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SECTION – I (40 Marks)

Attempt all questions from this Section.

Question 1(a) Find the 100th term of the sequence : 3 , 2 3 , 3 3 ........ [3]

(b) Use the Remainder Theorem to factorise the following expression :2x3 + x2 – 13x + 6 [4]

(c) A solid is composed of a cylinder with hemispherical ends. If the wholelength of the solid is 105 cm and the diameter of the hemispherical endsis 35 cm, find the cost of polishing the surface of the solid at the rate of21 paise per sq.cm. [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 (2018-2019) MARKS : 80

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

Arithmetic Progressions, Geometric Progressions, Quadratic Equations,SolvingProblems, Ratio and Proportion, Remainder and Factor Theorem, GraphicalRepresentation, Measures of Central Tendency, Loci, Circles, Constructions

(Circles), Cylinder, Cone and Sphere

This Paper consists of 5 printed pages

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Question 2(a) In the given figure, find AB if PT = 12.5 cm

and PA = 10 cm. [3]

(b) Find the next three terms of the sequence : 5 , 5, 5 5 , ........... . [3]

(c) What number must be added to each of the numbers 16, 26 and 40 sothat the resulting numbers may be in continued proportion ? [4]

Question 3(a) The following are the marks obtained by 70 boys in a class test.

Marks 30–40 40–50 50–60 60–70 70–80 80–90 90–100

No. of boys 10 12 14 12 9 7 6

Calculate the mean by step-deviation method [4]

(b) For the equation, given below, find the value of ‘m’ so that the equationhas equal roots. Also, find the solution of the equation :x² – (m + 2) x + (m + 5) = 0 [3]

(c) The sum of three numbers in G.P. is3910

and their product is 1. Find the

numbers. [4]

Question 4

(a) If2 2

2 2

x yx y = 2

18

, find :

(i)xy (ii)

3 3

3 3x yx y [4]

(b) Draw an angle ABC = 60º, having AB = 4.6 cm and BC = 5 cm. Find apoint P equidistant from AB and BC; and also equidistant from A and B. [3]

(c) The age of a father is twice the square of the age of his son. Eight yearshence, the age of the father will be 4 years more than three times theage of the son. Find their present ages. [4]

BP

T

12.5 cm

10 cm A

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

Question 5

(a) Solve using factorisation method : – 3 + 3 1

+ 2 + 3 – 3 2

=x xx x

[3]

(b) The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1) x – 16 leave thesame remainder when divided by x – 2. Find the value of ‘a’. [3]

(c) In a school, students decided to plant trees in and around the school toreduce air pollution. It was decided that the number of trees, that eachsection of each class will plant, will be five times of the class to whichthe respective section belongs. If there are 1 to 10 classes in the schooland each class has three sections, find how many trees were planted bythe students ? [4]

Question 6(a) In the adjoining figure, O is the centre of the

circle and AB is a tangent to it at point B.BDC = 65º. Find BAO. [3]

(b) In a certain positive fraction, the denominator is greater than thenumerator by 3. If 1 is subtracted from the numerator and the denominator

both, the fraction reduces by 114

. Find the fraction. [3]

(c) If a, b and c are in continued proportion, prove that :

2 2 2

2

a + b + ca + b + c =

a – b + ca + b + c [4]

Question 7(a) Solve the following equation and give your answer correct to 3 significant

figures : 5x2 – 3x – 4 = 0 [3]

(b) Which term of the series : 21, 18, 15, .......... is –81 ?Can any term of this series be zero ? If yes, find the number of term. [3]

(c) Find the values of m and n so that x – 1 and x + 2 both are factors ofx3 + (3m + 1) x2 + nx – 18. [4]

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B

D

A

65º

EO

C

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Question 8(a) The distance by road between two towns A and B is 216 km and by rail it

is 208 km. A car travels at an uniform speed and the train travels at aspeed which is 16 km/hr faster than the car.If the train takes 2 hours less than the car to reach town B, find the speedof the train. [4]

(b) The following distribution represents the height of 160 students of a school.

Height (in cm) 140 – 145 145 – 150 150 – 155 155 – 160No. of students 12 20 30 38

Height (in cm) 160 – 165 165 – 170 170 – 175 175 – 180No. of students 24 16 12 8

Draw an ogive for the given distribution taking 2 cm = 5 cm of heighton one axis and 2 cm = 20 students on the other axis. Using the graph,determine :(i) the median height(ii) the interquartile range(iii) the number of students whose height is above 172 cm. [6]

Question 9

(a)5 – 8

3x

4 7

2x

, x R [3]

(b) If5 65 6x yu v

=5 – 65 – 6x yu v ; then prove that x : y = u : v. [3]

(c) For the following frequency distribution draw a histogram. Hence,calculate the mode.

Class 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30

Frequency 7 18 10 8 5 [4]

Question 10(a) Construct a triangle ABC, having given AB = 4.8 cm, AC = 4 cm, and

A = 75º. Find a point P(i) inside the triangle ABC;(ii) outside the triangle ABC.Equidistant from B and C; and at a distance of 1.2 cm from BC. [3]

(b) Find the sum of all multiples of 7 lying between 300 and 700. [3]

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(c) In the given figure, BD is a side of a regular hexagon.DC is a side of a regular pentagon and AD is adiameter. Calculate :(i) ADC,(ii) BDA,(iii) ABC,(iv) AEC. [4]

Question 11(a) How many terms of the series 2 + 6 + 18 + ............... must be taken to

make the sum equal to 728 ? [3]

(b) Earth, taken out on digging a circular tank of diameter 17.5 m, is spreadall around the tank uniformly to a width of 4 m, to form an embankmentof height 2 m. Calculate the depth of the circular tank correct to 2 decimalplaces. The depth of the tank is uniform everywhere. [3]

(c) Solve :2

2

1+xx

– 31–xx

– 2 = 0 [4]

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All the Best

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C

A

B