
(B) 3/8
(C) 1/2
(D) 3/4
Ans: Option A : when coin is tossed getting a Head H or Tail T has pobability = 1/2;
If the coin was tossed 4 times to get the Head H exactly 3 times there are four different ways
1: THHH : 1/2 * 1/2 * 1/2 * 1/2 = 1/16
2: HTHH : 1/2 * 1/2 * 1/2 * 1/2 = 1/16
3: HHTH : 1/2 * 1/2 * 1/2 * 1/2 = 1/16
4: HHHT : 1/2 * 1/2 * 1/2 * 1/2 = 1/16
as there are 4 different ways this result can be obtained hence the actual probability is
Ans = 1/16 + 1/16 + 1/16 + 1/16 = 1/4

5. The divergence of the vector field (x-y)i + (y-x)j + (x+y+z)k is
(A) 0
(B) 1
(C) 2
(D) 3

Ans: D : the divergence is given by:
$\operatorname{div}\,\mathbf{F} = \nabla\cdot\mathbf{F} =\frac{\partial U}{\partial x} +\frac{\partial V}{\partial y} +\frac{\partial W}{\partial z }.$

6. A rod of length L and diameter D is subjcted to a tensile load P. Which of the following is sufficient to calculate resulting change in diameter?

(A) Young's Modulus
(B) Shear Modulus
(C) Poisson's ratio
(D) Both Young's modulus and shear modulus
Ans: C : Poissons ratio is the ratio of strains in lateral direction to longitudenal direction.
Hence if you calculate strain in logitudenal direction you can find strain in diameter and also resulting change in it.

7. A Mechanism has 8 links and 10 rotary joints. The number of degree of freedom using Gruebler's criterion is

(A) 0
(B) 1
(C) 2
(D) 3
Ans: B : According to Gruebler's criteria for planar mechanism the DOF is givn by
DOF = 3(N-1) - 2J
DOF = Degree of freedom
N   = No of links in mechanism
J   = No of joints in mechanism

8. Internal gear cutting operation can be performed by
(A) Milling
(B) Shaping with rack cutter
(C) Shaping with pinion cutter
(D) hobbing
Ans: B : All other processes are external gear cuttig processes.

9. 2 moles of oxygen is mixed with isentropically with another 2 moles of oxygen, so that final pressure and
temperature becomes same as that of their individual constituents at initial stage. The universal gas constant is
given as R. the change of entropy per mole of oxygen is given by
(A) –Rln2
(B) 0
(C) Rln2
(D) Rln4
Ans B: for isentropic process the heat transfer is zero hence change in entropy is zero.
Isentropic means No Change in Entropy, hence in above question the answer is Zero.

10. In a Cantilever type gate hinged at Q is as show in figure, P and R are center of gravity of cantilever part and counter weight respectively. The mass of cantilever part is 75 kg , the mass of the counterbalance for static balancing would be

(A) 75 kg
(B) 150 kg
(C) 225 kg
(D) 300 kg
Ans: D
By comparing the mass moment about the hinge Q
P x 2.0 = R x 0.5
R = 75 x 2.0 / 0.5 = 300 kg

11. If 3 coins are tossed simultaniously, the probability of getting atleast 1 Head is
(A) 1/8
(B) 3/8
(C) 1/2
(D) 7/8
Ans: D:
traditional solution:
The possible outcome when 3 coins are tossed are
TTT, HTT, THT, TTH, HHT, HTH, THH, HHH
We Need atleast 1 Head, there are 7 combinations out of 8 in which user will get atleast 1 Head
Hence answer is 7/8.

Quick Solution:
When single coin is tossed the probability of getting Head is 1/2.
When more than 1 coins are tossed and only one Head is expected then it is likely to occur more easily than when single coin is tossed. Hence the probability of getting atleast 1 Head when 3 coins are tossed is more than 1/2.
There is only one option out of four having value more than 1/2 is Option "D" i.e 7/8

12. If a closed system undergoes irreversible process, the Entropy of the system
(A) must increase
(B) always remains constant
(C) must decrease
(D) can increase, decrease or remain constant
Ans: A: irreversible process means increase in entropy hence answer is "A".

13. In an ideal vapour compression refrigeration cycle, the specific enthalpy of the refrigerent (kJ/kg) at different states are given as
Inlet of Condenser = 283
Exit of Condenser = 116
Exit of evaporator = 232
the COP of this cycle is
(A) 2.27
(B) 2.75
(C) 3.27
(D) 3.75
Ans: A:
Enthalpy @ exit of condenser = Enthalpy @ inlet of evaporator
Desired Output = Heat absorbed during Evaporation = Exit of evaporator - Exit of Condenser
Desired Output = 232-116 = 116 kJ/kg
Input to ref system = Workdone by compressor = Inlet of Condenser - Exit of evaporator
Input to ref system = 283-232 = 51 kJ/kg
COP = Desired Output/Input to ref system = 116/51 = 2.27

14. For the given matrix find the value of ‘x’ if Transpose of the matrix is equal to Inverse of the Matrix.

(A) -4/5
(B) -3/5
(C) 3/5
(D) 4/5
Ans: A:-4/5

15. The divergence of the vector field 3xz i + 2xy j – yz² k at a point (1,1,1) is equal to
(A) 7
(B) 4
(C) 3
(D) 0

Ans: (C):3

GATE Exam tutorials

Sunday, 5 August 2012

Free GATE 2013 Question Set 2

Monday, 16 July 2012

Free GATE 2013 Questions Set 1