Question 1
Which of the following functions is an odd function?
SNAP Functions, Graphs and Statistics Questions
SNAP Functions, Graphs and Statistics Questions
Solution
For odd function f(x) = -f(-x)
for option A : f(x) = $$2^{-x.x}$$, f(-x) = $$2^{-(-x).(-x)}$$ = $$2^{-x.x}$$ = f(x). Hence Option A is not correct
for Option B : f(x) = $$2^{x-x.x.x.x}$$, f(-x) = $$2^{(-x)-(-x).(-x).(-x).(-x)}$$ = $$2^{(-x)-x.x.x.x)}$$ $$\ne\ -f\left(-x\right)$$
Neither A or B are correct
Question 1
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
Solution
We are given that :
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80
Now taking mean
we get $$30 = a+b+8+5+10$$
so we get $$a+b = 7$$ (1)
Now variance = 6.80
so $$6.80 =( (a-6)^2 +(b-6)^2+(8-6)^2+(5-6)^2+(10-6)^2)/5$$
we get $$6.8(5) = (a-6)^2+(b-6)^2+1+16+4$$
So we get $$13 = (a-6)^2 +(b-6)^2$$
$$a=7-b$$
we get $$13 = (1-b)^2+(b-6)^2$$
we get $$b =4$$
and so $$a= 3$$
Question 2
If the algebraic sum of deviations of 20 observations measured from 23 is 70, mean of these observations would be
Solution
Sum of observation is given as = 70
Number of observation = 20
Therefore, Mean = 70/20=3.5
But, here observation starts from 23.
Therefore, Mean = 23 + 3.5 = 26.5
Answer the following questions based on the information given below
Question 1
From the failure data of electronics components presented here, which statement is true?
Solution
Option A: The reliability has not been compared to any other component. Hence A is incorrect.
Option B: Capacitors have more failure rate than picture tubes. Hence B is incorrect.
Option C: Picture tubes have the least failure rate among all components. Hence C is incorrect.
Option D: Hybrid Micro circuits have the most failure rate. Hence, they are the least reliable.
Answer the following questions based on the information given below
Question 2
Which of the following components has a failure rate 25% more than that of signal devices?
Solution
The failure rate of signal devices = 16
After increasing failure rate by 25%, 16(1+25/100) = 20
The failure rate of capacitors is 20. Hence B is the answer.
Answer the following questions based on the information given below
Question 3
Lowest priority for investing in any changes or additions to the component manufacturing units, in the company's investment plans, may be given to the following:
Solution
The lowest priority for investing in any changes or additions to the component manufacturing units can be given to the components which have the lowest failure rates. Here, pictures tubes and signal devices have lowest failure rate amongst all the components.
Answer the following questions based on the information given below
Question 4
For the equipments using Integrated Circuit Board: 400, Capacitors: 240 and Printed Circuits boards: 120 to run with minimum downtime, how many spares should be kept in the store respectively?
Solution
The failure rate of Integrated Circuit Board per 1000 is 30. Hence for 400, the failure will be (30*400)/1000=12
The failure rate of Capacitors per 1000 is 20. Hence for 240, the failure will be (20*240)/1000= 5 (Approximately)
The failure rate of Printed Circuit Board per 1000 is 33. Hence for 120, the failure will be (33*120)/1000= 4 (Approximately)
Hence 12,5,4 is the answer.
Question 1
Consider the following piecewise definition of the function f.
$$f(x) = \begin{cases}3 - x, if & x \leq 0\\x^2 + 2, if & x \geq 0\end{cases}$$
Evaluate f(-3).
Solution
f(x) = 3-x , if x$$\le\ $$0
$$\therefore\ $$ f(-3) = 3-(-3) = 6
