T17 II SP B003

Set B

This Paper consists of 4 printed pages Turn over© Copyright reserved.

SECTION – I (40 Marks)

Attempt all questions from this Section.Question 1

(a) Solve the following inequation and represent the solution set on thenumber line 2x – 5 < 5x + 4 < 11, where x I [3]

(b) Solve :1 + sin A

cos A +

cos A1 + sin A

= 2sec A [3]

MATHEMATICS

(2 and half hours)

Answers to this Paper must be written on the paper provided separately.

You will not be allowed to write during the first l5 minutes.

This time is to be spent in reading the Question Paper.

The time given at the head of this paper is the time allowed for writing the answers. 

Attempt all questions from Section A and any four questions from Section B.

All working, including rough work, must be clearly shown and must be done on the

same sheet as the rest of the answer.

Omission of essential working will result in the loss of marks.

The intended marks for questions or parts of questions are given in brackets [ ] .

Mathematical tables are provided.

MAHESH TUTORIALS I.C.S.E.GRADE - X (2017-2018)

Exam No. : MT/ICSE/SEMI PRELIM - II - SET - B 005

Linear Inequations, Quadratic Equations, Solving (Simple) Problems, Ratio andProportion, Remainder and Factor Theorems, Arithmetic Progression, Geometric

Progression, Circles, Tangents and Intersecting Chords, Construction,Trigonometrical Identities, Heights and Distances

T17 II SP B003

Set B... 2 ...

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... 2 ...

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(c) Using componendo and dividendo, find the value of x.

x + + x -x + – x -

3 4 3 53 4 3 5

= 9 [4]

Question 2(a) From the information given in the figure find

the value of :(i) CDB(ii) ABC(iii)ACB

[3]

(b) Solve the following equation and give your answer correct to 3

significant figures : 5x2 – 3x – 4 = 0 [3]

(c) Find the geometric progression with 4th term = 54 and 7th term = 1458. [4]

Question 3(a) A boy is flying a kite with a string. If the string is of length 100 m and the

angle of elevation of the kite is 26032. Find the height of the kite correctto one decimal place. [3]

(b) What number should be added to 3x3 – 5x2 + 6x so that when resultingpolynomial is divided by x – 3, the remainder is 8? [3]

(c) In the given figure, AB is the diameter.The tangent at C meets AB produced at Q.If CAB = 34º, find :(i) CBA (ii) CQB [4]

Question 4(a) Find the 100th term of the sequence : 3 , 2 3 , 3 3 ........ [3]

(b) Sum of a number and its reciprocal is 4.25. Find the number. [3]

(c) If sin A + cos A = m and sec A + cosec A = n, show that : n(m2 – 1)= 2m [4]

A

CD

B

43o

49o

C

A 34ºB Q

T17 II SP B003

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SECTION – II (40 Marks)Attempt any four questions from this Section.

Question 5(a) Calculate AB.

[3]

(b) Find the sum of G.P. : 1, –12

,14

, –18

, ........... to 9 terms. [3]

(c) Solve : x4 – 25x² + 144 = 0 [4]

Question 6

(a) Evaluate :2 2

2 2

cot 41º 2 sin 75º–tan 49º cos 15º [3]

(b) Find two numbers such that the mean proportional between them is 12and the third proportional to them is 96. [3]

(c) A manufacturer of TV sets produces 600 units in the third year and 700units in the 7th year. Assuming that the production increases uniformlyby a fixed number every year, find:(i) the production in the first year.(ii) the production in the 10th year. [4]

Question 7(a) A hotel bill for a number of people for overnight stay is ` 4,800. If there

were 4 people more, the bill each person had to pay, would have reducedby ` 200. Find the number of people staying overnight. [3]

(b) In the given figure, find AB if PT = 12.5 cmand PA = 10 cm.

[3]

(c) Factorise x3 + 6x2 + 11x + 6 completely using factor theorem. [4]

Turn overTurn over

BP

T

12.5 cm

10 cmA

P

A30º

6 m

R B

Q

47º

5 m

T17 II SP B003

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Question 8

(a) Prove the following identity : 1 –2sin A

1 cos A = cos A [3]

(b) Find the value of m, if the following equation has equal roots;(m – 2)x2 – (5 + m) x + 16 = 0 [3]

(c) Draw an inscribing circle of an equilateral triangle of side 5.6 cm [4]

Question 9(a) Find the sum of all natural numbers between 250 and 1000 which are

divisible by 9. [3]

(b) Find the value of k, if 2x + 1 is a factor of (3k + 2) x3 + (k – 1). [3]

(c) A man in a boat rowing away from a light house 150 m high, takes 2minutes to change the angle of elevation of the top of the light housefrom 60º to 45º. Find the speed of the boat. [4]

Question 10(a) In the given figure, ABCD is a cyclic quadrilateral

DAC = 27o , DBA = 50o, ADB = 33o

Calculate: (i) DBC (ii) DCB (iii) CAB.[3]

(b) Find the sum of G.P.: 3, 6, 12, .........., 1536. [3]

(c) An aeroplane travelled a distance of 400 km at an average speed of xkm/ hr. On the return journey, the speed was increased by 40 km/hr.Write down an expression for the time taken for :(i) the onward journey;(ii) the return journey.If the return journey took 30 minutes less than the onward journey,write down an equation in x and find its value. [4]

Question 11

(a) If a cb d , show that : (a + b) : (c + d) = 2 2+a b : 2 2+c d [3]

(b) Find the values of x, which satisfy the inequation

–2 <12

–23x

< 156

, x N Graph the solution on the number line. [3]

(c) Construct a regular hexagon of side 4 cm. Construct a circlecircumscribing the hexagon. [4]

All the Best

B

CD

A27o

33º

50o