CBSE Class 10 Question Paper 2021 Maths Standard (Compartment)

Series /C SET~1

Roll No. Code No. 30/3/1
Candidates must write the Code on the
title page of the answer-book.

NOTE :
(i) Please check that this question paper contains 11 printed pages.
(ii) Code number given on the right hand side of the question paper should be written on the title
page of the answer-book by the candidate.
(iii) Please check that this question paper contains 36 questions.
(iv) Please write down the serial number of the question in the answer-book before attempting it.
(v) 15 minute time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question
paper only and will not write any answer on the answer-book during this period.

MATHEMATICS (STANDARD)

Time allowed : 3 hours Maximum Marks : 80
General Instructions :
Read the following instructions very carefully and strictly follow them :
(i) This question paper contains two parts A and B.
(ii) Both Part A and Part B have internal choices.
Part A
(i) It consists of two Sections, I and II.
(ii) Section I has 16 questions of 1 mark each. Internal choices are provided in 5 questions.
(iii) Section II has 4 questions on case study (Q.No. 17 to 20). Each question has 5 sub-parts.
An examinee is to attempt any 4 out of 5 sub-parts. Each sub-part is of 1 mark.
Part B
(i) It consists of three sections, III, IV and V.
(ii) Section III has 6 questions No. 21 to 26 of Very-short Answer Type of 2 marks each.
(iii) Section IV has 7 questions No. 27 to 33 of Short Answer Type of 3 marks each.
(iv) Section V has 3 questions No. 34 to 36 of Long Answer Type of 5 marks each.
(v) Internal choice is provided in 2 questions in Section III, 2 questions in Section IV and
1 question in Section V.

30/3/1 Page 1 P.T.O.

PART A
SECTION I
1. Write the quadratic equation in x whose roots are 2 and 5. 1
2. Find the exponent of 2 in the prime factorisation of 288. 1
2
3. (a) If and are the zeroes of the quadratic polynomial f(x) = x x 4, find the
1 1
value of + . 1

OR
2
(b) If one zero of the quadratic polynomial x + 3x + k is 2, then find the value of k. 1
3
4. (a) If , a, 4 are three consecutive terms of an A.P., then find the value of a. 1
5
OR
(b) In an A.P., if the common difference d = 3 and the eleventh term a11 = 15, then
find the first term. 1
5. A man goes 5 metres due West and then 12 metres due North. How far is he from the
starting point ? 1
6. PQ is a tangent to a circle with centre O at the point P on the circle. If
OPQ is an isosceles triangle, then find OQP. 1
7. Two concentric circles have radii 10 cm and 6 cm. Find the length of the chord of the
larger circle which touches the smaller circle. 1

8. (a) If 3 sin A = 1, then find the value of sec A. 1

OR
(b) Show that : 1

1 cot 2 2
= cot
2
1 tan

9. From a point on the ground, 20 m away from the foot of a vertical tower, the angle of
elevation of the top of the tower is 60 . Find the height of the tower. 1
10. (a) Find the area of a circle whose circumference is 66 cm. 1
OR
(b) The perimeter of a semi-circular protractor is 108 cm. Find its diameter. 1
11. Write the relationship between three measures of central tendency Mean, Median
and Mode. 1
AD 4
12. In a ABC, if DE is parallel to BC, and AC = 15 cm, then find the length of
DB 5
AE. 1

30/3/1 Page 2

13. Simplify : 1
2 2 2
cosec 60 sin 30 sec 60

4 3 2 2
14. If tan + cot = , then find the value of tan + cot . 1
3
15. If tangents PA and PB from an external point P to a circle with centre O are inclined to
each other at an angle of 70 , then find POA. 1
16. (a) How many outcomes are possible when three dice are thrown together ? 1
OR
(b) If P(E) = 0·015, then find P(not E). 1
SECTION II
Case study based questions (Q. No. 17 20) are compulsory. Attempt any 4 sub-parts from each
question. Each sub-part carries 1 mark.
17. The residents of a housing society, on the occasion of environment day, decided to build
two straight paths in the central park of the society and also plant trees along the
boundary lines of each path.
Taking one corner of the park as origin and the two mutually perpendicular lines as the
x-axis and y-axis, the paths were represented by the two linear equations 2x 3y = 5
and 6x + 9y = 7.
Based on the above, answer the following questions :
(i) Two paths represented by the two equations here are 1
(A) intersecting
(B) overlapping
(C) parallel
(D) mutually perpendicular

(ii) Which one of the following points lie on the line 2x 3y = 5 ? 1
(A) ( 4, 1)
(B) (4, 1)
(C) (4, 1)
(D) ( 4, 1)

(iii) If the line 6x + 9y = 7 intersects the y-axis at a point, then its coordinates are : 1
7
(A) 0,
9
7
(B) ,0
9
7
(C) ,0
6
7
(D) 0,
6

30/3/1 Page 3 P.T.O.

