P-09 Mathematics Past Paper PDF 2023
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2023
P-09
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This is a mathematics past paper from 2023. It includes various types of questions, including objective and short answer questions related to topics like equations, graphs, and geometry. The exam paper is for secondary school.
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Zm_m§H$ Roll No. Tear Here Sl.No. : No. of Questions – 23 P–09–Mathematics No. of Printed Pages – 15 àdo{eH$m narj...
Zm_m§H$ Roll No. Tear Here Sl.No. : No. of Questions – 23 P–09–Mathematics No. of Printed Pages – 15 àdo{eH$m narjm, 2023 PRAVESHIKA EXAMINATION, 2023 TEAR HERE TO OPEN THE QUESTION PAPER J{UV MATHEMATICS àíZ nÌ H$mo ImobZo Ho$ {bE `hm± \$m‹S>| g_` : 3 KÊQ>o 15 {_{ZQ> nyUmªH$ : 80 narjm{W©`m| Ho$ {bE gm_mÝ` {ZX}e … GENERAL INSTRUCTIONS TO THE EXAMINEES : 1) narjmWu gd©àW_ AnZo àíZ nÌ na Zm_m§H$ A{Zdm`©V… {bI| & Candidate must write first his / her Roll No. on the question paper compulsorily. 2) g^r àíZ hb H$aZo A{Zdm`© h¢ & All the questions are compulsory. 3) àË`oH$ àíZ H$m CÎma Xr JB© CÎma-nwpñVH$m _| hr {bI| & Write the answer to each question in the given answer-book only. 4) {OZ àíZmo§ ‘| AmÝV[aH$ IÊS> h¢, CZ g^r Ho$ CÎma EH$ gmW hr {bI|& For questions having more than one part, the answers to those parts `hm± go H$m{Q>E are to be written together in continuity. P–09–Mathematics 1222 [ Turn Over 2 5) àíZ nÌ Ho$ {hÝXr d A§J«oOr ê$nmÝVa ‘| {H$gr àH$ma H$s Ìw{Q> / AÝVa / {damoYm^mg hmoZo na {hÝXr ^mfm Ho$ àíZ H$mo hr ghr ‘mZ|& If there is any error / difference / contradiction in Hindi & English versions of the question paper, the question of Hindi version should be treated valid. 6) àíZ H$m CÎma {bIZo go nyd© àíZ H$m H«$_m§H$ Adí` {bI|& Write down the serial number of the question before attempting it. 7) àíZ H«$‘m§H$ 21 go 23 VH$ ‘| AmÝV[aH$ {dH$ën h¢& There are internal choices in Question Nos. 21 to 23. 8) AnZr CÎma-nwpñVH$m Ho$ n¥ð>m| Ho$ XmoZm| Amoa {b{IE& ¶{X H$moB© aµ\$ H$m¶© H$aZm hmo, Vmo CÎma-nwpñVH$m Ho$ A§{V‘ n¥ð>m| na H$a| Am¡a BÝh| {VaN>r bmBZm| go H$mQ>H$a CZ na "aµ\$ H$m¶©' {bI X|& Write on both sides of the pages of your answer-book. If any rough work is to be done, do it on last pages of the answer-book and cross with slant lines and write ‘Rough Work’ on them. 9) àíZ H«$‘m§H$ 21 H$m boIm{MÌ J«m’$ nona