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If the system of linear equation x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a non zero solution, then a, b,c
If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to
Primitive of f(x) = x.2 ^{In (x2 + 1) }with respect to x is
A man of height 2m walks directly away from a lamp of height 5m, on a level road at 3 m/s. The rate at which the length of his shadow is increasing is
Divide 56 into two parts such that three times the first part exceeds onethird of the second by 48. Then the two parts are
A ladder20 ft long has one end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If the lower end of the ladder is 16 ft away from the wall, upper end is moving λ times as fast as the lower end, then λ is
Let OC be the wall. Let AB be the position of the ladder at any time t such that OA =x and OB=y. Length of the ladder AB =20 ft.
In ΔAOB,
If 'green' is called 'white', 'white' is called 'yellow', 'yellow' is called 'red', 'red' is called 'orange', then which of the following represents the colour of sunflower?
The colour of sunflower is yellow and yellow is called 'red'. Hence sunflower is red.
Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then R is
Clearly, the relation is symmetric but it is neither reflexive nor transitive.
The system of equations x + y + z =2, 3x − y + 2z =6 and 3x + y + z =−18 has
Ranjeev started from his office on duty. After traveling straight for a distance of 14 Km, he turned left for the market and traveled straight for 6 Km. He now turned left again and traveled another 2 Km, and then again left and traveled straight for 6 Km. How far is Ranjeev from office?
The demand and supply equations of a certain commodity are 4q+7p=17 and p= q/3+7/4 respectively, where p is the market price and q is the quantity. Then the equilibrium price and quantity are respectively
If E = 5 and HOTEL = 12, how will you code LAMB?
One day Anuneet left home and cycled 10 Km southwards, turned right and cycled 5 Km and turned right and cycled 10 Km and left and cycled 10 Km. How many Kms will he have to cycle to reach his home straight?
If the diagonal of a rectangle is 5 cm and one of its sides is 4 cm, then its area is
We have
We have seen that inverse exists only when function is oneone and onto, i.e. Bijective.
(x5)(x7)=8
∴x^{2}12x+35=8
∴x^{2}12x+27=0
∴x^{2}9x3x+27=0
∴x(x9)3(x9)=0
∴(x9)(x3)=0
∴x=9 or x=3
Hence, the roots of the equation are 3 and 9
Let A be the non – empty set of children in a family. The relation ‘x is a brother of y’ in A is
The slope of the tangent to the curve^{ x=t}2+3t−8, y=2t^{2}−2t−5 at the point t = 2 is
A boy starts walking straight towards the north and walks 10 feet, then he turns to his left and walks 5 feet, then he turns to his left and walks another 5 feet, then again he turns to his left and walks 10 feet and then turns to his right and walks 2 feet. How far is he now from his starting point?
Who is between the Lawyer and the Business Analyst?
In all the cases, it can be observed that Amit is between the Lawyer and the Business Analyst.
The angle of intersection of the curves y=2sin2 x and y= cos 2x at x =π/6 is
We have
Six persons Amit, Amitabh, Arnold, Aakash, Abhinav and Atul, each of a different profession, among Docot, Lawyer, Teacher, Manager, Business Analyst and Accountant, are seated around a table in six equispaced chairs. Atul is opposite to the Lawyer. Arnold is to the right of the Doctor and is opposite the person who is the Business Analyst. Aakash is opposite the Accountant. Abhinav is between the Manager and the Accountant and is not the Business Analyst. Amitabh is opposite the Manager, who is the left of Aakash.
Q. If Amitabh is the Business Analyst, then who is opposite Amitabh?
This question refers to case (2), where Arnold is sitting opposite Amitabh.
Six persons Amit, Amitabh, Arnold, Aakash, Abhinav and Atul, each of a different profession, among Docot, Lawyer, Teacher, Manager, Business Analyst and Accountant, are seated around a table in six equispaced chairs. Atul is opposite to the Lawyer. Arnold is to the right of the Doctor and is opposite the person who is the Business Analyst. Aakash is opposite the Accountant. Abhinav is between the Manager and the Accountant and is not the Business Analyst. Amitabh is opposite the Manager, who is the left of Aakash.