(iv) If a pair of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 has a unique

solution, then 1
a1 b1 c1
(A)
a2 b2 c2

a1 b1
(B)
a2 b2

a1 b1 c1
(C)
a2 b2 c2

a1 b1 c1
(D)
a2 b2 c2

a1 b1 c1
(v) If , then the two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are 1
a2 b2 c2

(A) parallel

(B) coincident

(C) intersecting

(D) perpendicular to each other

18. Students of a school are standing in rows and columns in their school playground to
celebrate their annual sports day. A, B, C and D are the positions of four students as
shown in the figure.

30/3/1 Page 4

Based on the above, answer the following questions :

(i) The figure formed by the four points A, B, C and D is a 1
(A) square
(B) parallelogram
(C) rhombus
(D) quadrilateral

(ii) If the sports teacher is sitting at the origin, then which of the four students is
closest to him ? 1
(A) A
(B) B
(C) C
(D) D
(iii) The distance between A and C is 1
(A) 37 units
(B) 35 units
(C) 6 units
(D) 5 units
(iv) The coordinates of the mid-point of line segment AC are 1
5
(A) , 11
2
5 11
(B) ,
2 2
11
(C) 5,
2
(D) (5, 11)
(v) If a point P divides the line segment AD in the ratio 1 : 2, then coordinates of P
are 1
8 8
(A) ,
3 3
10 13
(B) ,
3 3
13 10
(C) ,
3 3
16 11
(D) ,
3 3

30/3/1 Page 5 P.T.O.

19. During the annual sports meet in a school, all the athletes were very enthusiastic. They
all wanted to be the winner so that their house could stand first. The instructor noted
down the time taken by a group of students to complete a certain race. The data
recorded is given below :

Time (in sec.) : 0 20 20 40 40 60 60 80 80 100

Number of students : 1 4 3 7 5

Based on the above, answer the following questions :

(i) What is the class mark of the modal class ? 1
(A) 60
(B) 70
(C) 80
(D) 140

(ii) The mode of the given data is 1
(A) 70·33
(B) 71·33
(C) 72·33
(D) 73·33

(iii) The median class of the given data is 1
(A) 20 40
(B) 40 60
(C) 80 100
(D) 60 80

(iv) The sum of the lower limits of median class and modal class is 1
(A) 80
(B) 140
(C) 120
(D) 100

(v) The median time (in seconds) of the given data is 1
(A) 65·7
(B) 85·7
(C) 45·7
(D) 25·7

30/3/1 Page 6

20. During summer break, Harish wanted to play with his friends but it was too hot
outside, so he decided to play some indoor game with his friends. He collects 20 identical
cards and writes the numbers 1 to 20 on them (one number on one card). He puts them
in a box. He and his friends make a bet for the chances of drawing various cards out of
the box. Each was given a chance to tell the probability of picking one card out of the
box.

Based on the above, answer the following questions :

(i) The probability that the number on the card drawn is an odd prime number, is 1
3
(A)
5
2
(B)
5
9
(C)
20
7
(D)
20

(ii) The probability that the number on the card drawn is a composite number is 1
11
(A)
20
3
(B)
5
4
(C)
5
1
(D)
2

(iii) The probability that the number on the card drawn is a multiple of 3, 6 and 9 is 1

1
(A)
20

1
(B)
10

3
(C)
20

(D) 0

30/3/1 Page 7 P.T.O.

(iv) The probability that the number on the card drawn is a multiple of 3 and 7 is 1

3
(A)
10

1
(B)
10

(C) 0

2
(D)
5

(v) If all cards having odd numbers written on them are removed from the box and
then one card is drawn from the remaining cards, the probability of getting a
card having a prime number is 1

1
(A)
20

1
(B)
10

(C) 0

1
(D)
5
PART B
SECTION III

All questions are compulsory. In case of internal choices, attempt any one.

