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The point in the interval [0,2π] where f(x)=e^{x} sin x has maximum slope, is
We have
If f (x) is differentiable in the interval [2, 5], where f (2)=1/5 and f (5)=1/2, then there exists a number c, 2 < c < 5 for which f ' (c) is equal to
As f(x) is differentiable in [2,5], therefore, it is also
If in a certain code, LUTE is written as MUTE and FATE is written as GATE, then how will BLUE be written in that code?
In a certain code, PRODUCTIONS is written as QQPCVEUHPMT. How is ORIENTATION written in that code?
If a,b,c are non – zero real numbers and if the equations (a1) x = y + z, (b 1)y = z + x, (c  1)z = x + y has a non trivial solution, then ab + bc + ca is equal to
For non trival solution
Answer the question based on the following information.
The city K is 30 Km to the southeast of Z while Y is 50 Km to the northwest of K. Also , H is 38 Km to the southeast of Y. L lies in the direct route between Y and K and its distance from H is 14 Km. G also lies on this route and is exactly midway between L and Y.
Q. A car starting from K at 9 am and running at a constant speed towards Y reaches H at 9.24 am and then reaches G at
The car covers K to h  a distance of 12 kms in 24 minutes according to the figure (starting at 9 am and reaching at 9 : 24 am). From H to G, the distance is 26 kms.
(18 H to Z + 8 Z to G). Since the car has covered 12 kms in 24 minutes, it is obvious that it is taking 2 minutes to cover 1 km.
We also know that the sped of the car is constant throughout.
Hence, the car would take another 52 minutes to cover the 26 kms distance between H to G This means that the car would reach G at 10:16 am(52 minutes after 9:24 am).
In a certain code, FAVOUR is written as EBUPTS. How is DANGER written in that code?
Answer the question based on the following information.
The city K is 30 Km to the southeast of Z while Y is 50 Km to the northwest of K. Also , H is 38 Km to the southeast of Y. L lies in the direct route between Y and K and its distance from H is 14 Km. G also lies on this route and is exactly midway between L and Y.
Q. The distance from G to H is
G to Z, the distance is 8 km (20 km from Y to Z  12 km from Y to G). Further, from Z to H the distance is 18 km (from the figure based on the logic that if H is 38 km southeast of Y and Z is 20 km southeast of Y, the distance from Z to H would be 38  20).
Total distance would be 8 + 18 = 26 km.
Range of is (where [x] denotes the greatest integer function)
Let Where [x] denotes the greatest integer function. Then, the range of f is
The graph of y=x−[x ]is as shown below
Between any two real roots of the equation e^{x} sin x = 1, the equation e^{x} cos x =  1 has
In a certain code language, ORIENTAL is written as MBUOFJSP. How is COWARDLY written in that code language?
These question are based on the diagram given below showing four persons Amar, Bhushan, Chandu and Dilip stationed at four corners of a square piece of plot as shown.
From the positions in the original figure,Bhushan and Amar move diagonally to opposite corners and then one side each clockwise and anticlockwise respectively. Chandu and Dilip move three side each anticlockwise and clockwise respectively. Where is the Amar now?
Amar would reach Bhushan's original position as seen in the figure from the final positions. He would be at the southeast corner.
Refer the diagram.
The seven coaches that are attached to a rail engine are ACI, ACII, ACIII, I, II, General Compartment (GC) and Ladies Compartment (LC). The coaches with prefix AC are Air conditioned coached and those without that prefix are nonAC coaches. No two AC coaches are together and no two nonAC coaches are together.
GC and LC are immediately at the front and immediately at the back of ACII respectively and LC is not at an extreme end.
Compartment I is the only one between the compartments ACI and ACI.
In the previous question, if ACI is the fourth coach behind the engine, which is immediately in front of ACIII?
If ACI is the fourth coach behind the engine, the possible arrangement is as follows.
