Mathematics 2010-2011 (English Medium) ICSE Class 10 Question Paper Solution

Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

if `A = [(3,5),(4,-2)] and B = [(2),(4)]`is the product AB possible? Give a reason. If yes, find AB

Mr Kumar borrowed Rs. 15000 for two years. The rates of interest for two successive years are 8% and 10% respectively. If he repays Rs. 6200 at the end of the first year, find the outstanding amount at the end of the second year.

From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.

1) a face card (King, Jack or Queen)

2) an even-numbered red card

Solve the following equation:

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

In the given figure O is the centre of the circle. Tangents A and B meet at C. If ∠ACO = 30°, find

1) ∠BCO

2) ∠AOB

3) ∠APB

Ahmed has a recurring deposit account in a bank. He deposits Rs. 2,500 per month for 2 years. If he gets Rs. 66,250 at the time of maturity, find

1) The interest paid by the bank

2) The rate of interest

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

ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find ‘a’ and ‘b’. Find the length of side BC.

Solve the following inequation and represent the solution set on the number line 2x – 5 <= 5x + 4 < 11, where x ∈ I

Evaluate without using trigonometric tables. 

`2((tan 35^@)/(cot 55^@))^2 + ((cot 55^@)/(tan 35^@)) - 3((sec 40^@)/(cosec 50^@))`

A Mathematics aptitude test of 50 students was recorded as follows:

Draw a histogram from the above data using a graph paper and locate the mode.

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.

ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find

1) Coordinates of A

2) An equation of diagonal BD

Use a graph paper to answer the following questions (Take 1 cm = 1 unit on both axes)

1) Plot A(4,4), B(4,-6) and C(8,0), the vertices of a triangle ABC.

2) Reflect ABC on the y-axis and name it A’B’C’.

3) Write the coordinates of the images A’, B’ and C’.

4) Give a geometrical name for the figure AA’ C’ B’ BC.

5) Identify the line of symmetry of AA’ C’ BC’.

Mr Choudhury opened a Saving Bank Account at State Bank of India on 1st April 2007. The entries of one year as shown in his passbook are given below.

If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April 2008. Give your answer correct to the nearest rupee.

Using componendo and dividendo, find the value of x

`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5))  = 9`

If A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]` and I is the identity matric of the same order and A^t is the transpose of matrix A, find A^t.B + BI.

In the adjoining figure, ABC is a right angled triangle with ∠BAC = 90°.

1) Prove ΔADB ~ ΔCDA.

2) If BD = 18 cm CD = 8 cm Find AD.

3) Find the ratio of the area of ΔADB is to an area of ΔCDA.

1) Using step–deviation method, calculate the mean marks of the following distribution.

2) State the modal class.

Marks obtained by 200 students in an examination are given below:

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

1. The median marks.
2. The number of students who failed if minimum marks required to pass is 40.
3. If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs. 20. Find:

1. the annual dividend.
2. the profit earned including his dividend.

Draw a circle of radius 3.5 cm. Marks a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Prove that (cosec A – sin A)(sec A – cos A) sec² A = tan A.

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

In what period of time will Rs. 12,000 yield Rs. 3972 as compound interest at 10% per annum, if compounded on a yearly basis?

A man observes the angle of elevation of the top of a building to be 30o. He walks towards it in a horizontal line through its base. On covering 60 m the angle of elevation changes to 60o. Find the height of the building correct to the nearest metre.

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

Rs. 480 is divided equally among ‘x’ children. If the numbers of children were 20 more then each would have got Rs. 12 less. Find ‘x’.

Given the equation of line L, is y = 4.
(1) Write the slope of line L₂, if L₂, is the bisector of angle O.
(2) Write the co–ordinates of point P.
(3) Find the equation of L₂.