Class 10 Mathematics (Basic): Question Paper for 2023 (Set 2) | Mathematics (Maths) Class 10 PDF Download

 Page 1


 
430/4/2    2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
1. Bg àíZ-nÌ _| 38 àíZ h¢& g^r àíZ A{Zdm`© h¢& 
2. àíZ-nÌ nm±M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S> & 
3. IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ H$maU 
AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢& 
4. IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$mo§ Ho$ àíZ h¢& 
5. IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$ àíZ h¢& 
6. IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm±M-nm±M A§H$m| Ho$ àíZ h¢& 
7. IÊS> ‹S> _| àíZ g§»`m 36 go 38 òmoV/àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢& Am§V[aH$ 
{dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡& 
8. àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡& 
9. Ohm§ Amdí`H$ hmo ñdÀN> AmH¥${V`m± ~ZmE§& `{X Amdí`H$ hmo Vmo p = 22/7 b|& 
10. H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ H$m 1 A§H$ h¡& 
 
1.  _mZm E EH$ Eogr KQ>Zm h¡ {OgHo$ {bE P(E Zht) =
1
5
 h¡, Vmo P(E) ~am~a h¡ :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. `{X ~hþnX  p (x) = x
2 
+ 5x + 6 h¡, Vmo  p (- 2) H$m _mZ h¡ :   1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. g§»`mAm| 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 H$m ~hþbH$ h¡ :   1 
 (a) 2 (b) 3  (c) 4 (d) 5 
 
4. EH$ d¥Îm na pñWV EH$ q~Xþ go d¥Îm na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢ ? 1 
 (a) EH$ (b) Xmo  (c) AZoH$ (d) eyÝ` 
 
5. EH$ {ÛKmV g_rH$aU, {OgH$m EH$ _yb 2 Am¡a _ybm| H$m `moJ eyÝ` h¡, h¡ :  1 
 (a) x
2 
+ 4 = 0    (b) x
2 
- 2 = 0 
 (c) 4x
2 
- 1 = 0    (d) x
2 
- 4 = 0 
 
6. {ZåZ _| H$m¡Z, {ÛKmV g_rH$aU Zht h¡ ?      1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. EH$ {ÛKmV g_rH$aU {OgHo$ eyÝ`H$m| H$m `moJ Am¡a JwUZ\$b H«$_e: 2 Am¡a - 1 h¡, h¡ :  1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
MATHEMATICS	(Basic)
CBSE	Class	-X	(2023)
					Answers	&	Solutions
Page 2


 
430/4/2    2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
1. Bg àíZ-nÌ _| 38 àíZ h¢& g^r àíZ A{Zdm`© h¢& 
2. àíZ-nÌ nm±M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S> & 
3. IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ H$maU 
AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢& 
4. IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$mo§ Ho$ àíZ h¢& 
5. IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$ àíZ h¢& 
6. IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm±M-nm±M A§H$m| Ho$ àíZ h¢& 
7. IÊS> ‹S> _| àíZ g§»`m 36 go 38 òmoV/àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢& Am§V[aH$ 
{dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡& 
8. àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡& 
9. Ohm§ Amdí`H$ hmo ñdÀN> AmH¥${V`m± ~ZmE§& `{X Amdí`H$ hmo Vmo p = 22/7 b|& 
10. H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ H$m 1 A§H$ h¡& 
 
1.  _mZm E EH$ Eogr KQ>Zm h¡ {OgHo$ {bE P(E Zht) =
1
5
 h¡, Vmo P(E) ~am~a h¡ :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. `{X ~hþnX  p (x) = x
2 
+ 5x + 6 h¡, Vmo  p (- 2) H$m _mZ h¡ :   1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. g§»`mAm| 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 H$m ~hþbH$ h¡ :   1 
 (a) 2 (b) 3  (c) 4 (d) 5 
 
4. EH$ d¥Îm na pñWV EH$ q~Xþ go d¥Îm na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢ ? 1 
 (a) EH$ (b) Xmo  (c) AZoH$ (d) eyÝ` 
 
5. EH$ {ÛKmV g_rH$aU, {OgH$m EH$ _yb 2 Am¡a _ybm| H$m `moJ eyÝ` h¡, h¡ :  1 
 (a) x
2 
+ 4 = 0    (b) x
2 
- 2 = 0 
 (c) 4x
2 
- 1 = 0    (d) x
2 
- 4 = 0 
 
6. {ZåZ _| H$m¡Z, {ÛKmV g_rH$aU Zht h¡ ?      1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. EH$ {ÛKmV g_rH$aU {OgHo$ eyÝ`H$m| H$m `moJ Am¡a JwUZ\$b H«$_e: 2 Am¡a - 1 h¡, h¡ :  1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
MATHEMATICS	(Basic)
CBSE	Class	-X	(2023)
					Answers	&	Solutions
 