(1) GC
(2) ACII
(3) LC
(4) ACI
(5) I
(6) ACIII
(7) II
Hence, ACII is the second coach behind the engine.
then which of the following is definitely true if x is an integer
The equation x log x = 3  x has, in the interval (1, 3),
These question are based on the diagram given below showing four persons Amar, Bhushan, Chandu and Dilip stationed at four corners of a square piece of plot as shown.
From the original position, Bhushan and Dilip move one and the half length of sides clockwise and anti clockwise receptively.
Q. which one of the following statement is now true?
The final position would be:
Refer the diagram.
These question are based on the diagram given below showing four persons Amar, Bhushan, Chandu and Dilip stationed at four corners of a square piece of plot as shown.
Amar start crossing the plot diagonally, After walking half distance, he turns right (900) , walks some distance and turns left.
Q. Which direction is A facing now?
To get to the answer we must assume. Amar to be at the point of dissection of the two direction lines. After walking half the distance, Amar will reach the mid of the diagonal, then turn right and face northwest and after that would face the southwest direction when he turns left. (Note that the direction in the figure are different from the usual north, south, east, west directions as the north is in the east position).
3x+2y≤24; x≥5 & y≥2; then which of the following is a valid range?
Find the area enclosed by the curve x = y^{2} + 2, ordinates y = 0 & y = 3 and the Y  axis.
Answer the question based on the following information.
The city K is 30 Km to the southeast of Z while Y is 50 Km to the northwest of K. Also , H is 38 Km to the southeast of Y. L lies in the direct route between Y and K and its distance from H is 14 Km. G also lies on this route and is exactly midway between L and Y.
Q. If M is 1 Km to the Southeast of L, then it is exactly midway between
The total distance between Y and K is 50 km (20 km from Y to Z and 30 km from Z to K). If M is 1 km southeast of L, it means that M is 4 + 1 = 5 km from Z.This would also mean that M is 25 km from Y. Hence, M would be exactly midway between Y and K.
3x+9<3
∴3<3x+9<3
∴3x+9>3 or 3x+9<3
∴3x>12 or 3x<6
∴x>4 or x<2
∴4<x<2
With reference to a universal set, the inclusion of a subset in another, is relation, which is
Since it is an identity in λ so satisfied by every value of
In a certain code, ROAD is written as URDG. How is SWAN written in that code?
In a certain code language, OPERATION is written as NODQBUJPO. How is INVISIBLE written in that code?
If TRUTH is coded as SUQSTVSUGI, then the code for FALSE will be
In a certain code language, COMPUTER is written as RFUVQNPC. How is MEDICINE written in the same code?
If SUMMER is coded as RUNNER, the code for WINTER will be
These question are based on the diagram given below showing four persons Amar, Bhushan, Chandu and Dilip stationed at four corners of a square piece of plot as shown.
A road network has parallel and perpendicular roads running northsouth or eastwest only. Junction Intersection on this road network are marked as A, B, C, D .... all roads are at exactly half a Kilometer distance from each other. The following is know about junction A, B, C, H, and X.
'A' is east of 'B' and west of 'C' , 'H' is southwest of 'C' and Southeast of B. 'B' is southeast of 'X" which junction are the farthest south and the farthest east?
It can be inferred from figure below that H is the farthest south and C is the farthest east.
X
B A C
H
If m>n; which of the following is definitely true? (m&n are real numbers.)
The value of Where [.] denotes the greatest integer function, is equal to
If (x16)^{2}≥0 & x ∈ R; then which of the following is definitely true?
Consider each option.
Option 1: If x<16i.e. if x=15; the expression is (1516)^{2}⇒(1)^{2}=1≥0. Hence the expression is true for x≤16 also. Hence, option 1 can be eliminated.
Option 2: If x=16 as in the above case; the expression holds true. Hence, option 2 can also be eliminated.
Option 3:if we take the value of x other than these specified in the range; i.e. x=20; the expression is (2016)^{2}=4^{2}=16≥0.i.e.
it holds true. Hence, option 3 can be eliminated.
