BPSC TRE · Class 6–8 · Mathematics & Science Previous Year Questions
BPSC TRE Maths & Science Previous Year Questions (PYQs) – 240 Questions
TRE-2 · TRE-3 Original · TRE-3 Re-Exam · Mathematics · Science
Practice 240 BPSC TRE Class 6–8 Mathematics and Science previous year questions with the original A–E options and booklet question numbers. The bank contains 120 Mathematics and 120 Science PYQs from TRE-2, the TRE-3 original sitting and the TRE-3 re-exam.
BPSC TRE Class 6–8 Maths & Science Question Paper Coverage
For each included sitting, Part III contains Question Nos. 71–150. Mathematics runs from Q.71–110 and Science runs from Q.111–150, giving 80 subject questions per paper and 240 questions across the three source sittings.
BPSC TRE Maths & Science PYQ Bank – Complete 240 Questions
Use the search and filters to study the previous year questions paper-wise or subject-wise. Every card retains the original question number, all five answer options and its source-page reference.
Mathematics PYQs
120 questions across Q.71–110 from each sitting, covering the mathematical areas tested by BPSC in these papers.
Science PYQs
120 questions across Q.111–150 from each sitting, including the Physics, Chemistry and Biology content appearing in the source papers.
Find the single discount equivalent to two successive discounts of 20% and 10%.
In a certain experiment, the count of bacteria was increasing at the rate of 2.5% per hour. Initially, the count was 512000. Find the count of bacteria at the end of 2 hours.
The value of a machine depreciates at the rate of 20% per annum. It was purchased two years ago. If its present value is Rs. 40,000, for how much was it purchased?
Which of the following statements is not necessarily true? (I) A quadrilateral is a parallelogram if its diagonals bisect each other. (II) If the diagonals of a quadrilateral are equal, then it is a rectangle. (III) If the diagonals of a quadrilateral intersect at right angles, then it is a rhombus. (IV) A rectangle, a square and a rhombus are special types of parallelograms.
ABCD is a trapezium in which AB || DC, AB = 78 cm, CD = 52 cm, AD = 28 cm and BC = 30 cm. What is the area of this trapezium?
The capacity of a reservoir is 108 m³. Water is poured into it at the rate of 60 litres per minute. How many hours will it take to fill the reservoir?
If each side of a cuboid is doubled, its surface area
The following table gives the frequency distribution of marks: 0-10: 3, 10-20: 8, 20-30: 16, 30-40: 30, 40-50: 17, 50-60: 4. The median class is
Solve: (2^(3x-1) + 10) / 7 = 6.
A steamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/hr, then the speed of the steamer in still water is
The maximum value of sin theta + cos theta is
For what value of x is the line through the points (-2, 6) and (4, 8) perpendicular to the line through the points (8, 12) and (x, 24)?
If the angle between two lines is pi/4 and the slope of one of the lines is 1/2, then the slope of the other line is
If three points (h, 0), (a, b) and (0, k) lie on a line, then the value of a/h + b/k is
If the perpendicular drawn from the origin to a straight line makes an angle alpha with the positive direction of the y-axis and is of length p, then the equation of the straight line is
The intercepts made by the line 3x - 4y + 10 = 0 on the x- and y-axes are respectively
A vehicle covers a certain distance at a uniform speed. If its speed were 6 km/hr more, it would take 4 hours less; if its speed were 6 km/hr less, it would take 6 hours more. The distance is
Shyam borrowed Rs. 1,80,000 for repairing his house. This amount is to be refunded in three equal annual instalments with 10% interest. The amounts payable at the ends of the first, second and third years respectively are
The value of cos(-1710 degrees) is
The standard deviation of 11, 14, 15, 17, 18 is
The minute hand of a clock is 1.5 cm long. How far does its tip move in 40 minutes?
For every positive integer n, 41^n - 14^n is divisible by
A card is drawn from a well-shuffled pack of 52 cards. If every outcome is equally likely, what is the probability that the card will not be a diamond?
