BMSAT Kozhikode 2025

A dataset consists of five observations: $19, 15, 24, 26$ and $x$. If the median of the dataset is the same as the median of the three numbers: $24, 26,$ and $x,$ then the mean of the dataset is

Water flows at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank that is $50$ m long and $44$ m wide. Determine the time in which the level of the water in the tank will rise by $7$ cm. $\newline$ (Assume $\pi = 22/7$)

Consider the statement: "A point on the curve $y = x²$ is equidistant from the points $(-1,0)$ and $(5,0).$"

In a potato race, a bucket is placed at the starting point, which is $5$m from the first potato, and the other potatoes are placed $3$m apart in a straight line. There are $20$ potatoes in the line. Each competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it, and continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

The sum of 30 terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + ...$ is

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hrs less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hrs more than the scheduled time. Find the distance covered by the train.

If one of the roots of the equation $x^2 + ax + 3a = 0$ is $1$, then its other root is

A factory kept increasing its output by the same percentage every year. Find the percentage if it is known that the output has doubled in the last two years. (assume $\sqrt{2} = 1.4142$)

Two solid spheres made of the same metal have weights of 5920 gm and 740 gm. If the diameter of the smaller sphere is 5 cm, then the radius of the larger sphere will be

If $x = \sqrt[3]{28}$ and $y = \sqrt[3]{27}$, find the value of $x + y - \frac{1}{x^2+xy+y^2}$.

If $1 + \sin^2\theta = 3 \sin \theta \cos \theta$, then $\tan \theta$ can take values

The ratio of alcohol to water in two containers, $A$ and $B$, are $5:3$ and $1:3$, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain $2.1$ litre of liquid which is composed of equal quantities of alcohol and water. How much liquid should be drawn from $A$?

Three women, Isha, Nisha, and Sudha, earn a monthly salary in the ratio $3:4:5$. They also spend monthly in the ratio $3:5:6$, saving the rest. If Sudha's savings are $1/6$th of her income, what's the ratio of the three women's monthly savings?

An exporter estimates with certainty that a $26\%$ higher price for his product will decrease the volume of sales in a foreign market by $30\%$. After having to increase the price by $26\%$, the revenue obtained from sales in that market turned out to be $\text{INR } 44.1 \text{ Cr}$. What would the revenue have been if the exporter had been allowed to sell at the old price?

A parcel's shipping cost is proportional to the square of its volume in cubic meters. Suppose we break the parcel into 3 packages in the ratio $2:3:5$ of its original volume, to qualify for lower shipping cost. If the savings are the equivalent of $\sqrt{6200}$ cubic meters, what was the original volume of the parcel?

Shalini got $30\%$ of the maximum marks in an exam. She failed by $50$ marks. Malini scored $40\%$ of the maximum, and this score was $20$ marks more than the pass mark. What is the pass mark?

One country's GDP is currently $600 billion and is growing at 10% per annum. Another country's GDP is $700 billion, while it is growing at 5% per annum. How many years will it take for the GDP of the 1st country to overtake the 2nd?

If $y > 0,$ and $\log_{y}(x) = 4, \log_{10y} (25x) = 2$ hold, what is $y?$

Say $y = 3\sqrt{2} - 4$, find $y^2 + \frac{1}{y^2}$.

If $x^{\frac{1}{12}}=49^{\frac{1}{24}}$, the value of $x$ is:

If $360 = 2^x \times 3^y \times 5^z$, then $x+y+z=?$

A told B, “When I was as old as you are now, then your age was four years less than half of my present age". If the sum of the present ages of A and B is 61 years, what is B's present age in years?

By selling a cloth that is $33$m long, a draper loses an amount equal to the selling price of $3$m of cloth. What is his loss %?

The simple interest and compound interest on a certain sum for $2$ years is INR $1250$ and INR $1475$, respectively. The rate of interest per annum (compounded annually) in percentage is:

If a boat takes 4 hours longer to travel a distance of 45 km upstream than to travel the same distance downstream, then find the speed of the boat in still water if the speed of the stream is 2 km/hour.

A thief runs away from a police station with a uniform speed of 100m/minute. After 1 minute, a policeman runs behind the thief to catch him. He runs at a speed of 100m/min in the first minute and increases his speed by 10m/min in each succeeding minute. At the end of which minute, will the policeman be able to catch the thief?

A lift carrying 50 passengers from the ground floor of a 100-storeyed building is moving upwards. The lift stops at the 1st, 2nd, and 3rd floor, then skips the 4th floor, again stops at the 5th, 6th, and 7th, then skips the 8th floor, and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3..... On which floor does the lift become empty?

Simplify the following: $\dfrac{1}{\log_{8}(x)} - \dfrac{1}{\log_{7}(x)} + \dfrac{1}{\log_{6}(x)} - \dfrac{1}{\log_{5}(x)} + \dfrac{1}{\log_{4}(x)} - \dfrac{1}{\log_{3}(x)} + \dfrac{1}{\log_{2}(x)}$

What is the minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.95?

The zeroes of $ax² + bx + c = 0$ are in the ratio $1:2$ (assume the coefficients to be non-zero). Which of these is one of the zeroes?

The diameter of a solid sphere is 6 cm. If the sphere is melted and drawn into a wire of diameter 2 mm, the length of the wire will be

Find the area of a trapezium whose parallel sides measure 25 cm and 13 cm, while the other two sides measure 15cm each.

What must be added to $x^4+2x^3-2x^2+x-1$ so that the result is exactly divisible by $x^2+2x-3$?

If $x^{2}+\frac{1}{x^{2}}=83$ and $x>1$, then the value of $x^{3}-\frac{1}{x^{3}}$ is

The pair of tangents drawn from an external point to a circle are perpendicular to each other and the length of each tangent (from the point to the circle) is 5 cm. The radius of the circle is

If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then the sun's elevation is

$\dfrac{\sin \theta}{(1+ \cos \theta)}$ is equal to

If the radii of two concentric circles are 4 cm and 5 cm, then the length of a chord of one circle that is tangent to the other circle is

If one angle of a triangle is equal to the sum of the other two angles, then the triangle must be

If one angle of a parallelogram is $24^{\circ}$ less than twice its adjacent angle, then the largest angle of the parallelogram is

The average of any 4 consecutive odd positive integers, where the 1st number is a multiple of 3, must be divisible by which of these?

Let $A = \{a, b, c, d, e\}$. The no. of subsets that contain exactly 3 of these elements are?

3 bells ring at intervals of 3hrs, 4hrs and 16hrs respectively. If they have rung together once today, what day in the future will they ring together next?

If $p, q,$ and $r$ are in geometric progression, which of the following is true about $qr, pr,$ and $pq$?

There is a 4-in-5 chance that A can complete the marathon. There is a 5-in-8 chance that B can't complete the marathon, which is independent of A's performance. What is the probability that both A and B end up completing?

What's the area of the quadrilateral included inside the points: $(-1, 2), (-1, 4), (7, 2), (7, 4)?$

If $n \leq 4$ and $2 \leq m \leq n \leq 5,$ then what is the greatest possible value of $(n - m)(n + m)?$

$8\%$ of boys in a class made it past the 90th percentile, while $12\%$ of the girls in the same class made it past that mark. Suppose there are $120$ students in this class: what is the number of boys?

Coins of INR $2, 5,$ and $10$ denominations are in a bag in the ratio of $30:20:10,$ of which the INR $5$ coins amount to INR $250.$ What is the total value of coins in the bag?

A trader declares that he will sell his commodity at $10\%$ profit over his cost price. However, he alters his weighing balance to sell $10\%$ less to each customer. What is his true profit margin in percent?