430/4/2   [P.T.O. 3
General Instructions : 
Read the following instructions carefully and follow them : 
1. This question paper contains 38 questions. All questions are compulsory. 
2. Question paper is divided into FIVE sections - Section A, B, C, D and E. 
3. In section A, question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion - Reason based questions of 1 mark each. 
4. In section B, question number 21 to 25 are very short answer (VSA) type questions 
of 2 marks each. 
5. In section C, question number 26 to 31 are short answer (SA) type questions 
carrying 3 marks each. 
6. In section D, question number 32 to 35 are long answer (LA) type questions 
carrying 5 marks each. 
7. In section E, question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 
marks question in each case study. 
8. There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
9. Draw neat figures wherever required. Take p = 22/7 wherever required if not 
stated. 
10. Use of calculators is not allowed. 
 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each.  
1. Let E be an event such that P(not E) =
1
5
, then P(E) is equal to :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. If p (x) = x
2 
+ 5x + 6, then p (- 2) is :    1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is :  1 
 (a) 2 (b) 3 (c) 4 (d) 5 
 
4. How many tangents can be drawn to a circle from a point on it ?  1 
 (a) One  (b) Two (c) Infinite (d) Zero 
 
5. A quadratic equation whose one root is 2 and the sum of whose roots is 
zero,  is :       1 
 (a) x
2 
+ 4 = 0 (b) x
2 
- 2 = 0 (c) 4x
2 
- 1 = 0 (d) x
2 
- 4 = 0 
 
6. Which of the following is not a quadratic equation ?   1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -  x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and -1 
respectively is :      1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
Page 3


 
430/4/2    2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
1. Bg àíZ-nÌ _| 38 àíZ h¢& g^r àíZ A{Zdm`© h¢& 
2. àíZ-nÌ nm±M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S> & 
3. IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ H$maU 
AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢& 
4. IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$mo§ Ho$ àíZ h¢& 
5. IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$ àíZ h¢& 
6. IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm±M-nm±M A§H$m| Ho$ àíZ h¢& 
7. IÊS> ‹S> _| àíZ g§»`m 36 go 38 òmoV/àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢& Am§V[aH$ 
{dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡& 
8. àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡& 
9. Ohm§ Amdí`H$ hmo ñdÀN> AmH¥${V`m± ~ZmE§& `{X Amdí`H$ hmo Vmo p = 22/7 b|& 
10. H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ H$m 1 A§H$ h¡& 
 
1.  _mZm E EH$ Eogr KQ>Zm h¡ {OgHo$ {bE P(E Zht) =
1
5
 h¡, Vmo P(E) ~am~a h¡ :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. `{X ~hþnX  p (x) = x
2 
+ 5x + 6 h¡, Vmo  p (- 2) H$m _mZ h¡ :   1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. g§»`mAm| 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 H$m ~hþbH$ h¡ :   1 
 (a) 2 (b) 3  (c) 4 (d) 5 
 
4. EH$ d¥Îm na pñWV EH$ q~Xþ go d¥Îm na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢ ? 1 
 (a) EH$ (b) Xmo  (c) AZoH$ (d) eyÝ` 
 
5. EH$ {ÛKmV g_rH$aU, {OgH$m EH$ _yb 2 Am¡a _ybm| H$m `moJ eyÝ` h¡, h¡ :  1 
 (a) x
2 
+ 4 = 0    (b) x
2 
- 2 = 0 
 (c) 4x
2 
- 1 = 0    (d) x
2 
- 4 = 0 
 
6. {ZåZ _| H$m¡Z, {ÛKmV g_rH$aU Zht h¡ ?      1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. EH$ {ÛKmV g_rH$aU {OgHo$ eyÝ`H$m| H$m `moJ Am¡a JwUZ\$b H«$_e: 2 Am¡a - 1 h¡, h¡ :  1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
MATHEMATICS	(Basic)
CBSE	Class	-X	(2023)
					Answers	&	Solutions
 
430/4/2   [P.T.O. 3
General Instructions : 
Read the following instructions carefully and follow them : 
1. This question paper contains 38 questions. All questions are compulsory. 
2. Question paper is divided into FIVE sections - Section A, B, C, D and E. 
3. In section A, question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion - Reason based questions of 1 mark each. 
4. In section B, question number 21 to 25 are very short answer (VSA) type questions 
of 2 marks each. 
5. In section C, question number 26 to 31 are short answer (SA) type questions 
carrying 3 marks each. 
6. In section D, question number 32 to 35 are long answer (LA) type questions 
carrying 5 marks each. 
7. In section E, question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 
marks question in each case study. 
8. There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
9. Draw neat figures wherever required. Take p = 22/7 wherever required if not 
stated. 
10. Use of calculators is not allowed. 
 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each.  
1. Let E be an event such that P(not E) =
1
5
, then P(E) is equal to :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. If p (x) = x
2 
+ 5x + 6, then p (- 2) is :    1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is :  1 
 (a) 2 (b) 3 (c) 4 (d) 5 
 