P, Q and R can complete a work in 6 hours, 8 hours and 15 hours respectively. They together completed the work and received Rs. 9,460 as remuneration. Their shares in the remuneration are respectively
The sum of the squares of two natural numbers is 410. If the square of the larger number is 26 times the smaller number plus 3, then the difference between the two numbers is
When x^3 - 10x^2 + 2x + 3 is divided by (x + 1), the remainder is
Susheel earned Rs. 6,00,000 in a year. In each month after the first, he earned Rs. 1,500 more than he did in the previous month. How much did he earn in the first month?
Three consecutive natural numbers are such that the sum of the square of the first and the product of the second and third is 191. What are they?
The coordinates of three points A, B and C are (a/3, a), (2a/3, 2a) and (a/3, 3a) respectively. Triangle ABC is
If p and q are the lengths of the perpendiculars drawn from the origin on the lines x sin theta + y cos theta = 2b sin theta cos theta and x cos theta - y sin theta = b cos 2theta respectively, then the value of p^2 + q^2 is
The area of a square field is 60025 m². A man cycles along its boundary at the speed of 18 km/hr. In how much time will he return to the starting point?
Two cards are randomly drawn from a pack of 52 cards and thrown away. What is the probability of drawing an ace in a simple draw from the remaining 50 cards?
The product of cos(A+B) and cos(A-B) is
From the window of a house, the angle of elevation of the top of a flag is 60 degrees and the angle of depression of its base is 30 degrees. If the horizontal distance of the flag from the house is 6 m, then find the height of the flag.
The area of a rhombus is 480 cm² and the length of its shorter diagonal is 20 cm. The length of its longer diagonal is
Places A and B are 240 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 8 hours. If they travel towards each other with their previous speeds, they meet in 2 hours. What are the speeds of the two cars?
Calculate the arithmetic mean from the frequency distribution: class intervals 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 6, 10, 9, 4, 11 respectively.
The mean and median of a distribution are respectively 25.5 and 26. The mode is
Simplify: (sin theta + sin 3theta + sin 5theta) / (cos theta + cos 3theta + cos 5theta).
A cone and a hemisphere have the same base and the same volume. The ratio of their heights is
Two thin convergent lenses of powers 5 dioptres and 4 dioptres are placed coaxially 10 cm apart. The focal length of their combination would be
An ideal transformer is used on 220 V line to deliver 2 A at 110 V. The current flowing in the primary of the transformer is
The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to
Imagine a light planet is revolving around a star in circular orbit of radius R with the period of revolution T. If the gravitational force of attraction between the two is proportional to R^(-5/2), then
When a proton injected in magnetic field moves perpendicular to the lines of force, it follows
The resistivity of a given conductor depends upon
The area under velocity-time graph for a particle in a given interval of time represents
The least resistance obtained by using 2 ohm, 4 ohm, 1 ohm and 100 ohm is
The nucleus of the atom is positive
Voltage is equal to
As the wavelength is increased from violet to red, the luminosity
If the light moving in a straight line bends by a small but fixed angle, it may be a case of
Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?
If the speed and radius of a body moving in a circular path are doubled, then the magnitude of centripetal acceleration will be
Which of the following reactions represents a displacement reaction?
Carbon mainly forms covalent bonds because
Sodium carbonate is a basic salt because it is a salt of
Benzene reacts with chlorine in the presence of light to yield
Burning of lime to give calcium oxide and carbon dioxide is
A solution reacts with crushed eggshells to give a gas that turns limewater milky. The solution contains
10 mL of a solution of NaOH is found to be completely neutralized by 8 mL of a given solution of HCl. If we take 20 mL of the same solution of NaOH, the amount of HCl solution (the same solution as before) required to neutralize it will be
A drop of a liquid sample is put on pH paper. It is observed that the colour of pH paper turns blue. The liquid sample is
Which acid is found in tomato?
Na2CO3.10H2O is known as
In chemistry, pKa stands for
The colourless species is
Which metal is a part of German silver?
Kolbe's electrolytic method can be applied on
The main site of photosynthesis in the cells of a leaf is
The contraction and expansion movement of the wall of the food pipe is called
The tube connecting the kidney to the urinary bladder in humans is
The most conducive pH range for the life of freshwater plants and animals is
An unripe green fruit changes colour when it ripens. The reason is
In Amoeba, food is digested in
Which of the following is not a function of the vacuole in plants?
