Date & Time: 14th March 2016, 11:00 am

Duration: 2h30m

**Question 1 to Question 4 is Compulsory**

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

Using remainder theorem, find the value of k if on dividing 2x^{3} + 3x^{2} - kx + 5 by x - 2, leaves a remainder 7

Chapter: [0.0203] Factorization

Given A = `[(2,0),(-1,7)]` and I = `[(1,0),(0,1)]` and `A^2 = 9A+ ml`. Find m

Chapter: [0.0208] Matrices

The mean of following numbers is 68. Find the value of ‘x’.

45, 52, 60, x, 69, 70, 26, 81 and 94

Hence estimate the median.

Chapter: [0.06] Statistics

The slope of a line joining P(6, k) and Q (1-3k, 3) is `1/2` Find

1) k

2) A midpoint of PQ, using the value of ‘k’ found in (1).

Chapter: [0.021] Co-ordinate Geometry Equation of a Line

Without using trigonometrical tables, evaluate:

`cosec^2 57^@ - tan^2 33^@ + cos 44^@ cosec 46^@ - sqrt2 cos 45^@ - tan^2 60^@`

Chapter: [0.05] Trigonometry

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

Chapter: [0.04] Mensuration [0.04] Mensuration

Solve the following inequation, write the solution set and represent it on the number line.

`-3(x - 7) >= 15 - 7x > (x+1)/3`, x ∉ R

Chapter: [0.020499999999999997] Linear Inequations

In the figure given below, an AD is a diameter. O is the centre of the circle AD is parallel to BC and `angle CBD` = 32°. Find `angle OBD`

Chapter: [0.032] Circles

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

Chapter: [0.0204] Ratio and Proportion [0.0204] Ratio and Proportion

A game of numbers has cards marked with 11, 12, 13, … 40. A card is drawn at random. Find the probability that the number on the card drawn is :

1) A perfect square

2) Divisible by 7

Chapter: [0.07] Probability

Use graph paper for this question. (Take 2 cm = 1 unit along both x and y-axis.) Plot the points O(0, 0), A(-4, 4), B(-3, 0) and C(0, -3)

1) Reflect points A and B on the y-axis and name them A’ and B’ respectively. Write down their coordinates.

2) Name the figure OABCB’A’.

3) State the line of symmetry of this figure

Chapter: [0.034] Symmetry

Mr Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate

1) The rate of interest

2) The amount at the end of the second year, to the nearest rupee.

Chapter: [0.011000000000000001] Compound Interest

Solve the quadratic equation x^{2} - 3(x + 3) = 0; Give your answer correct two significant figures

Chapter: [0.0202] Quadratic Equations

A page from the savings bank account of Mrs Ravi is given below.

Date |
Particulars |
Withdrawal(Rs.) |
Deposit (Rs.) |
Balance (Rs.) |

April 3rd 2006 | B/F | 6000 | ||

April 7th | By cash | 2300 | 8300 | |

April 15th | By cheque | 3500 | 11800 | |

May 20th | To self | 4200 | 7600 | |

June 10th | By cash | 5800 | 13400 | |

June 15th | To self | 3100 | 10300 | |

August 13th | By cheque | 1000 | 11300 | |

August 25th | To self | 7400 | 3900 | |

September 6th 2006 |
By cash | 2000 | 5900 |

She closed the account on 30th September 2006. Calculate the interest Mrs Ravi earned

at the end of 30th September 2006 at 4.5% per annum interest. Hence, find the

amount she receives on closing the account.

Chapter: [0.013000000000000001] Banking

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

Chapter: [0.011000000000000001] Compound Interest

Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.

Chapter: [0.033] Constructions

In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T

1) Prove ΔTPS ~ ΔTRQ.

2) Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm

3) Find the area of quadrilateral PQRS if the area of ΔPTS = 27 cm^{2}.

Chapter: [0.032] Circles

Given matrix A = `[(4sin30^@, cos0^@),(cos0^@, 4sin30^@)]`and B = `[(4),(5)]`

if AX = B

1) Write the order of matrix X.

2) Find the matrix ‘X’.

Chapter: [0.0208] Matrices

An aeroplane at an altitude of 1500 metres, finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships

Chapter: [0.05] Trigonometry

The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2 cm = 10 scores on the X-axis and 2 cm = 20 shooters on the Y-axis).

Scores | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

No. of shooters |
9 | 13 | 20 | 26 | 30 | 22 | 15 | 10 | 8 | 7 |

Use your graph to estimate the following:

1) The median

2) The interquartile range.

3) The number of shooters who obtained a score of more than 85%.

Chapter: [0.06] Statistics

If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`

Chapter: [0.05] Trigonometry

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :

1) A circle of radius 2.5 cm, passing through A and C.

2) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Chapter: [0.033] Constructions

A line AB meets X – axis at A and Y –axis at B. P (4, -1) divides AB in the ratio 1 : 2.

1) Find the coordinates of A and B.

2) Find the equation of the line through P and perpendicular to AB.

Chapter: [0.021] Co-ordinate Geometry Equation of a Line

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of the VAT is 6%, find

1) The price paid by the shopkeeper including the tax.

2) The VAT paid by the dealer

Chapter: [0.013999999999999999] Gst (Goods and Services Tax)

The given figure represents a kite with a circular and a semicircular motifs stuck on it.

The radius of a circle is 2.5 cm and the semicircle is 2 cm. If diagonals AC and BD are

of lengths 12 cm and 8 cm respectively, find the area of the:

1) Shaded part. Give your answer correct to the nearest whole number.

2) Unshaded part

Chapter: [0.021] Co-ordinate Geometry Equation of a Line

A model of a ship is made to a scale 1: 300

1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.

2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.

3) The volume of the model in 6.5 m3. Calculate the volume of the ship.

Chapter: [0.04] Mensuration [0.04] Mensuration

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity find:

(i) the monthly instalment

(ii) the amount of maturity.

Chapter: [0.013000000000000001] Banking

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to :

1) Frame a frequency distribution table

2) To calculate mean

3) To determine the Modal class

Chapter: [0.06] Statistics [0.06] Statistics

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

Chapter: [0.05] Trigonometry

Prove that `cosA/(1+sinA) + tan A = secA`

Chapter: [0.05] Trigonometry

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct a ABC in which BC = 6.5 cm, ABC = 60°, AB = 5 cm.

Chapter: [0.033] Constructions

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown.

Construct the locus of points at a distance of 3.5 cm from A.

Chapter: [0.031] Loci

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct the locus of points equidistant from AC and BC.

Chapter: [0.031] Loci

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Mark 2 points X and Y which are a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Chapter: [0.031] Loci

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475. Find the :

1) number of shares he bought

2) The market value of each share

Chapter: [0.012] Shares and Dividends

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