4. How many tangents can be drawn to a circle from a point on it ?  1 
 (a) One  (b) Two (c) Infinite (d) Zero 
 
5. A quadratic equation whose one root is 2 and the sum of whose roots is 
zero,  is :       1 
 (a) x
2 
+ 4 = 0 (b) x
2 
- 2 = 0 (c) 4x
2 
- 1 = 0 (d) x
2 
- 4 = 0 
 
6. Which of the following is not a quadratic equation ?   1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -  x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and -1 
respectively is :      1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
 
430/4/2    4
8. g§»`mAm| 30 Am¡a 70 Ho$ {bE (HCF × LCM) ~am~a h¡ :    1 
 (a) 2100 (b) 21 (c) 210 (d) 70 
 
9. {ÌÁ`m 14 go_r. dmbo d¥Îm H$s EH$ Mmn H$s bå~mB©, Omo d¥Îm Ho$ H|$Ð na 60
o
 H$m H$moU 
A§V[aV H$aVm h¡, h¡ :       1 
 (a) 
44
3
 go_r. (b) 
88
3
 go_r. (c) 
308
3
 go_r. (d) 
616
3
 go_r. 
 
10. EH$ AY©d¥ÎmmH$ma Mm§Xo H$s {ÌÁ`m `{X 7 go_r. h¡, Vmo Bg Mm§Xo H$m n[a_mn hmoJm : 1 
 (a) 11 go_r. (b) 14 go_r. (c) 22 go_r. (d) 36 go_r. 
 
11. 15 _r. D±$Mo Q>m°da Ho$ nmX- q~Xþ go  15 3 _r. H$s Xÿar na pñWV EH$ q~Xþ go Q>m°da Ho$ 
{eIa H$m CÞ`Z H$moU h¡ :      1 
 (a) 30
o
 (b) 45
o
  (c) 60
 o
 (d) 90
o
  
 
12. 
o o
2 4
 sin0 cos0
3 5
? ?
? ?
? ?
- ~am~a h¡ :       1 
 (a) 
2
3
  (b) 
4
5
-
  (c) 0  (d) 
2
15
-
 
 
13. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r _| go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡& 
Bg nÎmo Ho "nmZ H$m ~mXemh' hmoZo H$s àm{`H$Vm Š`m h¡ ? 1 
 (a) 
1
52
 (b) 
1
26
 (c) 
1
13
 (d) 
12
13
 
 
14. g§»`m (5 - 3 5 + 5) EH$ :     1 
 (a) nyUmªH$ h¡ (b) n[a_o` g§»`m h¡ (c) An[a_o` g§»`m h¡ (d) nyU© g§»`m h¡ 
 
15. `{X x - y = 1, x + ky = 5 a¡{IH$ g_rH$aU `w½_ H$m A{ÛVr` hb x = 2, y = 1 h¡, Vmo 
k H$m _mZ h¡ :        1 
 (a) - 2 (b) - 3 (c) 3 (d) 4 
 
16. `{X ?ABC ~ ?DEF h¡ Am¡a ?A = 47
o
, ?E = 83
o  
h¡, Vmo ?C ~am~a h¡ : 1 
 (a) 47
o
 (b) 50
o 
(c) 83
o
 (d) 130
o
 
 
17. 3 go_r. {ÌÁ`m dmbo EH$ d¥Îm Ho$ EH$ ~mø q~Xþ A go ItMr JB© ñne© aoIm H$s bå~mB©  
4 go_r. h¡& d¥Îm Ho$ H|$Ð go {~§Xþ A H$s Xÿar h¡ :    1 
 (a) 7 go_r. (b) 5 go_r. (c) 7 go_r. (d) 25 go_r. 
 
