The relationship between two variables  and  is given by  and is shown in the figure. Find the values of p and q.

Note: The figure shown is representative.

What is the value of

In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii) ?

Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?

Spheres of unit diameter are centered at (𝑙 𝑚 𝑛) where 𝑙 𝑚 and l take every possible integer values.

The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, x is the distance to its nearest sphere and y is the distance to its next nearest sphere. The value of  is:

In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2.

ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as shown in the figure. Which one of the following statements is true about the shaded area PQS?

Note: The figure shown is representative.

P and Q have been allotted a hostel room with two beds, a study table, and an almirah.  is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q does not mind that as long as his bed is close to the ceiling fan.

Which one of the following arrangements suits them the most?

The decimal number system uses the characters , and the octal number system uses the characters .        

For example, the decimal number  is expressed as  in the octal number system.

The decimal number 108 in the octal number system is

A shopkeeper buys shirts from a producer and sells them at  profit. A customer has to pay ₹3,186.00 including  taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

If, for non-zero real variables , and real parameter ,        

then, the ratio  is

In the following figure,        

Points AFCD create a rhombus.

The length of  (in ) is

The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the country (in Million liters).

Considering the data presented in the chart, which one of the following options is true?

The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left  or the right  direction.        

If the object A (Rack) is translating towards the right  direction, the correct statement among the following is

A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints A and B. Points A, B, and C are not collinear. Each of the angles  and  are measured as . The distance (in m) of the reference point C from her position is nearest to

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5' and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

How many triangles are present in the given figure?

Which one of the following options represents the given graph?

The digit in the unit's place of the product  is

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is

In a  race, P and Q have speeds in the ratio of . Q starts the race when  has already covered . What is the distance between P and Q (in m) when  wins the race?

Three bells  and  are rung periodically in a school.  is rung every 20 minutes;  is rung every 30 minutes and  is rung every 50 minutes. If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.

What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes:

Q, U and V?

The price of an item is  cheaper in an online store  compared to the price at another online store M. Store S charges Rs. 150 for delivery. There are no delivery charges for orders from the store . A person bought the item from the store  and saved Rs. 100. What is the price of the item at the online store  (in Rs.) if there are no other charges than what is described above?

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements:

• The line segment joint R and S is longer than the line segment joining P and Q.
• The line segment joining R and S is perpendicular to the line segment joining P and Q.

The line segment joining R and U is parallel to the line segment joining T and Q.

Based on the above statements, which one of the following options is CORRECT?  

An ant is at the bottom-left corner of a grid (point. P) as shown below in the figure. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

Which one of the following numbers is exactly divisible by  ?

For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

A transparent square sheet below is folded along the dotted line. The folded sheet will look like __________.

Seven cars  and  are parked in a row not necessarily in that order. The cars  and  should be parked next to each other. The cars S and  also should be parked next to each other, whereas  and  cannot be parked next to each other.  and  must be parked next to each other.  is parked to the immediate right of .  is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

In the figure shown below, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (Shaded) as shown, in  is

Let  be a continuous random variable denoting the temperature measured. The range of temperature is (0,100) degree Celsius and let the probability density function of X be  for . The mean of X is

The number of students passing or failing in an exam for a particular subject is presented in the bar chart below. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are ________.

Given a semicircle with O as the centre; as shown in the figure, the ratio  is ________. Where  and  are chords.

The revenue and expenditure of four different companies  and  in 2015 are shown in the figure. If the revenue of company Q in 2015 was  more than that in 2014, and company Q had earned a profit of  on expenditure in 2014, then its expenditure (in million rupees) in 2014 was __________.

The missing number in the given sequence 343, 1331, ______, 4913 is

It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to mow the lawn?

Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of elements having minimum and maximum values in the set Z is ____________.

Consider five people – Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1. Lakshmi is taller than Rekha

2. Rekha is shorter than Mita

3. Rekha is taller than Sana

4. Sana is shorter than Ganga

How many integers are there between 100 and 1000 all of whose digits are even?

The ratio of number of boys and girls who participated in an examination is 4 : 3. The total percentage of candidates who passed the examination is 80 and the percentage of girls who passed is 90. The percentage of boys who passed is ___

Functions F(a, b) and G(a, b) are defined as follows:

and, where represents the absolute value of x. What would be the value of?

