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

Evaluate the following :

`|(2 , 3),(-4 , 0)| |(3 , -2),(-1 , 4)|`

Evaluate the following :

`|(2,1) ,(3,2),(1 , 1)|  |(1 , -2 , 1),(2 , 1 , 3)|` 

Evaluate the following :

`|(0 , 1),(-1 , 2),(-2 , 0)|  |(0 , -4 , 0),(3 , 0 , -1)|`

Evaluate the following :

`|(6 , 1),(3 , 1),(2 , 4)|  |(1 , -2 , 1),(2 , 1 , 3)|`

Evaluate the following :

`|(0 , 1 , 0),(2 , 0 , -3),(1 , 0 , -2)|  |(1 , -2),(3 , 4),(0 , 0)|`

If A = `|(1,3),(3,2)|` and B = `|(-2,3),(-4,1)|`   find AB

If A = `|(1,3),(3,2)|` and B = `|(-2 , 3),(-4 , 1)|`  find BA

If P = `|(1 , 2),(2 , 1)|` and Q = `|(2 , 1),(1 , 2)|` find P (QP).

If P =`|(1 , 2),(3 , 4)|` , Q = `|(5 , 1),(7 , 4)|` and R = `|(2 , 1),(4 , 2)|`  find the value of  P(Q + R)

If A = `|(3,-2),(-1 , 4)|` , B = `|(2"a"),(1)|` , C = `|(-4),(5)|` , D = `|(2),("b")|` and AB + 2C = 4D then find the values of a and b.

Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B)  (ii) A² - B² . Is (i) equal to (ii) ?

Draw a circle of radius 4 cm and take a point Pon its circumference. Construct a tangent to the circle at P. 

Draw a circle with centre O and radius 2.5 cm. Take a point P at a distance of 6 cm from the centre. Using ruler and compasses only construct the tangents to the circle from the point P.

Draw a circle with centre O and radius 3 cm. Take a point P outside the circle. Draw tangents to the circle from P without using the centre and using only ruler and compasses. 

Using ruler and compasses only, draw tangents to a circle of radius 3 cm from a point 5 cm from the centre. What is the length of each of them ? 

Draw two circles of radii 2.5 cm and 3.5 cm respectively so that their centres are 8 cm apart. Draw direct comm on tangents to the circle. 

Draw two circles of radii 3.5 cm and 2 cm respectively so that their centres are 6 cm apart. Draw direct common tangents to the circle and show that they are equal in length.

Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length. 

Draw two circles with radii 2.5 cm and 4 cm and with their centres 7 cm apart.
Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent. 

Find the number which bears the same ratio to `7/33` that `8/21` does to `4/9`.