21. (a) Check whether the points P(5, 2), Q(6, 4) and R(7, 2) are the vertices of an
isosceles triangle PQR. 2
OR
(b) Find the ratio in which P(4, 5) divides the join of A(2, 3) and B(7, 8). 2

22. (a) The sum of the numerator and the denominator of a fraction is 18. If the
1
denominator is increased by 2, the fraction reduces to . Find the fraction. 2
3
OR
(b) Find the value of k for which the system of equations x + 2y = 5 and
3x + ky + 15 = 0 has no solution. 2

30/3/1 Page 8

23. Explain why 2 3 5 + 5 and 5 7 11 + 7 5 are composite numbers. 2

24. Find the mean of first 10 composite numbers. 2

25. ABC is right triangle, right-angled at B, with BC = 6 cm and AB = 8 cm. A circle with
centre O and radius r cm has been inscribed in ABC as shown in the figure. Find the
value of r. 2

26. Draw a circle of radius 5 cm. From a point 8 cm away from its centre, construct a pair of
tangents to the circle. 2

SECTION IV

3 2 2
27. Divide the polynomial f(x) = 5x + 10x 30x 15 by the polynomial g(x) = x + 1 + x
and hence, find the quotient and the remainder. 3

28. Prove that 3 + 2 is an irrational number, given that 2 is an irrational number. 3

29. In the given figure, PT and PS are tangents to a circle with centre O, from a point P,
such that PT = 4 cm and TPS = 60 . Find the length of the chord TS. Also, find the
radius of the circle. 3

30/3/1 Page 9 P.T.O.

30. The areas of two similar triangles are 121 cm 2 and 64 cm2 respectively. If one median of
the first triangle is 12·1 cm long, then find the length of the corresponding median of the
other triangle. 3

31. (a) Prove : 3
1 1
cosec A = cosec A
(cot A) (sec A) cot A (cot A ) (sec A) cot A

OR
(b) Prove : 3

sin6 A + 3 sin2 A cos2 A = 1 cos6 A

2 5
32. (a) One root of the quadratic equation 2x 8x k = 0 is . Find the value of k.
2
Also, find the other root. 3

OR

(b) Using quadratic formula, solve the following equation for x : 3
2 2
abx + (b ac) x bc = 0

33. With vertices A, B and C of a triangle ABC as centres, arcs are drawn with radii 2 cm
each as shown in the figure. If AB = 6 cm, BC = 8 cm and AC = 10 cm, then find the area
of the shaded region. 3

30/3/1 Page 10

SECTION V

34. Water is being pumped out through a circular pipe whose internal diameter is 8 cm. If
the rate of flow of water is 80 cm/s, then how many litres of water is being pumped out
through this pipe in one hour ? 5

35. (a) A man on the top of a vertical tower observes a car moving at a uniform speed
coming directly towards it. If it takes 18 minutes for the angle of depression to
change from 30 to 60 , how soon after this will the car reach the tower ? 5
OR

(b) A girl on a ship standing on a wooden platform, which is 50 m above water level,
observes the angle of elevation of the top of a hill as 30 and the angle of
depression of the base of the hill as 60 . Calculate the distance of the hill from
the platform and the height of the hill. 5

36. If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3 (S8 S4). 5

30/3/1 Page 11 P.T.O.

Series /C SET~1

H$moS> Z§. 30/3/1
amob Z§.
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð
>na Adí` {bIo§ &

ZmoQ> :
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ &
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma -nwpñVH$m Ho$ _wI-n¥ð> na {bI| &
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >36 àíZ h¢ &
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` {bI| &
(v) Bg àíZ-nÌ 15 {_ZQ >H$m g_` {X`m J`m h¡ & àíZ- 10.15 ~Oo {H$`m
OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ- -nwpñVH$m na H$moB©
CÎma Zht {bI|Jo &

J{UV (_mZH$)
:3 : 80

:
:
(i)
(ii)

(i) I II
(ii) I 16 1 5
(iii) II 4 17 20 5 4
1

(i) III, IV V
(ii) III 6 21 26 2
(iii) IV 7 27 33 3
(iv) V 3 34 36 5
(v) III 2 IV 2 V 1