na ~ZmBE& Draw the graph of Question No. 21 on graph paper. P–09–Mathematics 1222 3 IÊS> - A SECTION - A (dñVw{Zð> Ed§ A{VbKwÎmamË_H$ àíZ) (Objective and Very Short Answer Type Questions) 1) {ZåZ dñVw{Zð> àíZm| Ho$ CÎma H$m ghr {dH$ën M`Z H$a CÎma nwpñVH$m _| {b{IE& Answer the following questions and write them in the answer book by selecting the correct option. i) 196 Ho$ A^mÁ¶ JwUZIÊ‹S>m| H$s KmVmo H$m ¶moJ’$b h¡ : A) 1 ~) 2 g) 4 X) 6 The sum of the powers of the prime factors of 196 is A) 1 B) 2 C) 4 D) 6 ii) ¶{X {ÛKmV g‘rH$aU x 2 kx 4 0 Ho$ ‘yb g‘mZ hmo, Vmo k H$m ‘mZ hmoJm - A) 1 ~) 2 g) 3 X) 4 If roots of the quadratic equation x 2 kx 4 0 are equal, then the value of k will be - A) 1 B) 2 C) 3 D) 4 P–09–Mathematics 1222 [ Turn Over 4 iii) {~ÝXþ (3, 4) H$s y-Aj go Xÿar hmoJr - A) 1 ~) 2 g) 3 X) 4 The distance of the point (3, 4) from the y - axis will be - A) 1 B) 2 C) 3 D) 4 iv) 3 x 2 y 11 H$mo gÝVwï> H$aZo dmbm ¶w½‘ h¡ - A) (1, 4) ~) (2, 3) g) (3, 5) X) (1, 3) The pair satisfying 3 x 2 y 11 is - A) (1, 4) B) (2, 3) C) (3, 5) D) (1, 3) v) {ÛKmV g‘rH$aU 3 3x 2 10 x 3 0 H$m {d{d{³VH$a hmoJm : A) 8 ~) 30 g) 46 X) 64 Discriminant of quadratic equation 3 3x 2 10 x 3 0 will be : A) 8 B) 30 C) 46 D) 64 P–09–Mathematics 1222 5 vi) ¶{X 18, a, b, –3 g‘mÝVa lo‹T>r ‘| h¡ Vmo a + b H$m ‘mZ hmoJm - A) 7 ~) 11 g) 15 X) 19 If 18, a, b, –3 are in A.P., then the value of a + b will be : A) 7 B) 11 C) 15 D) 19 vii) 3sec 45 cos 45 H$m ‘mZ hmoJm - A) 0 ~) 1 g) 2 X) 3 Value of 3sec 45 cos 45 will be : A) 0 B) 1 C) 2 D) 3 P–09–Mathematics 1222 [ Turn Over 6 viii) d¥Îm H$s dh Ordm {OgH$s bå~mB© d¥Îm H$s {ÌÁ¶m go XmoJwZr hmo, H$hbmVr h¡ - A) {ÌÁ¶IÊ‹S> ~) ì¶mg g) joÌ’$b X) n[a{Y A chord of a circle, whose length is twice the radius of the circle, is called : A) Sector B) Diameter C) Area D) Circumference ix) EH$ d¥Îm H$s {ÌÁ¶m 3.5 go‘r h¡, Vmo d¥Îm H$s n[a{Y hmoJr - A) 11 go‘r ~) 22 go‘r g) 33 go‘r X) 44 go‘r Radius of a circle is 3.5 cm. Find its circumference. A) 11 cm B) 22 cm C) 33 cm D) 44 cm x) KZ H$m gånyU© n¥ð>r¶ joÌ’$b 486 dJ© go‘r h¡, KZ H$s ^wOm H$m ‘mn hmoJm - A) 6 go‘r ~) 7 go‘r g) 8 go‘r X) 9 go‘r The total surface area of a cube is 486 cm2. Measure of side of the cube will be - A) 6 cm B) 7 cm C) 8 cm D) 9 cm P–09–Mathematics 1222 7 xi) ~§Q>Z 3, 5, 7, 4, 2, 1, 4, 3 Am¡a 4 H$m ~hþbH$ h¡ - A) 1 ~) 3 g) 4 X) 7 The mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3 