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

The expression 4x³ – bx² + x – c leaves remainders 0 and 30 when divided by x + 1 and 2x – 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely. 

Find the number that must be subtracted from the polynomial 3y³ + y² – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. 

Find the number that must be subtracted from the polynomial 3y³ + y² – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. 

Show that (x – 1) is a factor of x³ – 7x² + 14x – 8. Hence, completely factorise the given expression. 

Show that (x – 1) is a factor of x³ – 7x² + 14x – 8. Hence, completely factorise the given expression.

Using Remainder Theorem, factorise : x³ + 10x² – 37x + 26 completely.

If (x + 1) and (x – 2) are factors of x³ + (a + 1)x² – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.

Factorise x³ + 6x² + 11x + 6 completely using factor theorem. 

The polynomial px³ + 4x² – 3x + q is completely divisible by x² – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.

ABC is a right angles triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

Prove that the parallelogram, inscribed in a circle, is a rectangle.

Prove that the rhombus, inscribed in a circle, is a square.

Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.

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

In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°, calculate:

1. ∠DAB,
2. ∠BDC.

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

Calculate:

1. ∠EBA,
2. ∠BCD.

In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that ∠PQR = 58°,

Calculate:

1. ∠RPQ,
2. ∠STP.

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.