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Let $\dfrac{m}{n} = \dfrac{90^2+5 \times 90+4}{90^2+5\times 90+6} \times \dfrac{91^2+5\times 91+4}{91^2+5\times 91+6} \times .......\times \dfrac{98^2+5\times 98+4}{98^2+5\times 98+6}$ where m and n are co-primes.

What is the value of $|m - n|$ ?

If the number 123k578 is divisible by 11, then what is the value of k?

A shopkeeper sold article A at a profit of $18\%$ and article B at a loss of $10\%$, thus making an overall profit of Rs.$85$. If he had sold at article A at an $11\%$ loss and article B at an $8\%$ profit, he would have suffered a loss of Rs.$34$. Find the sum (in Rs.) of the cost prices of article A and article B.

A, B and C work in a workshop for creating identical idols. A can craft 10 idols in 150 days. Similarly, B and C can individually create 16 idols in 192 days and 320 days, respectively. B works every day, A works only on alternate days starting from the first day, i.e. 1st March, and C also works only on alternate days starting from the second day, i.e 2nd March. On which date will the construction of 2 idols be completed?

A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on third day and

so on, thus getting on any day twice the amount he received just the day before. How many rupees will the boy earn in all, if

he started working on the $5^{th}$ of March and completed the work on the $28^{th}$ of March?

Out of 7 different consonants and 4 different vowels, how many words (not necessarily meaningful) of 4 consonants and 2 vowels can be formed?

A room, with a length of 18m, a height of 15 m and a total surface area of 1332 m² is to be divided into 4 m wide small rooms, by inserting plywood sheets in the room. To minimize the expenditure on the purchase of these sheets, how many 18 m × 15 m sheets will be required to construct the maximum possible number of such small rooms, if the length and the height of the small rooms remain the same as that of the original room?

The simple interest on a certain sum of money invested at 7.5% per annum for 4 years is ₹243. What was the sum (in ₹) invested?

Nidhi reached her institute in 3 hours while travelling by bus with a wheel radius of 70 cm and making 250 revolutions in one minute. One day, she left for the institute one hour later than usual time. Then to reach her institute on time, she should increase her speed by ____. [Use $\pi = \frac{22}{7}$]

If the equation $(m - 3)x^2 - 2mx + 5m = 0$ has real and positive roots, then the possible value(s) of m lies in:

A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

The measure of each exterior angle of a regular polygon having ‘p' sides is half of the measure of each of its interior angles. The value of 'p' is:

The average of three numbers is 19 while the average of two of these numbers is 21.25. What is the value of the third number?

Regarding the function $f(x)=x^{2}-5 x+1$ and $g(x)=1-x-x^{3}$ on the set of real numbers, which of the following statements is not true?

Ravish paid ₹640 for a jar of 40 chocolates where the amount paid included the cost of the jar. Harish paid a total of ₹1540 for one jar containing 55 chocolates and a second jar containing 45 chocolates, where the amount paid included the cost of both the jars. If all jars cost the same, and all chocolates cost the same, how much (in ₹) would Satish have to pay for a jar containing 35 chocolates, if the amount he has to pay includes the cost of the jar as well as that of the chocolates he bought?

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. $\angle SQR$ measures $72^\circ$, and $\angle QPR$ measures $28^\circ$. What is the measure of $\angle QRS$?