These question are based on the diagram given below showing four persons Amar, Bhushan, Chandu and Dilip stationed at four corners of a square piece of plot as shown.
The Survana and Rekha river flows from west to east and on the way turns left and goes in a quarter circle around a Shiv temple, and then turns left in rightangles.
Q. In which direction is the river finally flowing?
From the given figure it is clear that the river would be flowing to north.
Raveena walks 10 Km from her house, turns left and walks 25 Km, again turns left and walks 40 Km, then turns right and walks 5 Km to reach her office. In which direction was the office from her house?
The journey would be as per the figure. Her office would be northeast from her house.
The approximate value of square root of 25.2 is
In a certain code, MONKEY is written as XDJMNL. How is TIGER written in that code?
The ages and weights of 5 children are given below. Calculate covariance.
An ideal index number would be one which takes into account as weights ______.
Prices and quantities of both base and current year when taken into consideration give a more consistent result as compared to other indexes deploying either only prices or quantities.
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
Study the pie chart and information given and answer the following question.There are 1150 students of a school opted sports as a hobby.
Q. What is the total number of students in the school?
23% of total students opted sports as a hobby
Let total number of students be x
0.23x=1150
x=5000
Reliability of sampling data depends on all of the mentioned factors
The quantity of goods produced and costs incurred by a firm are tabulated below. Find the correlation coefficient using Karl Pearson's formula.
Two samples of water of equal mass are heated to 60° Celsius (C). One sample is poured into an insulated container and the other sample is poured into a noninsulated container. The samples are then left for 70 minutes to cool in a room having a temperature of 25°. The graph above shows the temperature of each sample at 10minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change?
The below table shows the profit made by a group of shops in mall. Then the median is
The number of hours spent studying and percentage marks for 5 students are tabulated below. Find the correlation coefficient using Karl Pearson's formula.
Which of the following is not a source of primary data?
Only the data directly collected by a person or an entity is primary data. Therefore, governmentpublished records are secondary data.
In Economics, data and Statistics are important because _____ .
It helps a producer decide what to make and a consumer decide what to buy.
Below is given distribution of profit (in Rs.) per day of a shop in a certain town.
Q. Calculate median profit of shops.
For a data set, the coefficient of range is 0.5. The largest observation is 12. Find the smallest observation.
Given that the coefficient of range is 0.5.
(L−S)/(L+S)=0.5
⇒L=3S
Given that L=12.
∴ 3S=12
S=4
The marks obtained by 19 students of a class are 27,36,22,31,25,26,33,24,37,32,29,28,36,35,27,26,32,35 and 28. Find the upper quartile.
For a distribution,
Q. If the mean of the distribution is 6, what is the value of x?
Data A has a mean of 100 and standard deviation of 10. Data B has a mean of 1000 and standard deviation of 50. Which data shows more variability?
To compare dissimilar data, relative measures should be used. Here, the coefficient of variation of set A and set B can be compared.
Hence, data A shows more variability.
Find the variance of the series 5, 8, 11, 14 and 17.....
Data classification is the process of organizing data into categories for its _____.
Data classification is the process of organizing the data into categories for its division. The types of data are qualitative and quantitative data.
The method in which every class interval excludes the items corresponding to its upper limit is called _________.
Exclusive method is where the upper limit of a class interval corresponds to the successive class. For example : In a frequency distribution with classes 05,510 all the way upto 2530, the number 20 in the dataset will not fall under the class 1520 but instead will fall under 2025 according to the exclusive method.
The table above lists the annual budget, in thousands of dollars, for each of six different state programs in Kansas from 2007 to 2010.
Of the following, which program's ratio of its 2007 budget to its 2010 budget is closest to the human resources program's ratio of its 2007 budget to its 2010 budget?
A market survey was conducted to study the effectiveness of a new feature in a smart phone. For this purpose, a sample of 1000 people was chosen. However, only 947 people actually attended the survey. This is a type of ___.
Nonresponse error occurs when sampling units selected for a sample are not interviewed. The nonresponse may be due to unwillingness or unavailability. It is a nonsampling error.