Nodes of Ranvier are found in
The connecting link between birds and reptiles is
Dengue fever is caused by
The youngest secondary xylem occurs
Which of the following functions is performed by Malpighian tubules in cockroach?
Mohan buys Rs. 20 shares paying 9% dividend. He wants to earn an interest of 12% on his money. The market value of each share is
A number when divided by 342 gives a remainder 47. When the same number is divided by 19, what would be the remainder?
The area of a rectangle is equal to the area of a circle with radius 14 cm. If the breadth of the rectangle is 22 cm, what is its length?
What will be the perimeter of a semicircle if the radius of the semicircle is equal to half the side of a square of area 196 m²?
A father's age is 6 times his son's age. Four years after, the age of the father will be four times his son's age. The present ages (in years) of the son and the father are respectively
The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the sides of the rhombus is
If triangle ABC and triangle DEF are similar, where angle A = 30 degrees, angle C = 50 degrees, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then the value of DE is
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Then the length PQ is
Two cubes each of volume 64 cm³ are joined end-to-end. The surface area of the resulting cuboid is
The radius of a wheel is 21 cm. How many revolutions will it make in travelling 924 meters?
Three metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. The radius of this solid sphere is
If theta is an acute angle such that cos theta = 3/5, then (sin theta tan theta - 1) / (2 tan² theta) is equal to
For what value(s) of k, the equation kx² + kx + 1 = -4x² - x has real and equal roots?
If the 3rd term of an A.P. is 5 and the 7th term is 9, then its 17th term will be
The equation of a line passing through the point (3, 5) and perpendicular to the line x + 5y - 4 = 0 is
If the difference between the circumference and radius of a circle is 37 cm, then using pi = 22/7, the circumference of the circle is
The area of a square is 3/5 the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square?
The ratio of the length of a rod and its shadow is 1 : sqrt(3). The angle of elevation of the Sun is
The ratio of milk and water in 64 litres of a mixture is 5 : 3. What amount of water should be added to make the ratio 3 : 5?
Five years ago Meenu was thrice as old as Aman. Ten years later Meenu will be twice as old as Aman. The present ages (in years) of Meenu and Aman are respectively
If the mean of first n natural numbers is 3n/5, then the value of n is
A bag has 5 white balls, 8 red balls and 4 purple balls. If we take a ball randomly, then what is the probability of not getting a purple ball?
In a simultaneous throw of two coins, the probability of getting at least one head is
Ram can do a piece of work in 60 days. He works for 15 days and then Shyam alone finishes the remaining work in 30 days. The two together can finish the work in
Swati invests Rs. 1,87,000 in the stock market which is 20% of her annual income. Her monthly income is approximately
The points scored by a Kabaddi team in a series of matches are 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28. The median of the points will be
4/7 of a number is equal to 40% of another number. The ratio between the first number and the second number respectively is
A 120 m long train takes 10 seconds to cross a man standing on the platform. The speed (in m/s) of the train is
The largest number of four digits, which on divided by 15, 18, 21 and 24 gives remainders 11, 14, 17 and 20 respectively, is
In an examination, 35% of total students failed in Hindi, 45% failed in Mathematics and 20% in both. The percentage of those who passed in both the subjects is
A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?
An oil tank is 2/5 full. If 32 litres of oil is added to the tank, it becomes 6/7 full. The capacity of the tank is
A fan is sold for Rs. 4,900 at a loss of 30%. What is the cost price of the fan?
A principal amount becomes Rs. 169 in two years at 4% per annum compound interest. The principal amount is
A tank is of length 25 m, breadth 12 m and depth 6 m. The cost of plastering walls and bottom of the tank at the rate of 50 paise per square meter is
The volume of a sphere is equal to the volume of a cone with base 6 cm and height 24 cm. The radius of the sphere is
The lines representing the equations 6x - 3y + 10 = 0 and -2x + y - 9 = 0 are
Ram can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. The speed of the stream is
The value(s) of k for which the equation 2x² + kx + 3 = 0 has equal roots is/are
The value of cos²17 degrees - sin²73 degrees is
Which of the following is the formula for motion in a straight line?
