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

If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.

Find the value of k for which the following equation has equal roots.

x² + 4kx + (k² – k + 2) = 0

The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.

Without using trigonometric tables evaluate:

`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`

In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:

1) m∠BDC

2) m∠BEC

3) m∠BAC

Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)² - 3x + 4 = 0

A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

In the given figure, ∠BAD = 65°, ∠ABD = 70°, ∠BDC = 45°

1) Prove that AC is a diameter of the circle.

2) Find ∠ACB

Solve the following equation:

`x - 18/x = 6` Give your answer correct to two significant figures.

Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm. Take `pi = 22/7`

When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.

px² – 4x + 3 = 0

Using the Remainder Theorem, factorise each of the following completely. 

 3x³ + 2x² – 23x – 30

Factorise the expression f(x) = 2x³ – 7x² – 3x + 18. Hence, find all possible values of x for which f(x) = 0.

Given that x – 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

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.