30/3/1 Page 12

^mJ> H$
IÊS> I$
1. x _| dh {ÛKmV g_rH$aU {b{IE {OgHo$ _yb 2 VWm 5 h¢ & 1
2. 288 H$m A^mÁ` JwUZIÊS> H$aZo _| 2 H$m KmVm§H$ kmV H$s{OE & 1
1 1
3. (a) `{X VWm , {ÛKmV ~hþnX f(x) = x2 x 4 Ho$ eyÝ`H$ h¢, Vmo + H$m _mZ kmV
H$s{OE & 1
AWdm
(b) `{X {ÛKmV ~hþnX x2 + 3x + k H$m EH$ eyÝ`H$ 2 h¡, Vmo k H$m _mZ kmV H$s{OE & 1

4. (a) `{X 3 , a, 4 EH$ g_m§Va loT>r Ho$ VrZ H«$_mJV nX h¢, Vmo a H$m _mZ kmV H$s{OE & 1
5
AWdm
(b) `{X EH$ g_m§Va loT>r H$m gmd© A§Va d = 3 VWm 11dm± nX a11 = 15 h¡, Vmo BgH$m àW_ nX kmV
H$s{OE & 1
5. EH$ ì`{º$ 5 _rQ>a npíM_ H$s Amoa OmZo Ho$ ~mX 12 _rQ>a CÎma H$s Amoa OmVm h¡ & dh AnZo àma§{^H$ q~Xþ go
{H$VZr Xÿar na h¡ ? 1

6. PQ H|$Ð O dmbo d¥Îm Ho$ q~Xþ P na EH$ ñne©-aoIm h¡ & `{X OPQ EH$ g_{Û~mhþ {Ì^wO h¡, Vmo OQP kmV
H$s{OE & 1
7. Xmo g§H|$Ðr` d¥Îmm| H$s {ÌÁ`mE± 10 go_r VWm 6 go_r
d¥Îm H$mo ñne© H$aVr hmo & 1

8. (a) `{X 3 sin A = 1 h¡, Vmo sec A H$m _mZ kmV H$s{OE & 1
AWdm
(b) Xem©BE {H$ : 1

1 cot 2 2
2
= cot
1 tan
9. ^y{_ na pñWV EH$ {~§Xþ go, EH$ grYr (D$Üdm©Yaµ ) _rZma Ho$ nmX H$s Xÿar 20 _r. h¡ VWm Bg q~Xþ go _rZma
Ho$ {eIa H$m CÞ`Z H$moU 60 h¡ & _rZma H$s D±$MmB© kmV H$s{OE & 1
10. (a) Cg d¥Îm H$m joÌ\$b kmV H$s{OE {OgH$s n[a{Y 66 go_r h¡ & 1
AWdm
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11. VrZm| H|$Ðr` àd¥{Îm Ho$ _mnH$m| _mÜ`, _mÜ`H$ VWm ~hþbH$ _| g§~§Y {b{IE & 1

AD 4
12. EH$ ABC _|, `{X DE BC, VWm AC = 15 go_r h¡, Vmo AE H$s b§~mB© kmV H$s{OE &$ 1
DB 5

30/3/1 Page 13 P.T.O.

13. gab H$s{OE : 1
2 2 2
cosec 60 sin 30 sec 60
4 3
14. `{X tan + cot = h¡, Vmo tan2 + cot2 H$m _mZ kmV H$s{OE & 1
3
15. `{X H|$Ð O dmbo EH$ d¥Îm na EH$ ~mø {~ÝXþ P go ñne©-aoImE± PA VWm PB Bg àH$ma h¢ {H$ CZHo$ ~rM H$m
H$moU 70 h¡, Vmo POA kmV H$s{OE & 1
16. (a) VrZ nmgm| H$mo EH$ gmW CN>mbZo na {H$VZo n[aUm_ g§^d h¢ ? 1
AWdm
(b) `{X P(E) = 0·015 h¡, Vmo P(E Zht) kmV H$s{OE & 1
IÊS> II
17 20 4
1
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gr_mAm| na d¥j bJmZo H$m {ZU©` {b`m &
nmH©$ Ho$ EH$ H$moZo H$mo _yb-{~§Xþ VWm Bggo OmVr hþB© Xmo nañna b§~dV² aoImAm| H$mo x-Aj VWm y-Aj boVo hþE
BZ Xmo amñVm| H$mo Xmo a¡{IH$ g_rH$aUm| 2x 3y = 5 VWm 6x + 9y = 7 Ûmam {Zê${nV {H$`m J`m &
Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :
(i) Xmo g_rH$aUm| Ûmam {Zê${nV Xmo amñVo h¢ 1
(A) à{VÀN>oXr
(B) A{VN>m{XV (Overlapping)
(C) g_m§Va
(D) nañna b§~dV²
(ii) {ZåZ{b{IV _| go H$m¡Z-gm EH$ q~Xþ 2x 3y = 5 aoIm na pñWV h¡ ? 1
(A) ( 4, 1)
(B) (4, 1)
(C) (4, 1)
(D) ( 4, 1)