Q. Which of the following statements is false?
Statement I, II and III are always true.
Statement IV is false.
As in case (2), it can be observed that the Lawyer and the Accountant are opposite each other.
The value of x which satisfies the equation (3x1)^{2}5(2x+1)^{2}+(6x3)(2x+1)=(x1)^{2} is
What is the remainder when x^{4}+3x^{2}20 is divided by (x2)?
When a polynomial f(x) is divided by (xa),(xa) is said to be a factor of the polynomial if f(a) is 0.
Thus, the remainder when a polynomial f(x) is divided by (xa) is given by f(a).
Hence, f(2)=24+32^{3}20 =16+2420=20
26 A man from his house walks towards north and covers 15.5 Km and then turns left and travels 7 Km. He turns left again and after traveling 31 Km, again turns left and stops after traveling 7 Km. How far is he from his house?
x^{2}y^{2} – 8xy – 48=x^{2}y^{2} – 12 xy + 4xy – 48 =xy(xy12) + 4(xy12) =(xy12)(xy+4)
The 288th term of the series a,b,b,c,c,c,d,d,d,e,e,e,e,e,f,f,f,f,f,f,.......... is
Let R be a relation on the set N of natural numbers defined by nRm
⇔ n is a factor of m (i.e. n(m). Then R is
Since n  n for all n in N,
therefore R is reflexive.
Since 2  6 but 6  2, therefore R is not symmetric.
Let n R m and m R p ⇒ nm and mp ⇒ np ⇒ nRp
So. R is transitive.
The system of equations
X+2y+3z=4
2x+3y+4z=5
3x+4y+5z=6 has
21 If A = 2, M = 26, Z = 52, then BET will be equal to
As, A=2(1×2) ⇒M=26(13×2), Z=52(26×2) Similarly, BET =2+5+20 =27×2=54
If AT = 20, BAT = 40, then CAT will be equal to
If 341782 denotes MONKEY and 0596 denotes RAGD, then 75195044 will denote
If 4/x + 6/y = 0 and 3/x  4/y = 17/6 , then :x+y=
If x=secθ−cosθ,y=sec^{10}θ−cos^{10}θand(x^{2}+4) (dy/dx)^{2} =k(y^{2}+4), then k is equal to
Alok starts walking from his school toward his house as shown in the figure here. He start from the front gate of his school, walks 5 Km, turns left, walks 2 Km, then turns left again and walks 4 Kms, then he turns to his right and walks 3 Km and then turns left, walks 1 Km and then turns to his left again to walk 4 Km and then to his right and walks 10 Km and finally turns right, walks 3 Km and thus reaches the front gate of his house.
Q. Alok's house is in what direction with respect school?
Alok starts walking from his school toward his house as shown in the figure here. He start from the front gate of his school, walks 5 Km, turns left, walks 2 Km, then turns left again and walks 4 Kms, then he turns to his right and walks 3 Km and then turns left, walks 1 Km and then turns to his left again to walk 4 Km and then to his right and walks 10 Km and finally turns right, walks 3 Km and thus reaches the front gate of his house.
Q. If Alok's house is south facing, in which direction did he start walking?
If REQUEST is written as S2R52TU, then how will ACID be written?
Six persons Amit, Amitabh, Arnold, Aakash, Abhinav and Atul, each of a different profession, among Docot, Lawyer, Teacher, Manager, Business Analyst and Accountant, are seated around a table in six equispaced chairs. Atul is opposite to the Lawyer. Arnold is to the right of the Doctor and is opposite the person who is the Business Analyst. Aakash is opposite the Accountant. Abhinav is between the Manager and the Accountant and is not the Business Analyst. Amitabh is opposite the Manager, who is the left of Aakash.
Q. If Arnold is the Manger, then who is between Aakash and Abhinav?
This refers to case (2), where Arnold is between Aakash and Abhinav.
x > 2, y >  1 then which of the following holds good?
By putting different value of x and y we see that none of these three hold good.
