An irrational number between 2 and 2.5 is

Which of the following is a polynomial in one variable?

If p(x) = (x⁴ – x² + x), then

If p(x) = x³ + x² + ax + 115 is exactly divisible by (x + 5) then a = ?

The equation of y-axis is

In the given figure, the value of x is

In the given figure, CE || BA and EF || CD. If ∠BAC = 40°, ∠ACB = 65° and ∠CEF = x° then the value of x is

Factorize: √2x² + 3x + √2

Prove that √5 is an irrational number.

Draw the graph of the equation y = 2x + 3

If x = (3 + √8), find the value of

Find the area of the triangle whose sides measure 52 cm, 56 cm and 60 cm respectively.

In the given figure, AB || CD. Find the value of x.

Find the values of a and b so that the polynomial (x⁴ + ax³ – 7x² - 8x + b) is exactly divisible by (x + 2) as well as (x + 3).

Using remainder theorem, find the remainder when p(x) = x³ – 3x² + 4x + 50 is divided by (x + 3).

Factorize: (2x³ + 54)

Find the product (a – b – c) (a² + b² + c² + ab + ac – bc)

In a ΔABC, if ∠A - ∠B = 33° and ∠B - ∠C = 18°, find the measure of each angle of the triangle.

In the given figure, in ΔABC, the angle bisectors of ∠B and ∠C meet at a point O. Find the measure of ∠BOC.

In the given figure, AB || CD. If ∠BAO = 110°, ∠AOC = 20° and ∠OCD = x°, find the value of x.

In a right-angled triangle, prove that the hypotenuse is the longest side.

In the given figure, prove that:

x = α + β + γ

Find six rational numbers between 3 and 4.

Factorize:

12(x² + 7x)² – 8(x² + 7x) (2x – 1) – 15(2x – 1)²

If (x³ + ax² + bx + 6) has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the values of a and b.

Without actual division, show that (x³ – 3x² – 13x + 15) is exactly divisible by (x² + 2x - 3).

Factorize: a³ – b³ + 1 + 3ab

In the given figure, AB || CD, ∠ECD = 100°, ∠EAB = 50° and ∠AEC = x°. Find the value of x.

Prove that the bisectors of the angles of a linear pair are at right angles.

In the given figure, AD bisects ∠BAC in the ratio 1: 3 and AD = DB. Determine the value of x.

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, find ∠MAN.

If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.