(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

In each of the following determine whether the given values are solutions of the equation or not.
x² + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`

In each of the following determine whether the given values are solutions of the equation or not.
9x² - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`

In each of the following determine whether the given values are solutions of the equation or not.
x² + x + 1 = 0; x = 1, x = -1.

In each of the following, determine whether the given values are solution of the given equation or not:
x² - 3x + 2 = 0; x = 2, x = -1

In each of the following, determine whether the given values are solution of the given equation or not:
x² + x + 1 = 0; x = 0; x = 1

In each of the following, determine whether the given values are solution of the given equation or not:
x² - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`

In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`

In each of the following, determine whether the given values are solution of the given equation or not:
2x² - x + 9 = x² + 4x + 3; x = 2, x = 3

In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`

In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.

Name the figure formed by a triangle and its reflection, when:
An isosceles right-angled triangle is reflected in its hypotenuse.

Name the figure formed by a triangle and its reflection, when:
A right-angled triangle is reflected in its hypotenuse.

Name the figure formed by a triangle and its reflection, when:
An isosceles triangle is reflected in its unequal side.

Name the figure formed by a triangle and its reflection, when:
A scalene triangle is reflected in its greatest side.

The bisector of ∠ B and ∠C of a quadrilateral ABCD intersect in P, show that P is equidistant from the opposite sides AB and CD.

In ΔABC, the bisector AX of ∠A intersects BC ar X. XL ⊥ AB and XM ⊥ AC are drawn (Fig.) is XL = XM? why or why not?

l is the perpendicular bisector of line segment PQ and R is a point on the same side of l as P. The segment QR intersects l at X. Prove that PX + XR = QR.

Given a Δ ABC with unequal sides. Find a point which is equidistant from B and C as well as from AB and AC.

The diagonals of a quadrilateral bisect each other at right angles. Show that the quadrilateral is a rhombus.

What is the locus of points which are equidistant from the given non-collinear point A, B and C? Justify your answer.