There are three cities: A,B and C. Three friends are discussing the population (in millions) of the three cities. One says A has 9 million people. The second says: B has as many people as A and C combined. The third says: The number of people in A added to half of the number of people in B is the number of people in C. What is the total number of people (in millions) in all three cities combined?
Population of A (in millions) = 9
Let the number of people in city B (in millions) be b, while those in city C (in millions) be c.
From the given information,
b=9 + c(i)
and c=9+b/2
i.e. 2c = 18 + b(ii)
Solving equations (i) and (ii),
b=36 and c=27
:. The total number of people in cities A, B and C combined = 9+36+27=72 million.
If area bounded by the curves y2 = 4ax and y = mx is a^{2}/3 then the value of m is
If Atul is not the Teacher, then who is the Doctor?
This question refers to case (2), in which Abhinav is the Doctor.
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.
Q. Which of the following statements cannot be true?
If x and y are integers, then the equation 5 x + 19 y = 64 has
5x+19y=64 We see that, if y=1, we get an integer solution for x=9, now if y changes (increases or decrease) by 5.
Looking at options, if x=256 we get y=64. Using these values we see the option 1,2 and 4 are eliminated and also that these exists a solution 250<x≤300
If f (x) +f (x+a) + f(x+2a) +....+ f (x+na) = constant; ∀x ϵR and a>0 and f(x) is periodic,then period of f(x), is
The value of (127)^{1/3} to four decimal places is
A train leaves Delhi at 6.00 a.m and reaches Agra at 10.00 a.m. Another train leaves Agra at 8.00 a.m and reaches Delhi at 11. 30 am. At what time do the two trains cross each other if the distance between Delhi and Agra is 200 Km?
The average ambient temperatures (in degree celsius) for a region for 15 years from 20012015 is given below.
26.3, 29.7, 31, 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. Find the interquartile range of the temperatures.
The price per/kg of chicken and the quantity of chicken purchased per month in a household is tabulated below. Determine the type of correlation.
Mode of the data
15,14,19,20,14,15,16,14,15,18,14,19,15,17,15 is
Given Data:
15,14,19,20,14,15,16,14,15,18,14,19,15,17,15
Arranging it in ascending order: 14,14,14,14,1514,14,14,14,15,15,15,15,15,16,17,18,19,19,20
15 occurs 5 times and most number of time.
Hence, it is the mode of the data.
(I) The change in any price is reflected in an index number.
(II) The wholesale price index can be used to measure the monetary and real value of national income and expenditure.
The change in any price may or may not be reflected in a price index number as such index reflects the change in terms of averages. The wholesale price index can be used to measure the monetary and real value of national income and expenditure.
Your local supermarket plays the role of a______.
Supermarkets sell products to consumers. They play the role of distributors.
The distance travelled by a scooter during five months are respectively 890 km, 940 km, 640 km, 570 km and 760 km. Find the standard deviation of the distances.
Under the index of industrial production, highest weightage is given to _____.
Manufacturing is given about 79% weightage.
To present the data about the total sales of four car manufacturers along with the sales of individual models for a year, which of the following is the most appropriate?
Since the total sales and the breakdown of sales by models are required to be presented for each manufacturer, we can make use of component bar diagrams for this purpose. If only the total sales were required, a simple bar diagram would have sufficed.
Find the quartile deviation of the data given below.
7, 3, 6, 4, 2, 11, 7
Exit polls are an example of random sampling. A random sample of voters who exit the polling booths are asked whom they voted for and a prediction is made based on this data.
David is a wheat farmer. His resources include a piece of land and some farming equipment. Which of the following would be an alternative for him, given the resources?
Since David's equipment is appropriate for wheat cultivation, a viable alternative would be a similar crop which is grown in similar climatic conditions. Hence, cultivating barley would be a good alternative for him.
Ramesh and his friends drove through 66 midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the range of gasoline prices given below?
1.81,1.91,1.89,2.05,2.09,1.75
Range is the difference between the smallest and the largest values.
From the give data, the largest value is 2.09 and
the smallest value is 1.75
Therefore range is 2.09−1.75=0.34
Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation was 12. The teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true?