18. x + 2y + 5 = 0 Am¡a - 3x - 6y + 1 = 0 a¡{IH$ g_rH$aU `w½_ H$m/Ho$ :  1 
 (a) A{ÛVr` hb hmoVm h¡   (b) R>rH$ Xmo hb h¢ 
 (c) AZoH$ hb h¢    (d) H$moB© hb Zht hmoVm h¡ 
Page 4


 
430/4/2    2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
1. Bg àíZ-nÌ _| 38 àíZ h¢& g^r àíZ A{Zdm`© h¢& 
2. àíZ-nÌ nm±M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S> & 
3. IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ H$maU 
AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢& 
4. IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$mo§ Ho$ àíZ h¢& 
5. IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$ àíZ h¢& 
6. IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm±M-nm±M A§H$m| Ho$ àíZ h¢& 
7. IÊS> ‹S> _| àíZ g§»`m 36 go 38 òmoV/àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢& Am§V[aH$ 
{dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡& 
8. àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡& 
9. Ohm§ Amdí`H$ hmo ñdÀN> AmH¥${V`m± ~ZmE§& `{X Amdí`H$ hmo Vmo p = 22/7 b|& 
10. H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ H$m 1 A§H$ h¡& 
 
1.  _mZm E EH$ Eogr KQ>Zm h¡ {OgHo$ {bE P(E Zht) =
1
5
 h¡, Vmo P(E) ~am~a h¡ :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. `{X ~hþnX  p (x) = x
2 
+ 5x + 6 h¡, Vmo  p (- 2) H$m _mZ h¡ :   1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. g§»`mAm| 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 H$m ~hþbH$ h¡ :   1 
 (a) 2 (b) 3  (c) 4 (d) 5 
 
4. EH$ d¥Îm na pñWV EH$ q~Xþ go d¥Îm na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢ ? 1 
 (a) EH$ (b) Xmo  (c) AZoH$ (d) eyÝ` 
 
5. EH$ {ÛKmV g_rH$aU, {OgH$m EH$ _yb 2 Am¡a _ybm| H$m `moJ eyÝ` h¡, h¡ :  1 
 (a) x
2 
+ 4 = 0    (b) x
2 
- 2 = 0 
 (c) 4x
2 
- 1 = 0    (d) x
2 
- 4 = 0 
 
6. {ZåZ _| H$m¡Z, {ÛKmV g_rH$aU Zht h¡ ?      1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. EH$ {ÛKmV g_rH$aU {OgHo$ eyÝ`H$m| H$m `moJ Am¡a JwUZ\$b H«$_e: 2 Am¡a - 1 h¡, h¡ :  1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
MATHEMATICS	(Basic)
CBSE	Class	-X	(2023)
					Answers	&	Solutions
 
430/4/2   [P.T.O. 3
General Instructions : 
Read the following instructions carefully and follow them : 
1. This question paper contains 38 questions. All questions are compulsory. 
2. Question paper is divided into FIVE sections - Section A, B, C, D and E. 
3. In section A, question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion - Reason based questions of 1 mark each. 
4. In section B, question number 21 to 25 are very short answer (VSA) type questions 
of 2 marks each. 
5. In section C, question number 26 to 31 are short answer (SA) type questions 
carrying 3 marks each. 
6. In section D, question number 32 to 35 are long answer (LA) type questions 
carrying 5 marks each. 
7. In section E, question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 
marks question in each case study. 
8. There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
9. Draw neat figures wherever required. Take p = 22/7 wherever required if not 
stated. 
10. Use of calculators is not allowed. 
 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each.  
1. Let E be an event such that P(not E) =
1
5
, then P(E) is equal to :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. If p (x) = x
2 
+ 5x + 6, then p (- 2) is :    1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is :  1 
 (a) 2 (b) 3 (c) 4 (d) 5 
 
4. How many tangents can be drawn to a circle from a point on it ?  1 
 (a) One  (b) Two (c) Infinite (d) Zero 
 
5. A quadratic equation whose one root is 2 and the sum of whose roots is 
zero,  is :       1 
 (a) x
2 
+ 4 = 0 (b) x
2 
- 2 = 0 (c) 4x
2 
- 1 = 0 (d) x
2 
- 4 = 0 
 
6. Which of the following is not a quadratic equation ?   1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -  x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and -1 
respectively is :      1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
 
430/4/2    4
8. g§»`mAm| 30 Am¡a 70 Ho$ {bE (HCF × LCM) ~am~a h¡ :    1 
 (a) 2100 (b) 21 (c) 210 (d) 70 
 
9. {ÌÁ`m 14 go_r. dmbo d¥Îm H$s EH$ Mmn H$s bå~mB©, Omo d¥Îm Ho$ H|$Ð na 60
o
 H$m H$moU 
A§V[aV H$aVm h¡, h¡ :       1 
 (a) 
44
3
 go_r. (b) 
88
3
 go_r. (c) 
308
3
 go_r. (d) 
616
3
 go_r. 
 
10. EH$ AY©d¥ÎmmH$ma Mm§Xo H$s {ÌÁ`m `{X 7 go_r. h¡, Vmo Bg Mm§Xo H$m n[a_mn hmoJm : 1 
 (a) 11 go_r. (b) 14 go_r. (c) 22 go_r. (d) 36 go_r. 
 
