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

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`.

If the ratio between 8 and 11 is the same as the ratio of 2x - y to x + 2y, find the value of `(7"x")/(9"y")`

Divide Rs 1,290 into A, B and C such that A is `2/5` of B and B : C = 4 : 3.

A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.

In a mixture of 126 kg of milk and water, milk and water are in ratio 5 : 2. How much water must be added to the mixture to make this ratio 3 : 2?

If 2a = 3b and 4b = 5c, find: a : c.