Answers of Class 10 ICSE MATHEMATICS SEMESTER 1 EXAMINATION 2021 | Study Table

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ICSE SEMESTER 1 EXAMINATION

SPECIMEN QUESTION PAPER

MATHEMATICS

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Maximum Marks: 40

Time allowed: One and a half hours (inclusive of reading time)

ALL QUESTIONS ARE COMPULSORY.

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

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Select the correct option for each of the following questions.

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Section A [16 Marks] [16x1]


1. If matrix A is of order 3 x 2 and matrix B is of order 2 x 2 then the matrix AB is of order

(a) 3 x 2 (b) 3 x 1 (c) 2 x 3 (d) 1 x 3

Ans: (a)

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2. The percentage share of SGST of total GST for an Intra-State sale of an article is

(a) 25% (b) 50% (c) 75% (d) 100%

Ans: (b)

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3. 𝐴𝐡𝐢𝐷 𝑖𝑠 π‘Ž π‘‘π‘Ÿπ‘Žπ‘π‘’π‘§π‘–π‘’π‘š π‘€π‘–π‘‘β„Ž 𝐴𝐡 π‘π‘Žπ‘Ÿπ‘Žπ‘™π‘™π‘’π‘™ π‘‘π‘œ 𝐷𝐢.

π‘‡β„Žπ‘’π‘› π‘‘β„Žπ‘’ π‘‘π‘Ÿπ‘–π‘Žπ‘›π‘”π‘™π‘’ π‘ π‘–π‘šπ‘–π‘™π‘Žπ‘Ÿ π‘‘π‘œ βˆ†π΄π‘‚π΅ 𝑖𝑠

(a) βˆ†π΄π·π΅ (b) βˆ†π΄πΆπ΅ (c) βˆ†πΆπ‘‚π· (d) βˆ†πΆπ‘‚π΅

Ans: (c)

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4. The mean proportion between 9 and 16 is 

(a) 25 (b) 144 (c)7 (d) 12

Ans: (d)

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5. A man deposited β‚Ή 500 per month for 6 months and received β‚Ή3300 as the 

maturity value. The interest received by him is: -

(a) 1950 (b) 300 (c) 2800 (d) none of these

Ans: (b)

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6. The solution set representing the following number line is

(a) {x: x ∈ R, -3 ≀ x < 2}

(b) {x: x ∈ R, -3 < x < 2}

(c) {x: x ∈ R, -3 < x ≀ 2}

(d) {x: x ∈ R, -3 ≀ x ≀2}

Ans: (a)

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7. The first three terms of an arithmetic progression (A. P.) are 1, 9, 17, then the 

next two terms are

(a) 25 and 35 (b) 27 and 37 (c) 25 and 33 (d) none of these

Ans: (c)

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8. If βˆ†π΄π΅πΆ ~ βˆ†π‘„π‘…π‘ƒ π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘Ÿπ‘’π‘ π‘π‘œπ‘›π‘‘π‘–π‘›π‘” π‘π‘Ÿπ‘œπ‘π‘œπ‘Ÿπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ 𝑠𝑖𝑑𝑒𝑠 π‘Žπ‘Ÿπ‘’

(a) 𝐴𝐡/𝑄𝑅=𝐡𝐢/𝑅𝑃

(b) 𝐴𝐢/QR=BC/RP

(c) 𝐴𝐡/QR=BC/QP

(d) 𝐴𝐡/PQ=BC/RP

Ans: (a)

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9. If x∈ π‘Š , then the solution set of the inequation -x > -7, is

(a) {8,9,10…} (b) {0,1,2,3,4,5,6} (c) {0,1,2,3 …} (d) { -8, -9, -10…}

Ans: (b)

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10. The roots of the quadratic equation 4π‘₯

2

- 7x + 2 = 0 are 1.390, 0. 359.The roots 

correct to 2 significant figures are

(a) 1.39 and 0.36 (b) 1.3 and 0.35 (c) 1.4 and 0.36 (d) 1.390 and 

0.360

Ans: (a)

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11. 1.5, 3, x and 8 are in proportion, then x is equal to 

(a) 6 (b) 4 (c) 4.5 (d) 16

Ans: (b)

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12. If a polynomial 2π‘₯

2 – 7x – 1 is divided by (x + 3), then the remainder is

(a) - 4 (b)38 (c)-3 (d) 2

Ans: (b)

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13. If 73 is the nth term of the arithmetic progression 3, 8, 13, 18…, then β€˜n’ is

(a) 13 (b) 14 (c) 15 (d) 16

Ans: (c)

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14. The roots of the quadratic equation x2+2x+1 = 0 are

(a) Real and distinct (b) Real and equal (c) Distinct (d) Not real/ imaginary

Ans: (b)

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15. Which of the following statement is not true?