and 4 is - A) 1 B) 3 C) 4 D) 7 xii) EH$ nmgo H$mo ’|$H$Zo na 4 go ~‹S>m A§H$ AmZo H$s àm{¶H$Vm kmV H$s{OE& 1 1 A) ~) 2 3 3 g) X) 1 4 In a throw of a die, determine the probability of getting a number more than 4 : 1 1 A) B) 2 3 3 C) D) 1 4 2) {ZåZ{b{IV àíZm| _| [aº$ ñWmZm| H$s ny{V© H$aVo hþE CÎmanwpñVH$m _| {b{IE& Fill in the blanks in the following questions and write them in the answerbook. i) 95 VWm 152 H$m ‘hÎm‘ g‘mndÎm©H$ (HCF) __________ h¢& Highest Common Factor (HCF) of 95 and 152 is __________. ii) d¥Îm na pñWV EH$ {~ÝXþ go ________ ñne© aoIm ItMr Om gH$Vr h¡& ________ tangent can be drawn from a point on the circle. P–09–Mathematics 1222 [ Turn Over 8 iii) cos 2 45 H$m ‘mZ _____________ h¡& The value of cos 2 45 is _____________. iv) d¥Îm VWm CgH$s ñne© aoIm Ho$ C^¶{ZîR> {~ÝXþ H$mo _______ H$hVo h¢& The common point of the circle and its tangent line is called __________. v) ¶{X 5, 7, 9, x H$m g‘mÝVa ‘mܶ 9 hmo, Vmo x H$m ‘mZ _________ hmoJm& If Arithmetic mean of a distribution 5, 7, 9, x is 9, then value of x will be _________. vi) Xmo nmgm| H$mo EH$ gmW ’|$H$Zo na A§H$m| H$m ¶moJ 7 AmZo H$s àm{¶H$Vm __________ hmoJr& In a single throw of two dice, probability of getting a total of 7 will be __________. 3) A{V bKwÎmamË_H$ àíZ&> Very short answer type questions. i) k Ho$ {H$g ‘mZ na g‘rH$aU ¶w½‘ 3 x 2 y 0 VWm kx 5 y 0 Ho$ AZÝV hb hm|Jo? For which value of k, linear pair 3 x 2 y 0 and kx 5 y 0 will have Infinite Solutions? ii) {ÛKmV g‘rH$aU ax 2 bx c 0 Ho$ ‘yb kmV H$aZo H$m lrYamMm¶© gyÌ {b{IE& Write the Sridharacharya formula to find roots of quadratic equation ax 2 bx c 0. iii) {H$gr g‘mÝVa lo‹T>r (A.P.) H$m àW‘ nX “a” Ed§ gmd©AÝVa “d ” hmo, Vmo nm±Mdm nX ³¶m hmoJm? What will be the Fifth term of a Arithmetic Progression (A.P.) whose First term is “a” and common difference is “d ”? P–09–Mathematics 1222 9 iv) g‘ê$n AmH¥${V¶m| H$mo n[a^m{fV H$s{OE& Define similar figures. 2 tan 30 v) H$m ‘mZ kmV H$s{OE& 1 tan 2 30 2 tan 30 Find the value of. 1 tan 2 30 vi) 1 cos 2 H$m ‘mZ 60 na kmV H$s{OE& Find the value of 1 cos 2 at 60. vii) 10 ‘rQ>a D±$Mr ‘rZma Ho$ {eIa go n¥Ïdr na EH$ {~ÝXþ H$m AdZ‘Z H$moU 30° h¡& {~ÝXþ H$s ‘rZma Ho$ AmYma go Xÿar {H$VZr hmoJr? From the top of 10 meter high tower, angle of depression at a point on earth is 30°. What will be the distance of point from the base of tower? viii) EH$ CÜdm©Ya N>‹S> H$s bå~mB© VWm BgH$s N>m¶m H$s bå~mB© H$m