For what values of k given below is an integer?

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%, Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design?

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9. one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code. AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

The probability that a k-digit number does NOT contain the digits 0, 5, or 9 is

Find the smallest number y such that y × 162 is a perfect cube.

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right.

None of the women are right-handed. The number of women at the table is

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot. If in a flood, the water level rises to 525 m, which of the villages P, Q, R, S, T get submerged?

The expression  is equal to

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts colored red, pink, blue and white respectively. Arun dislikes the color red and Shweta dislikes the colour white. Gulab and Neel like all the colors. In how many different ways can they choose the shirts so that no one has a shirt with a color he or she dislikes?

There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W. Z is to the East of X and the West of V. W is to the West of Y. Which is the building in the middle?

A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number  will have

The number of roots of in the range [–5, 5] is

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

In a quadratic function, the value of the product of the roots  is 4. Find the value of

Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through whatsapp. 30 faculty members do not have Facebook or whatsapp accounts. The number of faculty members connected only through facebook accounts is __________.

In a  rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

Choose the correct expression for  given in the graph.

Pick the odd one out in the following:

13, 23, 33, 43, 53

If , then  is ______________.

The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tones is ________________.

Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully makes exactly 6 free throws in 10 attempts?

The numeral in the units position of  is _________ .

Given Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each departments is 5 : 4. There are 40 males in Electrical Engineering. What is the difference between the numbers of female student in the civil departments and the female students in the Mechanical departments?

The number of students in a class who have answered correctly, wrongly or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

What is the average of the marks obtained by the class in the examination?

The probabilities that a student passes in Mathematics, physics and Chemistry are m, p, and c respectively of these subject, the student has 75% chance of passing in a least one, a 50 % chance of passing at least two a 40% chance of passing exactly two, following relations are drawn in m, p, c:

(I) p + m + c = 27/20

(II) p + m + c  = 13/20

(III) (p)x(m)x(c) = 1/20

Consider a function   on. The value of x at which the function attains a maximum, and the maximum value of the function are:

If p, q, r, s are distinct integers such that:

f (p, q, r, s)=max(p, q, r, s)

g (p, q, r, s)=min(p, q, r, s)

h (p, q, r, s)=remainder of  if  or remainder of  if

Also a function fgh (p, q, r, s) = f (p, q, r, s)  g (p, q, r, s) h (p, q, r, s)

Also the same operations are valid with two variable functions of the form f(p, q).

What is the value of fg ( h(2, 5, 7, 3), 4, 6, 8)?

In a triangle PQR, PS is the angle bisector of  and . What is the length of PS?

If the letters P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence?

(I) 2P, 2R, 2S, 2T, 2U

(II) P-3, R-3, S-3, T-3, U-3

(III)

Four branches of a company are located at M, N, O, and P. M is north of N at a distance of 4 Km; P is south of O at a distance of 2Km; N is southeast of O by 1Km. What is the distance between M and P in Km?

If , compute .

The roots of  are real and positive. A, b and c are real. Then  has                

Round – trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs.100, a group of 5 tourists purchasing round – trip tickets will be charged Rs _______.

In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines?

What is the average of all multiples of 10 from 2 to 198?

The value of

If x is real and , then possible values of  include

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?

At what time between 6a.m. and 7a.m. will the minute hand and hour hand of a clock make an angle closest to ?

Which number does not belong in the series below?

2, 5, 10, 17, 26, 37, 50, 64

The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination.

What is the average of the marks obtained by the class in the examination?

The Gross Domestic Product (GDP) in rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (US(d) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for thee USD increased from Rs. 50/USD to Rs. 60/USD. India’s GDP in USD during the period 2012-2013.

The ratio of male to female students in a collage for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?

Consider the equation; , where  stands for X to the base N. Find Y.

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday of Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday

What is the chance that a leap year, selected at random, will contain 53 Saturdays?

The set values of p for which the roots of the equation are of opposite sign is

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is

Find the sum to n terms of the series

If  and , then

A and Bare friends. They decide to meet between 1PM and 2PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is