I. The new mean is 75.
II. The new median is 71.
III. The new standard deviation is 7.
New Mean = Old Mean +7=68+7=75
New median = Old median+7+64+7=71
New standard deviation= old standard deviation =12
___ explains the specific feature of the table which is not selfexplanatory.
Footnotes are not mandatory and are mostly used to simply explain a feature of the table that is neither self explanatory nor one that’s been explained before.
Mode is the most frequently observed value.
In a diagnostic test in mathematics given to students, the following marks (out of 100100) are recorded:
46,52,48,11,41,62,54,53,96,40,98,44
Q. Which average will be a good representative of the above data?
Median will be a good representative of the data, because (i)(i)each value occurs once, (ii)(ii)the data is influenced by extreme values. Hence, option BB is the correct answer.
If the mean of x and 1/x is M, then the mean of x^{3} and 1/x^{3}
In which of the following modes of data collection is a respondent least likely to be inhibited?
In the mailing questionnaire method, because of the absence of an interviewer, there will be no inhibition on part of the respondent. Also, since the anonymity of the respondent can be protected in this method, there will be fewer inhibitions.
There are 500 students in a class in which there are 100 boys. 50 boys like Mathematics and 100 girls dislike Mathematics. Tabulate the given data and calculate the number of girls who like the subject Mathematics.
Swetha has created a short film and uploaded it on Youtube. Arun watched the short film.
Identify the correct statement(s) about the above scenario.
Since Swetha has created the film(the product), she is the creator. Youtube acts as the distributor and Arun, the viewer, is the consumer.
Identify the type of classifications from the given table.
Since the given distribution is classified on the basis of year and geography (revenue of states), it consists of chronological and spatial classifications respectively.
Find the standard deviation of 210,240,250,260,220,230 and 270.
Discrete variables and continuous variables are examples of _________
Discrete variables and continuous variables are examples of quantitative classification.
A database consists of the poverty levels of all the states in India for the last 10 years. In order to present the data of the most and the least poor states in the last 5 years, which of the following can be used to show it on a graph?
Since the data to be presented has 2 bars of the same category(the most poor and the least poor) and it is required to show the trends of these in the last 5 years, multiple bar diagram is the best suited for a graph.
Mode is the most common observation. In the given data, 8 occurs 3 times, more than any other number. Hence, the mode is 8.
The scores of 8 students in a test are 16, 13, 21, 14, 9, 19, 24, 25. Find the standard deviation of their scores using direct method.
The demand for a good at different price points is given in the below. Find the correlation coefficeint between price and quantity demanded.
Find the shop with greatest fraction of sale on tuesday
A company X was acquired by another company Y. Company Y came into possession of customer feedback data collected by company X. What can be said about the nature of the data?
The data collected by another party is classified as secondary data irrespective of the purpose which it is used for.
Identify the correct statement(s) about the correlation between two variables.
Statement 1: Correlation does not show that there is a causal relationship between two variables
Statement 2: Correlation shows the degree to which variations in one variable explain the variation of the second variable
Correlation shows the degree to which variations in one variable explain the variation of the second variable. It does not show that there is a causal relationship between two variables.
Temperature, height, weight and marks are all examples of a _________.
There is no restriction to the type of values that can be taken by variables like temperature, height, weight and marks. Hence they would be examples of continuous variables.
Which of the following can be used as measures of dispersions?
Following terms used as measures of dispersion are:
a) Range
b) Percentile
c) Standard eviation
d) Mean deviation.
Identify the type of classification from the below table.
Since the given distribution is classified on the basis of income level, which is a qualitative characterisitc, this is a qualitative classification.
Variables in a correlation are called covariables.
The following numbers are given as 61,62,63,61,63,64,64,60,65,63,64,65,66,64 The difference between their mean and median is
You are the hiring manager for a telemarketing company. The business is expanding and you need to hire new people. You are short on time and your budget is restricted. Which method would you use to collect data to identify a suitable candidate for the job?
Telephonic interviews are cheap and time efficient. Hence, a large number of people can be interviewed within a short time.
Construct a price index for the following using Average of price relative method.
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