(iii) `{X aoIm 6x + 9y = 7, y-Aj H$mo EH$ q~Xþ na H$mQ>Vr h¡, Vmo Cg q~Xþ Ho$ {ZX}em§H$ hm|Jo 1
7
(A) 0,
9
7
(B) ,0
9
7
(C) ,0
6
7
(D) 0,
6

30/3/1 Page 14

(iv) `{X EH$ g_rH$aU `w½_ a1x + b1y + c1 = 0 VWm a2x + b2y + c2 = 0 H$m EH$ A{ÛVr` hb h¡, Vmo 1

a1 b1 c1
(A)
a2 b2 c2

a1 b1
(B)
a2 b2

a1 b1 c1
(C)
a2 b2 c2

a1 b1 c1
(D)
a2 b2 c2

a1 b1 c1
(v) `{X h¡, Vmo Xmo aoImE± a1x + b1y + c1 = 0 VWm a2x + b2y + c2 = 0 h¢ 1
a2 b2 c2
(A) g_m§Va
(B) gånmVr
(C) à{VÀN>oXr
(D) nañna b§~dV²

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ê$n _| h¢ & Mma {dÚm{W©`m| A, B, C VWm D Ho$ ñWmZ {ZåZ AmH¥${V _| Xem©E JE h¢ :

30/3/1 Page 15 P.T.O.

Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :

(i) A, B, C VWm D Mma q~XþAm| Ûmam ~Zr AmH¥${V h¡ 1
(A) EH$ dJ©
(B) EH$ g_m§Va MVw^w©O
(C) EH$ g_MVw^w©O
(D) EH$ MVw^w©O

(ii) `{X Iob AÜ`mnH$ _yb-q~Xþ na h¡, Vmo Mmam| {dÚm{W©`m| _| go H$m¡Z AÜ`mnH$ go {ZH$Q>V_ h¡ ? 1
(A) A
(B) B
(C) C
(D) D

(iii) A VWm C Ho$ ~rM H$s Xÿar h¡ 1
(A) 37 BH$mB©
(B) 35 BH$mB©
(C) 6 BH$mB©
(D) 5 BH$mB©

(iv) aoImIÊS> AC Ho$ _Ü`-q~Xþ Ho$ {ZX}em§H$ h¢ 1
5
(A) , 11
2
5 11
(B) ,
2 2
11
(C) 5,
2
(D) (5, 11)

(v) `{X q~Xþ P aoImIÊS> AD H$mo 1 : 2 Ho$ AZwnmV _| {d^m{OV H$aVm h¡, Vmo P Ho$ {ZX©oem§H$ h¢ 1

8 8
(A) ,
3 3

10 13
(B) ,
3 3

13 10
(C) ,
3 3

16 11
(D) ,
3 3

30/3/1 Page 16

19.

hmCg àW_ Am gHo$ & à{ejH$, {dÚm{W©`m| Ho$ EH$ g_yh Ûmam EH$ Xm bJo g_` H$mo ZmoQ> H$a ahm Wm & CgHo$
h¢ :

g_` (goH$ÊS>m| _|) : 0 20 20 40 40 60 60 80 80 100

{dÚm{W©`m| H$s g§»`m : 1 4 3 7 5

Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :

(i) ~hþbH$ dJ© H$m dJ© A§H$ ? 1
(A) 60
(B) 70
(C) 80
(D) 140

(ii) 1
(A) 70·33
(B) 71·33
(C) 72·33
(D) 73·33

(iii) 1
(A) 20 40
(B) 40 60
(C) 80 100
(D) 60 80

(iv) _mÜ`H$ dJ© VWm ~hþbH$ dJ© H$s {ZMbr gr_mAm| H$m `moJ\$b h¡ 1
(A) 80
(B) 140
(C) 120
(D) 100

(v) 1
(A) 65·7
(B) 85·7
(C) 45·7
(D) 25·7

30/3/1 Page 17 P.T.O.

