T17 II SP A003

Set A

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 in equations and graph the solution set on the numberline : 2x – 3 < x + 2 < 3x + 5; x R [3]

(b) Prove the identity :1

sinA + cosA +

1sinA – cosA

= 2

2 sin A1 2 cos A [3]

(c) Using properties of proportion, solve for x :5 – 165 – – 16

x xx x

=73

[4]

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 - A 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 A003

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Question 2(a) In the adjoining fig. O is the centre of the circle.

PBA = 45o. Calculate PQB

[3]

(b) Solve the following equation for x and give your answer correct to 2 decimalplaces : x2 – 5x – 10 = 0 [3]

(c) The fifth term of a G.P. is 81 and its second term is 24.Find the geometric progression. [4]

Question 3(a) The height of a tree is 3 times the length of its shadow. Find the angle

of elevation of the sun. [3]

(b) What should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it byx – 2, the remainder is 10 ? [3]

(c) In the given figure, QAP is the tangent at point A andPBD is a straight line.If ACB = 36º and APB = 42º, find :(i) BAP(ii) ABD(iii)QAD(iv) BCD [4]

Question 4

(a) Find the 30th term of the sequence :12 , 1,

32 , ........ [3]

(b) Two natural numbers differ by 3. Find the numbers, if the sum of their

reciprocals is7

10. [3]

(c) If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that :x2 + y2 + z2 = r2 [4]

A

P

B

Q

O45o

C D

B

AP Q

T17 II SP A003

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

Question 5(a) From the figure, given below, calculate the length of CD.

[3]

(b) Find the sum of G.P. : 1 + 3 + 9 + 27 + ............. to 12 terms. [3]

(c) Solve : x4 – 10x2 + 9 = 0 [4]

Question 6

(a) Evaluate : 22

tan35ºcot55º

+2

cot55ºtan35º

– 32

sec40ºcosec50º

[3]

(b) What least number must be subtracted from each of the numbers 7, 17and 47 so that the numbers are in continued proportion ? [3]

(c) An article can be bought by paying ` 28,000 at once or by making 12monthly instalments. If the first instalment paid is ` 3,000 and everyother instalment is ` 100 less than the previous one, find :(i) amount of instalment paid in the 9th month(ii) total amount paid in the instalment scheme. [4]

Question 7(a) ` 480 is divided equally among ‘x’ children. If the number of children

were 20 more then each would have got ` 12 less. Find ‘x’. [3]

(b) In the given figure, O is the centre of the circleand AB is a tangent at B. If AB = 15 cm andAC = 7.5 cm, calculate the radius of the circle.

[3]

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

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C

D

A

B15 m

47o

22oE

B

OD C A

15 cm

7.5 cm

T17 II SP A003

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Question 8

(a) Prove the following identity : cosec A – cot A =sin A

1 cos A [3]

(b) The equation 3x2 – 12 x + (n– 5) = 0, has equal roots. Find the value of n [3]

(c) Construct an equilateral triangle ABC with side 6 cm. Draw a criclecircumscribing the triangle ABC. [4]

Question 9(a) Find the sum of all multiples of 7 lying between 300 and 700. [3]

(b) Find the value of k, if 3x – 4 is a factor of expression 3x2 – 2x – k [3]

(c) 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 buildingcorrect to nearest metre. [4]

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

BAD = 75o, ABD = 58o,ADC = 77o

Find 1) BDC 2) BCD and 3) BCA

[3]

(b) A geometric progression has common ratio = 3 and last term = 486. If thesum of its terms is 728; find its first term. [3]

(c) The speed of an ordinary train is x km/hr and that of an express train is(x + 25) km/hr.(i) Find the time taken by each train to cover 300 km.(ii) If the ordinary train takes 2 hrs more than the express train;

calculate speed of the express train. [4]

Question 11(a) Given four quantities a, b, c, and d are in proportion show that

(a – c) b2 : (b – d) cd = (a2 – b2 – ab) : (c2 – d2 – cd) [3]

(b) Solve and graph the solution set of :–83 x +

13

< 313

; x R. [3]

(c) Draw an inscribing circle of a regular hexagon of side 5 cm. [4]

BA

D C77o

58o75o

All the Best