# GATE ME 2002

 Question 1
Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight?
 A $\frac{5}{36}$ B $\frac{5}{18}$ C $\frac{1}{4}$ D $\frac{1}{3}$
Engineering Mathematics   Probability and Statistics
 Question 2
Which of the following functions is not differentiable in the domain [-1,1]?
 A $f(x)=x^{2}$ B f(x)=x-1 C f(x)=2 D f(x)=maximum(x,-x)
Engineering Mathematics   Calculus
Question 2 Explanation:
we know that |x| is not differentiable at x=0 which is in interval [-1,1].
Rest of the functions are continuous and differentiable everywhere.
 Question 3
A regression model is used to express a variable Y as a function of another variable X. This implies that
 A there is a causal relationship between Y and X B a value of X may be used to estimate a value of Y C values of X exactly determine values of Y D there is no causal relationship between Y and X
Industrial Engineering   Production Planning and Control
 Question 4
The principles of motion economy are mostly used while conducting
 A a method study on an operation B a time study on an operation C a financial appraisal of an operation D a feasibility study of the proposed manufacturing plant

 Question 5
The standard time of an operation while conducting a time study is
 A mean observed time + allowances B normal time + allowances C mean observed time x rating factor + allowances D normal time x rating factor + allowances
Industrial Engineering   Production Planning and Control
 Question 6
In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made?
 A (0.16,0.24) B (0.12,0.28) C (0.08,0.32) D none of these

 Question 7
An item can be purchased for Rs.100. The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is
 A 50 B 100 C 200 D 400
Industrial Engineering   Inventory Control
 Question 8
The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth gear mechanism with $20^{\circ}$ pressure angle is
 A 14 B 12 C 18 D 32
Machine Design   Gears
Question 8 Explanation:
$Z_{\text {tin }}=$ minimum no. of teeth on pinion to
avoid interference. since gear ratio is not given so we assumed
that arrangement is rack & pinion arrangement.
\begin{aligned} z_{\min } &=\frac{2 \times A w}{\sin ^{2} \phi}=\frac{2 \times 1}{\sin ^{2} 20}=17.09 \\ & \simeq 18 \text { teeth } \end{aligned}
 Question 9
The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is
 A 2 B 3 C 4 D 5
Theory of Machine   Planar Mechanisms
 Question 10
The Coriolis component of acceleration is present in
 A 4-bar mechanisms with 4 turning pairs B slider-crank mechanism C shape mechanism D Scotch Yoke mechanism
Theory of Machine   Displacement, Velocity and Acceleration
There are 10 questions to complete. 