20. J_u H$s Nw>{Å>`m| _|o hare AnZo {_Ìm| Ho$ gmW IobZm MmhVm Wm naÝVw ~mha ~hþV J_u Wr & Bg{bE CgZo Ka Ho$
A§Xa hr AnZo {_Ìm| Ho$ gmW IobZo Ho$ ~mao _| {ZU©` {b`m & CgZo 20 EH$ O¡go H$mS>mªo na 1 go 20 VH$ H$s
g§»`mE± (EH$ na EH$) {bIt VWm BZ H$mS>m] H$mo EH$ {_Ìm| Zo
{d{^Þ H$mS>mªo H$mo {ZH$mbZo H$s àm{`H$Vm H$s eVªo bJmBª & àË`oH$ H$mo EH$ H$mS>© {ZH$mbZo H$s àm{`H$Vm
~VmZo H$s EH$ ~mar Xr OmVr Wr &
Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :
(i) {ZH$mbo JE H$mS>© na H$s g§»`m Ho$ EH$ {df_ A^mÁ` g§»`m hmoZo H$s àm{`H$Vm h¡ 1

3
(A)
5
2
(B)
5

9
(C)
20
7
(D)
20
(ii) {ZH$mbo JE H$mS>© H$s g§»`m EH$ ^mÁ` g§»`m hmoZo H$s àm{`H$Vm h¡ 1

11
(A)
20
3
(B)
5

4
(C)
5
1
(D)
2

(iii) {ZH$mbo JE H$mS>© na A§{H$V g§»`m Ho$ 3, 6 VWm 9 Ho$ JwUO hmoZo H$s àm{`H$Vm h¡ 1

1
(A)
20

1
(B)
10

3
(C)
20

(D) 0

30/3/1 Page 18

(iv) {ZH$mbo JE H$mS>© na A§{H$V g§»`m Ho$ 3 Am¡a 7 H$m JwUO hmoZo H$s àm{`H$Vm h¡ 1

3
(A)
10

1
(B)
10

(C) 0

2
(D)
5

(v) `{X dh g^r H$mS>© {OZ na {df_ g§»`mE± {bIr h¢ {ZH$mb {XE JE hm|, Vmo eof H$mS>m] _| go
EH$ A^mÁ` g§»`m dmbm H$mS>© {ZH$mbZo H$s àm{`H$Vm h¡ 1

1
(A)
20

1
(B)
10

(C) 0

1
(D)
5
^mJ> I
IÊS> III

21. (a) P(5, 2), Q(6, 4) VWm R(7, 2) EH$ g_{Û~mhþ {Ì^wO PQR Ho$ erf©
h¢ & 2

AWdm
(b) dh AZwnmV kmV H$s{OE {Og_| {~§Xþ P(4, 5) q~XþAm| A(2, 3) VWm B(7, 8) H$mo {_bmZo dmbo aoImIÊS>
H$mo {d^m{OV H$aVm h¡ & 2

22. (a) EH$ {^Þ Ho$ A§e VWm ha H$m `moJ\$b 18 h¡ & `{X BgHo$ ha H$mo 2 , Vmo `h {^Þ
1
ah OmVr h¡ & {^Þ kmV H$s{OE & 2
3
AWdm
(b) k H$m dh _mZ kmV H$s{OE {OgHo$ {bE g_rH$aU {ZH$m` x + 2y = 5 VWm 3x + ky + 15 = 0
H$m H$moB© hb Z hmo & 2

30/3/1 Page 19 P.T.O.

23. ì`m»`m H$s{OE {H$ 2 3 5 + 5 VWm 5 7 11 + 7 5 2

24. àW_ 10 ^mÁ` g§»`mAm| H$m _mÜ` kmV H$s{OE & 2

25. ABC EH$ g_H$moU {Ì^wO h¡, {Og_| B na g_H$moU h¡, BC = 6 go_r VWm AB = 8 go_r h¢ & ABC Ho$

A§VJ©V EH$ d¥Îm ItMm J`m, {OgH$m H|$Ð O h¡, O¡gm {H$ AmH¥${V _| Xem©`m J`m h¡ & `{X d¥Îm H$s {ÌÁ`m r h¡, Vmo
r H$m _mZ kmV H$s{OE & 2

