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

Solve the following quadratic equation using formula method only 

 3a²x² +8abx + 4b² = 0, a ≠ 0 

Solve the following quadratic equation using formula method only

`"x"^2 + 1/2 "x" - 1 = 0`

Solve the following quadratic equation using formula method only

`"x"^2 - 4 sqrt 15 "x" - 4 = 0`

Find the values of a and b in the polynomial f(x) = 2x³ + ax² + bx + 10, if it is exactly divisible by (x+2) and (2x-1).

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

Find the value of m for which the equation (m + 4)x² + (m + 1)x + 1 = 0 has real and equal roots.

Find the value of k for which equation 4x² + 8x – k = 0 has real roots.

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