___ is formed by joining midpoints of the top edges of all the rectangles in a histogram.
Frequency polygons are plotted in the described manner.
A grouped frequency distribution table with classes of equal sizes using 63−72(72 included)) as one of the class is constructed for the following data:
30,32,45,54,74,78,108,112,66,76,88,
40,14,20,15,35,44,66,75,84,95,96,
102,110,88,74,112,14,34,44
Q. The number of classes in the distribution will be:
If one the classes is 63−72 then the range of the class is 10(72 included))
Range of the given data points =112−30=82
Number of classes =82/10=8.2
Classes required will be 9 after round off.
The frequency distribution that uses two variables is called _________
If the median of the following data is 50, then find p.
The average ambient temperatures (in degrees celsius) for a region for 15 years from 20012015 is given below.26.3, 29.7, 31.0, 29.8, 26.8, 27.6, 27.4, 27.0, 27.6, 27.8, 30.0, 32.0, 28.9, 30.5, 29.5
Q. Calculate the coefficient of range for the temperatures.
The lowest temperature is 26.3 degrees and the highest temperature is 32.0 degrees.
Given below is the Lorenz curve representing the percentage revenues of car manufacturing companies worldwide.
Q. The top 20 percentage of the companies generate what percentage of revenue?
From the Lorenz curve, the bottom 80% of the companies generate 40% of the revenue. Hence, the top 20% of the companies generate 60% of the revenue.
When the stock market goes up, an investor in the companies listed on it will find his investments ___.
It depends on in which stocks he has made his investment and their weightage in that index/stock market. There could be a possibility that the particular stocks in which the investor has invested are in red despite the overall index in green.
The give bar graph here shows the percentage distribution of the total production of a car manufacture company into various models over two years. Study the graph carefully and answer the question.
Percentage of six different types of car manufactured by a company over two year.
Difference between total number of cars of models P, Q and T manufactured in 2000 and 2001 is _____.
The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively. Their standard deviations were 3 and 4 respectively. The varience of combined sample size of 500 is
The number of people in a given state have been divided into these age groups(classes): 1019 and 2029. What are the lower limits of these classes?
Since the number of people are discrete variables, the lower limits of these classes are 10 and 20.
(I) A rising price index implies a growing level of economic activity.
(II) Simple index number can be constructed only by the simple aggregative method.
The rise in price index could be due to other reasons as well and not necessarily due to higher economic activity.
As for statement (II), simple average of price relatives is another method.
A frequency array depicts how many times a particular observation occurs in a data set. This prevents the loss of information.
Mean of twenty observations is 15. If two observations 3 and 14 are replaced by 8 and 9 respectively, then the new mean will be
Mean of 20 observations =15
∴ Sum of 20 observations =15×20=300
Replacing 3 and 14 by 8 and 9 will mean that 3+14=17 is replaced by 8+9=17.
Hence there will be no effect on the sum. It will still remain 300, so the mean will not change and will remain 15.
A huge amount of data has to be analysed on priority. Which of the following would best suit to present this data?
In geometric diagrams, the representations are shown through geometric shapes and figures. Circles and rectangles are among the shapes that are used for geometric diagrams. This helps in easily analysing a huge amount of data.
Select and write the appropriate answer from the given alternatives in each of the following subquestions:
Let the p.m.f of a random variable X be
P(x)=(3−x)/10 for x = −1,0,
otherwise
Then E(X) is _______.
For what number of days, x$, will the total cost of buying the materials and renting the tools from store B be less than or equal to the total cost of buying the materials and renting the tools from Store A ?
Which of the following representations is right using tally marks?
Representing tally mark with straight bars till the count of 4 and a slash for the 5th count.
The coefficient of variation of data pertaining to the goals scored by two teams A and B in a football season are 0.35 and 0.72 respectively. The true statement is
The coefficient of variation is a measure of consistency. Lower, the C.V, more consistent the data is. In this case, team A has a lower C.V and hence, is more consistent.
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