26. 5 go_r {ÌÁ`m H$m EH$ d¥Îm It{ME & BgHo$ H|$Ð go 8 go_r H$s Xÿar na pñWV EH$ q~Xþ go d¥Îm na Xmo ñne© -aoImAm|

H$s aMZm H$s{OE & 2

IÊS> IV
27. ~hþnX f(x) = 5x3 + 10x2 30x
2
15 H$mo ~hþnX g(x) = x + 1 + x go ^mJ Xr{OE Am¡a AV: ^mJ\$b d
eof\$b kmV H$s{OE & 3

28. {gÕ H$s{OE {H$ 3 + 2 EH$ An[a_o` g§»`m h¡, O~{H$ {X`m J`m h¡ {H$ 2 EH$ An[a_o` g§»`m h¡ & 3

29. Xr JB© AmH¥${V _|, PT VWm PS, EH$ ~mø q~Xþ P go H|$Ð O dmbo d¥Îm na ItMr JB© ñne©-aoImE± h¢ &
PT = 4 go_r VWm TPS = 60 h¡ & Ordm TS H$s b§~mB© kmV H$s{OE & d¥Îm H$s {ÌÁ`m ^r kmV H$s{OE & 3

30/3/1 Page 20

2 2
30. Xmo g_ê$n {Ì^wOm| Ho$ joÌ\$b H«$_e: 121 go_r VWm 64 go_r h¢ & `{X àW_ {Ì^wO H$s EH$ _mpÜ`H$m
12·1 go_r bå~r h¡, Vmo Xÿgar {Ì^wO H$s g§JV _mpÜ`H$m H$s b§~mB© kmV H$s{OE & 3

31. (a) {gÕ H$s{OE : 3
1 1
cosec A = cosec A
(cot A) (sec A) cot A (cot A) (sec A ) cot A

AWdm
(b) {gÕ H$s{OE : 3
6 2 2 6
sin A + 3 sin A cos A = 1 cos A

5
32. (a) {ÛKmV g_rH$aU 2x2 8x k = 0 H$m EH$ _yb h¡ & k H$m _mZ kmV H$s{OE & g_rH$aU H$m
2
Xÿgam _yb ^r kmV H$s{OE & 3

AWdm
(b) {ÛKmV gyÌ Ho$ à`moJ go, {ZåZ g_rH$aU H$mo x Ho$ {bE hb H$s{OE : 3
2 2
abx + (b ac) x bc = 0

33. EH$ {Ì^wO ABC Ho$ erfmªo A, B VWm C go 2 go_r {ÌÁ`m dmbr Mmn| S>mbr JBª, O¡gm {H$ AmH¥${V _| Xem©`m J`m
h¡ & `{X AB = 6 go_r, BC = 8 go_r VWm AC = 10 go_r h¡, Vmo N>m`m§{H$V joÌ H$m joÌ\$b kmV H$s{OE & 3

30/3/1 Page 21 P.T.O.

IÊS> V

34. EH$ d¥ÎmmH$ma nmBn, {OgH$m A§V:ì`mg 8 go_r h¡, Ho$ Ûmam nmZr ~mha {ZH$mbm Om ahm h¡ & `{X nmZr H$s Mmb
80 go_r/go. h¡, Vmo EH$ K§Q>o _| Bg nmBn Ûmam {H$VZo {bQ>a nmZr ~mha {ZH$mbm OmVm h¡ ? 5

35. (a) (D$Üdm©Ya) EH$g_mZ Mmb go AmVr
hþB© EH$ H$ma H$mo XoIVm h¡ & CgHo$ AdZ_Z H$moU H$mo 30 go 60 VH$ ~XbZo _| 18 {_ZQ> bJVo h¢ &
BgHo$ ~mX {H$VZr Xoa _| H$ma, _rZma VH$ nhþ±M OmEJr ? 5

AWdm
(b) EH$ 50 _r. D±$Mo EH$ ßboQ>\$m°
30 VWm BgHo$ AmYma H$m AdZ_Z H$moU 60 XoIVr h¡ & Bg
ßboQ>\$m° 5

36. `{X {H$gr g_m§Va loT>r Ho$ àW_ n nXm| Ho$ `moJ\$b H$mo Sn Ûmam Xem©`m OmVm h¡, Vmo {gÕ H$s{OE {H$
S12 = 3 (S8 S4). 5

30/3/1 Page 22