(a) All identity matrices are square matrix

(b) All null matrices are square matrix

(c) For a square matrix number of rows is equal to the number of columns

(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

Ans: (b)

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16. If (x – 2) is a factor of the polynomial x3 + 2x2

– 13 x + k, then β€˜k’ is equal to 

(a) -10 (b)26 (c)-26 (d) 10

Ans: (d)

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Section B [12 Marks] [6x2]


17. A man deposited β‚Ή1200 in a recurring deposit account for 1 year at 5% per 

annum simple interest. The interest earned by him on maturity is

(a) 14790 (b) 390 (c) 4680 (d) 780

Ans: (b)

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18. If x2

– 4 is a factor of polynomial x3+ x2

- 4x- 4, then its factors are

(a) (x-2) (x+2) (x+1)

(b) (x-2) (x+2) (x-1)

(c) (x-2) (x-2) (x+1)

(d) (x-2) (x-2) (x-1)

Ans: (a)

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19. The following bill shows the GST rates and the marked price of articles A and 

B:

BILL: GENERAL STORE

Articles Marked price Rate of GST

A β‚Ή300 12%

B β‚Ή1200 5%

The total amount to be paid for the above bill is: -

(a) 1548 (b) 1596 (c) 1560 (d) 1536

Ans: (b)

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20. The solution set for the linear inequation -8 ≀ x – 7 < - 4, x∈ 𝐼 is 

(a) {x: x ∈ R, -1≀ x < 3}

(b) {0, 1, 2, 3}

(c) {-1, 0, 1, 2, 3}

(d) { -1, 0, 1, 2}

Ans: (d)

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21. If 5π‘Ž/7b=4c/3d , then by Componendo and dividendo 

(a) 5π‘Ž+7𝑏/5π‘Žβˆ’7𝑏= 4π‘βˆ’3𝑑/4𝑐+ 3𝑑

(b) 5π‘Žβˆ’7𝑏/5π‘Ž+7𝑏= 4𝑐+3𝑑/4π‘βˆ’3𝑑

(c) 5π‘Ž+7𝑏/5π‘Žβˆ’7𝑏= 4𝑐+3𝑑/4π‘βˆ’3𝑑

(d) 5π‘Ž+7𝑏/5π‘Ž+7𝑏= 4π‘βˆ’3𝑑/4π‘βˆ’3𝑑

Ans: (a)

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22. If A = [--] then A2 is

Ans: (b)

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Section C [12 Marks] [3x4]

 

23. The distance between station A and B by road is 240 km and by train it is 300 km. 

A car starts from station A with a speed x km/hr whereas a train starts from station 

B with a speed 20km/hr more than the speed of the car.

(i) The time taken by car to reach station B is

(a) 240/x

(b) 300/x

(c) 20/x

(d) 300/π‘₯+20

Ans: (a)

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 (ii) The time taken by train to reach station A

(a) 240/π‘₯

(b) 300/π‘₯

(c) 20/π‘₯

(d) 300/π‘₯+20

Ans: (d)

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 (iii) If the time taken by train is 1 hour less than that taken by the car, then the quadratic 

equation formed is

(a) x2 + 80x - 6000=0

(b) x2 + 80x - 4800=0

(c) x2 + 240x - 1600 =0

(d) x2-80x +4800 = 0

Ans: (b)

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 (iv) The speed of the car is

(a) 60km/hr (b) 120km/hr (c) 40km/hr (d) 80km/hr

Ans: (c)

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24. In the given triangle PQR, AB || QR, QP || CB and AR intersects CB at O. 

Using the given diagram answer the following question:

(i) The triangle similar to Ξ”ARQ is

(a) Ξ”ORC (b) Ξ”ARP (c) Ξ”OBR (d) Ξ”QRP

Ans: (b)

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(ii) Ξ”PQR ~Ξ”BCR by axiom

(a) SAS (b)AAA (c) SSS (d) AAS

Ans: (c)

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(iii) If QC =6 cm, CR = 4 cm, BR = 3 cm. The length of RP is

(a) 4.5 cm (b) 8cm (c) 7.5cm (d) 5cm

Ans: (c)

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(iv) The ratio PQ: BC is

(a) 2 : 3 (b) 3 : 2 (c) 5 : 2 (d) 2 : 5

Ans: (b)

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25 The nth term of an arithmetic progression (A.P.) is (3n + 1)

(i) The first three terms of this A. P. are 

(a) 5, 6, 7 (b) 3, 6, 9 (c) 1, 4, 7 (d) 4, 7, 10

Ans: (d)

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(ii) The common difference of the A.P. is

(a) 3 (b)1 (c) -3 (d) 2

Ans: (a)

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(iii) Which of the following is not a term of this A.P.

(a) 25 (b) 27 (c) 28 (d) 31

Ans: (b)

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(iv) Sum of the first 10 terms of this A.P. is 

(a) 350 (b) 175 (c) -95 (d) 70

Ans: (b)

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