SSLC (English Medium) Class 10 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

If A = `x/(x + 1)` B = `1/(x + 1)` prove that `(("A" + "B")^2 + ("A" - "B")^2)/("A" + "B") = (2(x^2 + 1))/(x(x + 1)^2`

Pari needs 4 hours to complete the work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?

Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?

`(3y - 3)/y ÷ (7y - 7)/(3y^2)` is

Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)

One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections

In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number

Reduce the given Rational expression to its lowest form

`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`

Reduce the given Rational expression to its lowest form

`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2)`

Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`

Arul, Madan and Ram working together can clean a store in 6 hours. Working alone, Madan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?

A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?

Is it possible to design a rectangular park of perimeter 320 m and area 4800 m²? If so find its length and breadth.

At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than `("t"^2)/4`. Find t.

The number of seats in a row is equal to the total number of rows in a hall. The total number of seats in the hall will increase by 375 if the number of rows is doubled and the number of seats in each row is reduced by 5. Find the number of rows in the hall at the beginning.

Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.

          `{:("April sale in"  ₹)/("rice"   "wheat"   "ragi"):}`

A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`

and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.

What is the average sales for the months of April and May

Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.

          `{:"April sale in"  ₹)/("rice"   "wheat"   "ragi":}`

A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`

and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.

If the sales continue to increase in the same way in the successive months, what will be sales in the month of August?

A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?

There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?

To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?