**Attempt all questions From Question 1 to Question 4**

**Attempt any four questions From Question 5 to Question 11**

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.

Concept: Factor Theorem

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

Concept: Multiplication of Matrix

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.

Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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

Concept: Simple Problems on Single Events

Solve the following equation:

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

Concept: Nature of Roots

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

Concept: Tangent to a Circle

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

Concept: Computation of Interest

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

Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle

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.

Concept: Distance Formula

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

Concept: Equation of a Line

Evaluate without using trigonometric tables.

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

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

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

Marks | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 – 100 |

No. of Students | 4 | 8 | 14 | 19 | 5 |

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

Concept: Graphical Representation of Histograms

A manufacturer sells a washing machine to a wholesaler for Rs. 15000. The wholesaler sells it to a trader at a profit of Rs. 1200 and the trader in turns sell it to a consumer at a profit of Rs. 1800. If the rate of the VAT is 8% find:

1) The amount of VAT received by the state government on the sale of this machine from the manufacturer and the wholesaler.

2) The amount that the consumer pays for the machine.

Concept: Introduction to Sales Tax and Value Added Tax

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.

Concept: Area and Volume of Solids - Sphere

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

Concept: Mid-point Formula

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’.

Concept: Lines of Symmetry

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.

Date |
Particulars |
Withdrawals (in Rs.) |
Deposits (in Rs.) |
Balance (in Rs.) |

Ist April 2007 | By Cash | - | 8550.00 | 8550.00 |

12th- April 2007 | To Self | 1200.00 | -- | 7350.00 |

24th April 2007 | By Cash | - | 4550.00 | 11900.00 |

8th July 2007 | By Cheque | - | 1500.00 | 13400.00 |

10th Sept. 2007 | By Cheque | - | 3500.00 | 16900.00 |

17th Sept. 2007 | By Cheque | 2500.00 | - | 14400.00 |

11th Oct. 2007 | By Cash | - | 800.00 | 15200.00 |

6th Jan. 2008 | To Self | 2000.00 | - | 13200.00 |

9th March 2008 | By Cheque | - | 950.00 | 14150.00 |

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.

Concept: Computation of Interest

Using componendo and dividendo, find the value of x

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

Concept: Componendo and Dividendo Properties

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

Concept: Matrices Examples

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.

Concept: Similarity of Triangles

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

2) State the modal class.

Class Interval | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 | 85 – 90 |

Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |

Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data

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.

Concept: Median from the Ogive

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.

Concept: Shares and Dividends

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.

Concept: Tangent to a Circle

Prove that (cosec A – sin A)(sec A – cos A) sec^{2} A = tan A.

Concept: Trigonometric Identities

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

Concept: Proportions

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?

Concept: Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

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.

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

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.

Concept: Areas of Sector and Segment of a Circle

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’.

Concept: Shares and Dividends

Given the equation of line L, is y = 4.

(1) Write the slope of line L_{2}, if L_{2}, is the bisector of angle O.

(2) Write the co–ordinates of point P.

(3) Find the equation of L_{2}.

Concept: Equation of a Line