AZwnmV 1: 3 hmo, Vmo gy¶© H$m CÝZ¶Z H$moU kmV H$s{OE& If ratio of length of a vertical rod and length of its shadow is 1: 3 , then find the angle of elevation of Sun. ix) 3 go‘r {ÌÁ¶m boH$a EH$ d¥Îm ~ZmB©¶o VWm Ho$ÝÐ O go 5 go‘r Xÿa pñWV {~ÝXþ P go d¥Îm H$s Xmo ñne© aoImE± It{ME Am¡a CZH$m ‘mn {b{IE& Draw a circle with centre O and radius 3 cm and draw two tangents to the circle from a point P which is 5 cm away from its centre and write the measurement of them. P–09–Mathematics 1222 [ Turn Over 10 x) 5 go‘r bå~m EH$ aoImIÊ‹S> AB It{ME Ed§ Cgo 2 : 3 Ho$ AZwnmV ‘| {d^m{OV H$s{OE& XmoZm| ^mJm| H$m ‘mn {b{IE& Draw a line segment AB of length 5 cm and divide it into the ratio 2 : 3. Write the measurement of both the parts. xi) {H$gr d¥Îm H$m {ÌÁ¶IÊ‹S> Cg d¥Îm H$m MVwWmªe h¢, Vmo {ÌÁ¶IÊ‹S> ‘| Ho$ÝÐ na ~ZZo dmbo H$moU H$m ‘mn ³¶m hmoJm? If the sector of a circle is a quadrant of that circle, then what will be the measure of the angle formed by the sector on centre? xii) AÀN>r àH$ma go ’|$Q>r JB© 52 nÎmm| H$s EH$ JS²>‹S>r ‘| go EH$ nÎmm {ZH$mbm OmVm h¡& Bg nÎmo Ho$ Xhbm hmoZo H$s àm{¶H$Vm kmV H$s{OE& A card is drawn from a well shuffled deck of 52 cards. Find the probability of it being a ten. IÊS> - ~ SECTION - B 13 4) n[a‘o¶ g§»¶m H$m Xe‘bd àgma {b{IE& 125 13 Write down the decimal expansion of the rational number. 125 5) ~hþnX x 2 x 6 Ho$ eyݶH$ kmV H$s{OE& Find the zeroes of the polynomial x 2 x 6. P–09–Mathematics 1222 11 6) {ÛKmV g_rH$aU 4 x 2 12 x 9 0 Ho$ _ybm| H$s àH¥${V H$m nVm bJmB©¶o& Find out the nature of roots of the quadratic equation 4 x 2 12 x 9 0. 7) {~ÝXþAm| (0, 0) Am¡a (5, –3) H$mo OmoS>Zo dmbo aoImIÊ‹S> Ho$ ‘ܶ {~ÝXþ Ho$ {ZX}em§H$ kmV H$s{OE? Find the co-ordinates of the mid point of the line segment joining the points (0, 0) and (5, –3). 8) EH$ g‘Vb O‘rZ na I‹S>r ‘rZma H$s N>m¶m Cg pñW{V ‘| 40 ‘rQ>a A{YH$ bå~r hmo OmVr h¡ O~{H$ gy¶© H$m CÝZVm§e H$moU 60° go KQ>H$a 30° hmo OmVm h¡& ‘rZma H$s D±$MmB© kmV H$s{OE& The shadow of a tower on a level ground is increased by 40 meter, when the altitude of the Sun changes from 60° to 30°. Find the height of the tower. 9) 6 go‘r ^wOm Ho$ Zmn dmbo EH$ g‘~mhþ{Ì^wO H$s aMZm H$s{OE Am¡a {’$a EH$ Aݶ {Ì^wO H$s aMZm H$s{OE, 2 {OgH$s ^wOmE± {XE hþE {Ì^wO H$s g§JV ^wOmAm| H$s JwZr hm|& 3 Construct an equilateral triangle whose measurement of side is 6 cm and then 2 construct another triangle whose sides are times the corresponding sides of the 3 given equilateral triangle. 