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

Find, using the quadratic formula, the roots of the following quadratic equations, if they exist

3x² – 5x + 2 = 0

Find, using the quadratic formula, the roots of the following quadratic equations, if they exist

x² + 4x + 5 = 0

In the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°. Calculate : ∠NRM

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate : ∠BCD. 

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°. 

Calculate : ∠DBA 

Also, show that the ΔAOD is an equilateral triangle.

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°. 

Calculate : ∠DBC 

Also, show that the ΔAOD is an equilateral triangle.

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°. 

Calculate: ∠ADC 

Also, show that the ΔAOD is an equilateral triangle.

In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠FAB.

Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.

Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.

(3x - 5)(2x + 7) = 0

48x² – 13x -1 = 0

`10x -(1)/x` = 3

`(2)/x^2 - (5)/x + 2` = 0

`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0

`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0

ax² + (4a² - 3b)x - 12 ab = 0

Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0

Find the value of k for which the following equation has equal roots:
(k − 12)x² + 2(k − 12)x + 2 = 0.

If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.