Which of the following energy changes involves the frictional force?
When you stretch a rubber band, the energy transferred is stored in the form of
How much work is done in moving a charge of 5 C across two points having a potential difference of 16 V?
If the distance between the two masses is doubled, then what happens to the gravitational force between them?
What is the energy required to move a body of mass m from an orbit with radius 2R to radius 3R?
Which of the following is the relation between kinetic energy (E) of a gas and its pressure (P)?
A mass of 1 kg is attracted towards the Earth with a force which is
Artificial 'gene' was created by
Who had given the concept of photovoltaic effect?
Who introduced the metric system?
Which of the following mirrors is used by ENT specialists?
Resistance of a wire is given by which of the following?
Which of the following helps to act as the catalyst which breaks down food?
What is the colour of AgBr?
What is the term used for liquid dispersion in another liquid?
Which of the following slows down the reaction rate?
Which of the following is not an example of lyophobic colloids?
Which of the following is an example of sorption?
Which of the following should never be used to treat people directly?
Which of the following is acidic in nature?
Acid reacts with bases to form salt and water. This reaction is
Which of the following elements would lose an electron easily?
Which of the following gases turns limewater milky?
The metal found free in nature is
The reaction in which heat energy is released is called
What is the chemical name of vitamin B12?
Which of the following is a good source of vitamin A?
Which of the following is warm blooded?
Pungency in chillies is due to the presence of which of the following?
The process of converting nitrates into N2 is called
Which part of DNA provides information for a protein?
The process where the characteristics are transmitted from parent to offsprings is called
Input and output nerves meet at
Night blindness is caused by the deficiency of which of the following vitamins?
Energy which is stored in food that we eat is only released in cells of the body by which of the following processes?
What is the cause of cold?
Vibration of ear drum is due to which of the following?
What is the respiratory pigment in human body?
One-cell thick vessels are called
The sum of the exponents of the prime factors in the prime factorisation of 196 is
If alpha and beta are the roots of the quadratic equation 4x² + 3x + 7 = 0, then 1/alpha + 1/beta =
If 11 times the 11th term of an A.P. is equal to 7 times its 7th term, then its 18th term will be
If point p(x, y) is equidistant from A(5, 1) and B(-1, 5), then
The shadow of a tower is equal to its height at 10.45 a.m. The sun’s altitude is
The radii of bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. The ratio between the volume of cylinder to that of cone is
The length of the hypotenuse of an isosceles right triangle whose one side is 4sqrt(2) cm is
A sum of Rs. 10,000 is borrowed by Akshit for 2 years at an interest of 10% compounded annually. Find the compound interest and amount he has to pay at the end of 2 years.
If a number x is chosen from the numbers 1, 2, 3 and a number y is selected from the numbers 1, 4, 9, then P(xy < 9) is
The sum and product of the roots of the equation 2x² - 5x + 4 = 0 are in ratio
In an equilateral triangle ABC, AD is perpendicular to BC. Then which of the following is true?
If the difference between the circumference and radius of a circle is 37 cm, then using pi = 22/7, the circumference of the circle is
If triangle ABC is right-angled at C, then the value of cos(A+B) is
In a throw of two dice, the probability of getting a sum of 10 is
If P is a prime number, then LCM of P, P² and P³ is
The area of the circle that can be inscribed in a square of side 10 cm is
The area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees is
(n+1)² - 1 is divisible by 8, if n is
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
If the points A(1, 2), b(0, 0) and C(a, b) are collinear, then
Find the market price of 5% Rs. 100 share when a person gets a dividend of Rs. 65 by investing Rs. 1,430.
If the perimeter of a circle is equal to that of a square, then the ratio of their area is
If m^n = 32 where m and n are positive integers, then the value of n^(mn) is
The graph of y = f(x), where f(x) is a quadratic polynomial, meets the x-axis at A(-2, 0) and B(-3, 0). Then the expression for f(x) is
If the mean of first n natural numbers is 3n/5, then the value of n is
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of smaller cone to the whole cone is
A company declares 8 percent dividend to the shareholders. If a man receives Rs. 2,840 as his dividend, find the nominal value of his shares.
sin(45 degrees + theta) - cos(45 degrees - theta) is equal to
If the line segment is divided in the ratio 3 : 7, then how many parts does it contain while constructing the point of division ?