11. 15 _r. D±$Mo Q>m°da Ho$ nmX- q~Xþ go  15 3 _r. H$s Xÿar na pñWV EH$ q~Xþ go Q>m°da Ho$ 
{eIa H$m CÞ`Z H$moU h¡ :      1 
 (a) 30
o
 (b) 45
o
  (c) 60
 o
 (d) 90
o
  
 
12. 
o o
2 4
 sin0 cos0
3 5
? ?
? ?
? ?
- ~am~a h¡ :       1 
 (a) 
2
3
  (b) 
4
5
-
  (c) 0  (d) 
2
15
-
 
 
13. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r _| go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡& 
Bg nÎmo Ho "nmZ H$m ~mXemh' hmoZo H$s àm{`H$Vm Š`m h¡ ? 1 
 (a) 
1
52
 (b) 
1
26
 (c) 
1
13
 (d) 
12
13
 
 
14. g§»`m (5 - 3 5 + 5) EH$ :     1 
 (a) nyUmªH$ h¡ (b) n[a_o` g§»`m h¡ (c) An[a_o` g§»`m h¡ (d) nyU© g§»`m h¡ 
 
15. `{X x - y = 1, x + ky = 5 a¡{IH$ g_rH$aU `w½_ H$m A{ÛVr` hb x = 2, y = 1 h¡, Vmo 
k H$m _mZ h¡ :        1 
 (a) - 2 (b) - 3 (c) 3 (d) 4 
 
16. `{X ?ABC ~ ?DEF h¡ Am¡a ?A = 47
o
, ?E = 83
o  
h¡, Vmo ?C ~am~a h¡ : 1 
 (a) 47
o
 (b) 50
o 
(c) 83
o
 (d) 130
o
 
 
17. 3 go_r. {ÌÁ`m dmbo EH$ d¥Îm Ho$ EH$ ~mø q~Xþ A go ItMr JB© ñne© aoIm H$s bå~mB©  
4 go_r. h¡& d¥Îm Ho$ H|$Ð go {~§Xþ A H$s Xÿar h¡ :    1 
 (a) 7 go_r. (b) 5 go_r. (c) 7 go_r. (d) 25 go_r. 
 
18. x + 2y + 5 = 0 Am¡a - 3x - 6y + 1 = 0 a¡{IH$ g_rH$aU `w½_ H$m/Ho$ :  1 
 (a) A{ÛVr` hb hmoVm h¡   (b) R>rH$ Xmo hb h¢ 
 (c) AZoH$ hb h¢    (d) H$moB© hb Zht hmoVm h¡ 
 
430/4/2   [P.T.O. 5
8. (HCF × LCM) for the numbers 30 and 70 is :   1 
 (a) 2100 (b) 21 (c) 210 (d) 70 
 
9. The length of the arc of a circle of radius 14 cm which subtends an angle of 
60
o 
at the centre of the circle is :     1 
 (a) 
44
3
 cm (b) 
88
3
 cm (c) 
308
3
 cm (d) 
616
3
 cm 
 
10. If the radius of a semi-circular protractor is 7cm, then its perimeter is : 1 
 (a) 11 cm  (b) 14 cm (c) 22 cm (d) 36 cm 
 
11. The angle of elevation of the top of a 15 m high tower at a point 15 3 m 
away from the base of the tower is :     1 
 (a) 30
o
 (b) 45
o
  (c) 60
 o
 (d) 90
o
  
  
12. 
o o
2 4
 sin0 cos0
3 5
? ?
? ?
? ?
- is equal to
 
:     1 
 (a) 
2
3
  (b) 
4
5
-
  (c) 0  (d) 
2
15
-
  
 
13. From a well-shuffled deck of 52 cards, a card is drawn at random. What is 
the probability of getting king of hearts ?     1 
 (a) 
1
52
 (b) 
1
26
 (c) 
1
13
 (d) 
12
13
 
 
14. The number (5 -  3 5 + 5 ) is :     1 
 (a) an integer    (b) a rational number 
 (c) an irrational number (d) a whole number 
 
15. If the pair of linear equations x - y = 1, x + ky = 5 has a unique solution  
x = 2, y = 1, then the value of k is :     1 
 (a) -  2 (b) -  3 (c) 3 (d) 4 
 
16. If ?ABC ~ ?DEF and ?A = 47
o
, ?E = 83
o
, then ?C is equal :  1 
 (a) 47
o
 (b) 50
o 
(c) 83
o
 (d) 130
o
 
 
17. The length of the tangent from an external point A to a circle, of radius 
3 cm, is 4 cm. The distance of A from the centre of the circle is :  1 
 (a) 7 cm (b) 5 cm (c) 7 cm (d) 25 cm 
 
