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

The roots of quadratic equation x(x + 8) + 12 = 0 are ______.

If one root of equation (p – 3) x² + x + p = 0 is 2, the value of p is ______.

Equation 2x² – 3x + 1 = 0 has ______.

Which of the following equations has two real and distinct roots?

If the roots of x² – px + 4 = 0 are equal, the value (values) of p is ______.

Which of the following equations has imaginary roots?

One root of equation 3x² – mx + 4 = 0 is 1, the value of m is ______.

If the quadratic equation kx² + kx + 1 = 0 has real and distinct roots, the value of k is ______.

The speed of a boat is 32 km/h. If the speed of stream is 8 km/h, the speed of boat upstream is ______.

The speed of train A is x km/h and speed of train B is (x – 5) km/h. How much time will each train take to cover 400 km?

A car is moving with a speed of 100 km/h. If the speed of car first increases by x% and then decreases by x%, the final speed of the car is 96 km/h. The value of x is ______.

The speed of a boat in still water is 15 km/h and speed of stream is 5 km/h. The boat goes x km downstream and then returns back to the point of start is ______.

One factor of x³ – kx² + 11x – 6 is x – 1. The value of k is ______.

If (x – a) is a factor of x³ – ax² + x + 5; the value of a is ______.

(x – 2) is a factor of ______.

For the polynomial x⁵ – x⁴ + x³ – 8x² + 6x + 15, the maximum number of linear factors is ______.

If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.

If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.

The daily wages of 80 workers in a project are given below.

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1. the median wage of the workers.
2. the lower quartile wage of workers.
3. the numbers of workers who earn more than Rs. 625 daily.

Using properties of proportion, solve for x. Given that x is positive:

`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`