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

If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.

Find two consecutive natural numbers such that the sum of their squares is 61.

Find two consecutive integers such that the sum of their squares is 61

If the product of two positive consecutive even integers is 288, find the integers.

If the product of two consecutive even integers is 224, find the integers.

Find two consecutive even natural numbers such that the sum of their squares is 340.

Find two consecutive odd integers such that the sum of their squares is 394.

The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.

The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?

Find three successive even natural numbers, the sum of whose squares is 308.

Find three consecutive odd integers, the sum of whose squares is 83.

In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.

The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.

A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.

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.

A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.