18. The pair of linear equations x + 2y  + 5 = 0 and - 3x - 6y + 1 = 0 has : 1 
 (a) a unique solution  (b) exactly two solutions 
 (c) infinitely many solutions (d) no solution  
Page 5


 
430/4/2    2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
1. Bg àíZ-nÌ _| 38 àíZ h¢& g^r àíZ A{Zdm`© h¢& 
2. àíZ-nÌ nm±M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S> & 
3. IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ H$maU 
AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢& 
4. IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$mo§ Ho$ àíZ h¢& 
5. IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$ àíZ h¢& 
6. IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm±M-nm±M A§H$m| Ho$ àíZ h¢& 
7. IÊS> ‹S> _| àíZ g§»`m 36 go 38 òmoV/àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢& Am§V[aH$ 
{dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡& 
8. àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡& 
9. Ohm§ Amdí`H$ hmo ñdÀN> AmH¥${V`m± ~ZmE§& `{X Amdí`H$ hmo Vmo p = 22/7 b|& 
10. H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ H$m 1 A§H$ h¡& 
 
1.  _mZm E EH$ Eogr KQ>Zm h¡ {OgHo$ {bE P(E Zht) =
1
5
 h¡, Vmo P(E) ~am~a h¡ :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. `{X ~hþnX  p (x) = x
2 
+ 5x + 6 h¡, Vmo  p (- 2) H$m _mZ h¡ :   1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. g§»`mAm| 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 H$m ~hþbH$ h¡ :   1 
 (a) 2 (b) 3  (c) 4 (d) 5 
 
4. EH$ d¥Îm na pñWV EH$ q~Xþ go d¥Îm na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢ ? 1 
 (a) EH$ (b) Xmo  (c) AZoH$ (d) eyÝ` 
 
5. EH$ {ÛKmV g_rH$aU, {OgH$m EH$ _yb 2 Am¡a _ybm| H$m `moJ eyÝ` h¡, h¡ :  1 
 (a) x
2 
+ 4 = 0    (b) x
2 
- 2 = 0 
 (c) 4x
2 
- 1 = 0    (d) x
2 
- 4 = 0 
 
6. {ZåZ _| H$m¡Z, {ÛKmV g_rH$aU Zht h¡ ?      1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. EH$ {ÛKmV g_rH$aU {OgHo$ eyÝ`H$m| H$m `moJ Am¡a JwUZ\$b H«$_e: 2 Am¡a - 1 h¡, h¡ :  1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
MATHEMATICS	(Basic)
CBSE	Class	-X	(2023)
					Answers	&	Solutions
 
430/4/2   [P.T.O. 3
General Instructions : 
Read the following instructions carefully and follow them : 
1. This question paper contains 38 questions. All questions are compulsory. 
2. Question paper is divided into FIVE sections - Section A, B, C, D and E. 
3. In section A, question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion - Reason based questions of 1 mark each. 
4. In section B, question number 21 to 25 are very short answer (VSA) type questions 
of 2 marks each. 
5. In section C, question number 26 to 31 are short answer (SA) type questions 
carrying 3 marks each. 
6. In section D, question number 32 to 35 are long answer (LA) type questions 
carrying 5 marks each. 
7. In section E, question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 
marks question in each case study. 
8. There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
9. Draw neat figures wherever required. Take p = 22/7 wherever required if not 
stated. 
10. Use of calculators is not allowed. 
 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each.  
1. Let E be an event such that P(not E) =
1
5
, then P(E) is equal to :  1 
 (a) 
1
5
 (b) 
2
5
 (c) 0 (d) 
4
5
 
 
2. If p (x) = x
2 
+ 5x + 6, then p (- 2) is :    1 
 (a) 20 (b) 0  (c) - 8 (d) 8 
  
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is :  1 
 (a) 2 (b) 3 (c) 4 (d) 5 
 
4. How many tangents can be drawn to a circle from a point on it ?  1 
 (a) One  (b) Two (c) Infinite (d) Zero 
 
5. A quadratic equation whose one root is 2 and the sum of whose roots is 
zero,  is :       1 
 (a) x
2 
+ 4 = 0 (b) x
2 
- 2 = 0 (c) 4x
2 
- 1 = 0 (d) x
2 
- 4 = 0 
 
6. Which of the following is not a quadratic equation ?   1 
 (a) 2(x -1)
2
 = 4x
2
 - 2x + 1 (b) 2x -  x
 2
 = x
2
 + 5 
 (c) ( 2 x + 3 )
2
 + x
2 
= 3x
2 
- 5x (d) (x
2 
+2x)
2
 = x
4 
+ 3 + 4x
3
 
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and -1 
respectively is :      1 
 (a) x
2
 + 2x + 1 (b) x
2 
- 2x - 1 (c) x
2
 + 2x - 1 (d) x
2 
- 2x + 1  
 
430/4/2    4
8. g§»`mAm| 30 Am¡a 70 Ho$ {bE (HCF × LCM) ~am~a h¡ :    1 
 (a) 2100 (b) 21 (c) 210 (d) 70 
 
9. {ÌÁ`m 14 go_r. dmbo d¥Îm H$s EH$ Mmn H$s bå~mB©, Omo d¥Îm Ho$ H|$Ð na 60
o
 H$m H$moU 
A§V[aV H$aVm h¡, h¡ :       1 
 (a) 
44
3
 go_r. (b) 
88
3
 go_r. (c) 
308
3
 go_r. (d) 
616
3
 go_r. 
 
