The 12 musical notes are given as , and . Frequency of each note is  times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes  and  is:

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:

Note: The figures shown are representative.

Which one of the following plots represents , where  is a nonzero real number?

Note: The figures shown are representative.

A stick of length one meter is broken at two locations at distances of  and  from the origin (0), as shown in the figure. Note that . Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?

Note: All lengths are in meter. The figure shown is representative.

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.

After the  round,  student behind  leaves the game. After  round,  student behind Q leaves the game. After  round,  student behind  leaves the game. After  round,  student behind  leaves the game. Who all are left in the game after the  round?

Note: The figure shown is representative.

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to
₹ 5,00,000. For higher fees, the overhead is ₹ 1,00,000 plus 10% of the amount by which the fee exceeds ₹ 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than ₹ 10,00,000, what is the maximum consulting fee that the employee can charge?

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. If S and Q are single children, and the room allocations shown below are acceptable to all,

then, which one of the given options is the siblings?

Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. What was his father’s age when Aman was born?

For a real number

The value of is

The greatest prime factor of is

Four identical cylindrical chalk-sticks, each of radius and length are bound tightly together using a duct tape as shown in the following figure.

The width of the duct tape is equal to the length of the chalk-stick. The area  of the duct tape required to wrap the bundle of chalk-sticks once, is

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023.

Based on the data provided, which one of the following options is INCORRECT?

Examples of mirror and water reflections are shown in the figures below:

An object appears as the following image after first reflecting in a mirror and then reflecting on water.

The original object is

Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or FO2.

In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.

If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is

What is the smallest number with distinct digits whose digits add up to 45 ?

In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

How many rectangles are present in the given figure?

Which one of the following options represents the given graph?

Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:        

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than ________testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

 rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions .

The total number of creases visible when the sheet is unfolded is ________.

A sum of money is to be distributed among P, Q, R and  in the proportion , respectively.

If R gets Rs. 1000 more than , what is the share of  (in Rs.)?

A trapezium has vertices marked as  and  (in that order anticlockwise). The side  is parallel to side SR.

Further, it is given that, ,  and .

What is the shortest distance between  and  (in  )?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a "hole in the interior" that can be formed within the  grid using the unit squares as building blocks?

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard. If the security guard does not move around the posted location and has a  view, which one of the following correctly represents the set of ALL possible locations among the locations  and , where the security guard can be posted to watch over the entire inner space of the gallery.

Consider the following inequalities.        

(i)

(ii)

Which one of the following expressions below satisfies the above two inequalities?

Four points , and  represent the vertices of a quadrilateral.

What is the area enclosed by the quadrilateral?

The current population of a city is . If it has been increasing at the rate of  per annum, what was its population 2 years ago?

p and q are positive integers and , then,

The least number of squares that must be added so that the line  becomes the line of symmetry is ________.

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is __________.

The number of minutes spent by two students,  and , exercising every day in a given week are shown in the bar chart below.

The number of days in the given week in which one of the students spent a minimum of  more than the other student, on a given day, is

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure below.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is        

A super additive function  satisfies the following property

Which of the following functions is a super additive function for  ?

It is quarter past three in your watch. The angle between the hour hand and the minute hand is __________.

A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is , then the area of the shaded portion is __________.

a, b, c are real numbers. The quadratic equation  has equal roots, which is , then

The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools  and . During this period, the ratio of the average number of the students enrolled in school  to the average of the difference of the number of students enrolled in schools  and  is _________

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is ________        

It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is _____ hours

The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively.

The total population did not change during this period. The percentage increase in the total number of literates from 2001 to 2011 is ________

Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD________ remaining in the budget.

Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that:

1. Mathew is not standing next to Seema

2. There are two people standing between Lohit and the engineer

3. Rahul is not a doctor

4. The teacher and the dancer are standing next to each other

5. Seema is turning to her right to speak to the doctor standing next to her

Who among them is an engineer?

Five people P, Q, R, S and T work in a bank. P and Q don't like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T? (O =Office, WR =Washroom)

A 1.5m tall person is standing at a distance of 3m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

If the number 715■423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ■ is_________

What is the value of 

A cab was involved in a hit and ran accident at night. You are given the following data about the cabs in the city and the accident.

(i) 85% of cabs in the city are green and the remaining cabs are blue.

(ii) A witness identified the cab involved in the accident as blue.

(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.

Which of the following options is closest to the probability that the accident was caused by a blue cab?

Two alloys A and B contain gold and copper m the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is _______.

Leila aspires to buy a car worth Rs. 10.00.000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

In the summer water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statements is correct?

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbours are Y and V.Z is seated third to the left of T and second to the right of S. U’s neighbors are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

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.        

The path from P to Q is best described by

Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q, She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should go to reach point P?

A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old. Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics, Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 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.          

Which of the following is the steepest path leaving from P?

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% areunripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information
provided here, what is one possible distance (in km) at which I live from Arun's place?

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

Leela is older than her cousin Pavithra. Pavithra's brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.

Which one of the following statements must be TRUE based on the above?

If andand, the value of abc is _________

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Given (9 inches) =(0.25 yards) , which one of the following statements is

S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?

The Venn diagram shows the preference of the student population for leisure activities.

From the data given, the number of students who like to read books or play sports is _______.  

Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock?

M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?

A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ration of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a

M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-law of M. How is P related to M.

The number that least fits this set: (324, 441, 97 and 64) is ___________.

It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ___________.        

The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m)?        

A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat?

Find the area bounded by the lines 3x+2y=14, 2x-3y=5 in the first quadrant.

A straight line is fit to a data sets (1n x,y). This line intercepts the abscissa at 1n x=0.1 and has a slope of -0.02. What is the value of y at x=5 from the fit?

If , then the value of x is

A cube side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

Fill in the missing value

An electric bus has onboard instrument that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P, in that order. The cumulative distance travelled and the corresponding electricity consumption are shown in the Table below:

The stretch where the electricity consumption per km is minimum is

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

If , then ab + bc + ac lies in the interval

A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively, what distance in metres will the tiger have to run before it catches the deer?

If x > y > 1, which of the following must be true?

 (i) ln x > ln y        (ii)

(iii)         (iv) cos x > cos y

Ms. X will be Bagdogra from 01/05/2014 to 20/05/2014 and from 22/05/2014 to 31/05/2014. On the morning of 21/05/2014, she will reach Kochi via Mumbai.        

Which one of the statements below is logically valid and can be inferred from the above sentences?

log tan 1°+log tan2° +……+ log tan 89° is __________.

From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is __________.

Find the missing sequence in the letter series below:

A, CD, GHl?, UVWXY

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batman of these four?        

What is the next number in the series?        

12        35        81        173        357        _______

Find the odd one from the following group        

W, E, K, O     I, Q, W, A        F, N, T, X        N, V, B, D

A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?        

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: ; ; ; ; ; . We call this die