SSLC (English Medium) कक्षा १० - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

PQRS is a rectangle formed by joining the points P(– 1, – 1), Q(– 1, 4), R(5, 4) and S(5, – 1). A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

If vertices of a quadrilateral are at A(– 5, 7), B(– 4, k), C(– 1, – 6) and D(4, 5) and its area is 72 sq. units. Find the value of k.

For what value of natural number n, 4ⁿ can end with the digit 6?

If m, n are natural numbers, for what values of m, does 2ⁿ × 5^m ends in 5?

Find the H.C.F. of 252525 and 363636

If 13824 = 2^a × 3^b then find a and b

If p₁^x₁ × p₂^x₂ × p₃^x₃ × p₄^x₄ = 113400 where p₁, p₂, p₃, p₄ are primes in ascending order and x₁, x₂, x₃, x₄, are integers, find the value of p₁, p₂, p₃, p₄ and x₁, x₂, x₃, x₄

Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic

Find the greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36?

What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?

Find the least number that is divisible by the first ten natural numbers

Find the least positive value of x such that 89 ≡ (x + 3) (mod 4)

The sum of the exponents of the prime factors in the prime factorization of 1729 is

Reduce the following rational expression to its lowest form

`(x^2 - 1)/(x^2 + x)`

Reduce the following rational expression to its lowest form

`(x^2 - 11x + 18)/(x^2 - 4x + 4)`

Reduce the following rational expression to its lowest form

`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`

Reduce the following rational expression to its lowest form

`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`

Find the excluded values, of the following expression

`y/(y^2 - 25)`

Find the excluded values, of the following expression

`"t"/("t"^2 - 5"t" + 6)`

Find the excluded values, of the following expression

`(x^2 + 6x + 8)/(x^2 + x - 2)`