10. EH$ AY©d¥ÎmmH$ma Mm§Xo H$s {ÌÁ`m `{X 7 go_r. h¡, Vmo Bg Mm§Xo H$m n[a_mn hmoJm : 1 
 (a) 11 go_r. (b) 14 go_r. (c) 22 go_r. (d) 36 go_r. 
 
11. 15 _r. D±$Mo Q>m°da Ho$ nmX- q~Xþ go  15 3 _r. H$s Xÿar na pñWV EH$ q~Xþ go Q>m°da Ho$ 
{eIa H$m CÞ`Z H$moU h¡ :      1 
 (a) 30
o
 (b) 45
o
  (c) 60
 o
 (d) 90
o
  
 
12. 
o o
2 4
 sin0 cos0
3 5
? ?
? ?
? ?
- ~am~a h¡ :       1 
 (a) 
2
3
  (b) 
4
5
-
  (c) 0  (d) 
2
15
-
 
 
13. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r _| go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡& 
Bg nÎmo Ho "nmZ H$m ~mXemh' hmoZo H$s àm{`H$Vm Š`m h¡ ? 1 
 (a) 
1
52
 (b) 
1
26
 (c) 
1
13
 (d) 
12
13
 
 
14. g§»`m (5 - 3 5 + 5) EH$ :     1 
 (a) nyUmªH$ h¡ (b) n[a_o` g§»`m h¡ (c) An[a_o` g§»`m h¡ (d) nyU© g§»`m h¡ 
 
15. `{X x - y = 1, x + ky = 5 a¡{IH$ g_rH$aU `w½_ H$m A{ÛVr` hb x = 2, y = 1 h¡, Vmo 
k H$m _mZ h¡ :        1 
 (a) - 2 (b) - 3 (c) 3 (d) 4 
 
16. `{X ?ABC ~ ?DEF h¡ Am¡a ?A = 47
o
, ?E = 83
o  
h¡, Vmo ?C ~am~a h¡ : 1 
 (a) 47
o
 (b) 50
o 
(c) 83
o
 (d) 130
o
 
 
17. 3 go_r. {ÌÁ`m dmbo EH$ d¥Îm Ho$ EH$ ~mø q~Xþ A go ItMr JB© ñne© aoIm H$s bå~mB©  
4 go_r. h¡& d¥Îm Ho$ H|$Ð go {~§Xþ A H$s Xÿar h¡ :    1 
 (a) 7 go_r. (b) 5 go_r. (c) 7 go_r. (d) 25 go_r. 
 
18. x + 2y + 5 = 0 Am¡a - 3x - 6y + 1 = 0 a¡{IH$ g_rH$aU `w½_ H$m/Ho$ :  1 
 (a) A{ÛVr` hb hmoVm h¡   (b) R>rH$ Xmo hb h¢ 
 (c) AZoH$ hb h¢    (d) H$moB© hb Zht hmoVm h¡ 
 
430/4/2   [P.T.O. 5
8. (HCF × LCM) for the numbers 30 and 70 is :   1 
 (a) 2100 (b) 21 (c) 210 (d) 70 
 
9. The length of the arc of a circle of radius 14 cm which subtends an angle of 
60
o 
at the centre of the circle is :     1 
 (a) 
44
3
 cm (b) 
88
3
 cm (c) 
308
3
 cm (d) 
616
3
 cm 
 
10. If the radius of a semi-circular protractor is 7cm, then its perimeter is : 1 
 (a) 11 cm  (b) 14 cm (c) 22 cm (d) 36 cm 
 
11. The angle of elevation of the top of a 15 m high tower at a point 15 3 m 
away from the base of the tower is :     1 
 (a) 30
o
 (b) 45
o
  (c) 60
 o
 (d) 90
o
  
  
12. 
o o
2 4
 sin0 cos0
3 5
? ?
? ?
? ?
- is equal to
 
:     1 
 (a) 
2
3
  (b) 
4
5
-
  (c) 0  (d) 
2
15
-
  
 
13. From a well-shuffled deck of 52 cards, a card is drawn at random. What is 
the probability of getting king of hearts ?     1 
 (a) 
1
52
 (b) 
1
26
 (c) 
1
13
 (d) 
12
13
 