If PA and PB are tangents to the circle with centre O such that angle APB = 50°, then angle OAB =
A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is
If n is a natural number, then 6^n - 5^n always ends with
The pair of equation x = a and y = b graphically representing lines which are
In a cricket match, a batsman hits the boundary 8 times out of 40 balls he plays. Find the probability that he did not hit the boundary.
If tan A = cot (30° + A), then A =
For a given data with 50 observations, the ‘less than ogive’ and the ‘more than ogive’ intersect at (15.5, 20). The median of the data is
The probability that a non-leap year has 53 Sundays is
From the top of a cliff 25 m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is
The force required to maintain an object at a constant velocity is
Which of the following is an unsaturated hydrocarbon ?
The membrane surrounding the cell is called
The study of the inheritance of traits in humans is called
A car covers a distance of 200 km in 4 hours. What is its average speed ?
The breakdown of pyruvate to give carbon dioxide, water and energy takes place in
Which subatomic particle has negligible mass ?
The speed of sound is maximum in which of the following ?
Food cans are coated with tin and not with zinc because
What happens to the gravitational force between two objects if the distance between them is doubled ?
Which of the following are environment-friendly practices ?
Butanone is a four-carbon compound with the functional group
What is the function of meristematic tissue in plants ?
What is the work to be done to increase the velocity of a car from 30 km h^-1 to 60 km h^-1 if the mass of the car is 1500 kg?
Lichens are sensitive to which air pollutant?
In which of the following sphere, weather phenomenon occurs ?
The gap between two neurons is called as
Which of the following represents the correct electronic configuration of nitrogen ?
Which of the following constitutes a food chain ?
The magnetic field lines around a straight current carrying conductor are
What happens when dilute hydrochloric acid is added to iron fillings ?
The kidneys in human beings are a part of the system for
Which of the following terms does not represent electrical power in a circuit?
Which of the following is not a characteristic of solids ?
The phenomenon due to which the sky appears blue is
Starting from a stationary position, Rahul pedals his bicycle to attain a velocity of 6 m s^-1 in 30 s. Then he applies brakes such that the velocity of the bicycle comes down to 4 m s^-1 in the next 5 s. Calculate the acceleration of the bicycle in both the cases.
Which of the following statements about permanent tissues is correct ?
Which of the following is a characteristic property of acids ?
According to Newton’s second law of motion, the acceleration of an object is directly proportional to the
Which of the following is a plant hormone ?
What is the process of changing a substance directly from solid to gas called ?
The anther contains
What is the common name of calcium hydroxide ?
Who discovered the cell for the first time ?
The SI unit of work is
Which of the following is not a physical change ?
Which of the following is not a vector borne disease ?
What happens when light enters a glass slab from air ?
Which of the following methods is suitable for preventing an iron frying pan from rusting ?
The acceleration due to gravity on the surface of the earth is approximately
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Source & Verification
The question bank is built from the three Maths & Science source papers used for extraction. English wording is preserved; only obvious PDF/scan typography such as flattened superscripts, fractions, square roots and rupee symbols was normalized for readable web display.
BPSC TRE Maths & Science PYQ – Frequently Asked Questions
How many BPSC TRE Maths & Science PYQs are included?
The bank contains 240 subject questions in total: 80 from each of the three included Class 6–8 source sittings.
How are Mathematics and Science questions divided?
There are 120 Mathematics questions and 120 Science questions. In each paper, Mathematics is Q.71–110 and Science is Q.111–150.
Which TRE papers are included?
The bank includes TRE-2 dated 9 December 2023, TRE-3 Original dated 15 March 2024, and the TRE-3 Re-Exam dated 19 July 2024.
Why is the March 2024 TRE-3 paper included if it was cancelled?
It remains useful as a previous-question practice source, but the page labels it as a cancelled sitting so it is not confused with the official July 2024 re-exam.
Are correct answers included on this page?
No. This version preserves the extracted questions and A–E options only. No answer has been invented or inferred without mapping the relevant official answer keys.