 
14. The number (5 -  3 5 + 5 ) is :     1 
 (a) an integer    (b) a rational number 
 (c) an irrational number (d) a whole number 
 
15. If the pair of linear equations x - y = 1, x + ky = 5 has a unique solution  
x = 2, y = 1, then the value of k is :     1 
 (a) -  2 (b) -  3 (c) 3 (d) 4 
 
16. If ?ABC ~ ?DEF and ?A = 47
o
, ?E = 83
o
, then ?C is equal :  1 
 (a) 47
o
 (b) 50
o 
(c) 83
o
 (d) 130
o
 
 
17. The length of the tangent from an external point A to a circle, of radius 
3 cm, is 4 cm. The distance of A from the centre of the circle is :  1 
 (a) 7 cm (b) 5 cm (c) 7 cm (d) 25 cm 
 
18. The pair of linear equations x + 2y  + 5 = 0 and - 3x - 6y + 1 = 0 has : 1 
 (a) a unique solution  (b) exactly two solutions 
 (c) infinitely many solutions (d) no solution  
 
430/4/2    6
2 
(A{^H$WZ - VH©$ àH$ma Ho$ àíZ) 
àíZ g§»`m 19 VWm 20 _| EH$ A{^H$WZ (A) Ho$ ~mX EH$ VH$©-H$WZ (R) {X`m h¡& {ZåZ _| go 
ghr {dH$ën Mw{ZE : 
(a) A{^H$WZ (A) VWm VH$© (R) XmoZmo§ gË` h¢& VH$© (R), A{^H$WZ (A) H$s nyar ì`m»`m H$aVm h¡& 
(b) A{^H$WZ (A) VWm VH$© (R) XmoZmo§ gË` h¢& VH$© (R), A{^H$WZ (A) H$s ì`m»`m Zht H$aVm h¡& 
(c) A{^H$WZ (A) gË` h¡ naÝVw VH$© (R) AgË` h¡&  
(d) A{^H$WZ (A) AgË` h¡ O~{H$ VH$© (R)  gË` h¡& 
19. A{^H$WZ (A) : `{X {ÛKmV g_rH$aU 4x
2
 -  10x + (k - 4) = 0 H$m EH$ _yb Xÿgao 
_yb H$m ì`wËH«$_ h¡, Vmo k H$m _mZ 8 hmoJm&      
 VH©$ (R) : {ÛKmV g_rH$aU x
2
 -  x + 1 = 0 Ho$ _yb dmñV{dH$ h¢&   1 
 
20. A{^H$WZ (A) : d¥Îm Ho$ {H$gr q~Xþ na ñne© aoIm ñne© {~§Xþ go OmZo dmbr {ÌÁ`m na b§~ 
hmoVr h¡& 
 VH©$ (R) : EH$ d¥Îm Ho$ ~mha pñWV EH$ q~Xþ go Cg na ItMr JB© ñne© aoImAm| H$s bå~mB© 
EH$g_mZ hmoVr h¡&       1 
 
IÊS> - I 
IÊS> - I _| A{V bKw-CÎma (VSA) àH$ma Ho$ àíZ h¢ Am¡a àË`oH$ àíZ Ho$ 2 A§H$ h¢& 
21. (A) {ÛKmV g_rH$aU 3x
2
 - 2x + 
1
3
 = 0 H$m {d{dº$H$a kmV H$s{OE Am¡a {\$a BgHo$ _ybm|  
    H$s àH¥${V kmV H$s{OE&      2 
 AWdm 
 (B) {ÛKmV g_rH$aU x
2
 - x - 2 = 0 Ho$ _yb kmV H$s{OE&   2 
 
22. ~Jb _| ~Zr AmH¥${V _| H«$_e: OP, OQ Am¡a OR na pñWV 
{~ÝXþ A, B Am¡a C Bg àH$ma h¢ {H$ AB||PQ Am¡a AC||PR h¡& 
Xem©BE {H$ BC||QR h¡&  
 
 
 
 
 
23. `{X sin a = 
1
2
 h¡, Vmo (3 cos a - 4 cos
3
 a) H$m _mZ kmV H$s{OE&  2 
 
24. (A) Cg {~§Xþ Ho$ {ZX}em§H$ kmV H$s{OE Omo q~XþAm| A (-1, 7) Am¡a B (4, -3) H$mo Omo‹S>Zo  
   dmbo aoImI§S> H$mo Am§V[aH$ ê$n go 2 : 3 Ho$ AZwnmV _| {d^m{OV H$aVm h¡& 2 
AWdm