10) 4 go‘r {ÌÁ¶m Ho$ EH$ d¥Îm na Eogr Xmo ñne© aoImE± It{ME Omo EH$ Xÿgao Ho$ g‘mÝVa hmo& Draw a pair of tangents to a circle of radius 4 cm, which are parallel to each other. P–09–Mathematics 1222 [ Turn Over 12 11) ¶{X Xmo g‘ê$n {Ì^wOm| Ho$ joÌ’$b ~am~a hmo, Vmo {gÕ H$s{OE {H$ do {Ì^wO gdmªJg‘ hmoVo h¢? If the area of the two similar triangles are equal, prove that they are congruent? 12) EH$ d¥Îm H$s {ÌÁ¶m 7 go‘r h¡ VWm EH$ Mmn Ûmam Ho$ÝÐ na AÝV[aV H$moU 60° h¡& Bg {ÌÁ¶IÊ‹S> H$m joÌ’$b kmV H$s{OE& Radius of a circle is 7 cm and the angle subtended at the centre by an arc is 60°. Find the area of this sector. 13) EH$ e§Hw$ Ho$ {N>ÝZH$ H$s {V¶©H$ D±$MmB© 4 go‘r h¡ VWm BgHo$ d¥Îmr¶ {gam| Ho$ n[a‘mn (n[a{Y¶m±) 18 go‘r Am¡a 6 go‘r h¢& Bg {N>ÝZH$ H$m dH«$ n¥îR>r¶ joÌ’$b kmV H$s{OE& The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. 14) Xmoo KZm|, {OZ‘| go à˶oH$ H$m Am¶VZ 64 go‘r3 h¡, Ho$ g§b½Z ’$bH$m| H$mo {‘bmH$a EH$ R>mog ~Zm¶m OmVm h¡& n[aUm‘r KZm^ H$m n¥îR>r¶ joÌ’$b kmV H$s{OE& Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid. 15) {ZåZ ~maå~maVm ~§Q>Z H$m ‘mܶ kmV H$s{OE& x 1 2 3 4 5 6 f 2 4 5 4 2 2 Find the mean of the following frequency distribution. x 1 2 3 4 5 6 f 2 4 5 4 2 2 P–09–Mathematics 1222 13 16) EH$ {S>ã~o ‘| 8 bmb H§$Mo, 5 g’o$X H§$Mo Am¡a 2 hao H§$Mo h¢& Bg {S>ã~o ‘| go EH$ H§$Mm ¶mÑÀN>¶m {ZH$mbm OmVm h¡& BgH$s ³¶m àm{¶H$Vm h¡ {H$ {ZH$mbm J¶m H§$Mm : (i) bmb h¡? (ii) ham Zht h¡? A box contains 8 red marbles, 5 white marbles and 2 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out is : (i) red? (ii) not green? IÊS> - g SECTION - C 17) Eogo àW‘ 40 YZmË‘H$ nyUmªH$m| H$m ¶moJ kmV H$s{OE Omo 6 go {d^mÁ¶ h¡& Find the sum of the first 40 Positive Integers divisible by 6. 18) Cg {Ì^wO H$m joÌ’$b kmV H$s{OE {OgHo$ erf© (2, 3), (–1, 0) VWm (2, –4) h¡& Find the area of triangle whose vertices are (2, 3), (–1, 0) and (2, –4). 19) EH$ H$jm Ho$ N>mÌm| Ho$ n«mßVm§H$ {ZåZ ~§Q>Z ‘| {XE hþE h¢& BZH$m ‘mܶH$ kmV H$s{OE& àmßVm§H$ 0-10 10-20 20-30 30-40 40-50 N>mÌm| H$s g§»¶m 4 28 42 20 6 The marks of students of a class are given in following frequency distribution. Find their median. Marks Obtained 0-10 10-20 20-30 30-40 40-50 No. of Students 4 28 42 20 6 P–09–Mathematics 1222 [ Turn Over 14 20) Ho$ÝÐ O dmbo d¥Îm na ~mø {~ÝXþ T go Xmo ñne© aoImE± TP VWm TQ ItMr JB© h¡& {gÕ H$s{OE {H$ PTQ 2 OPQ h¡& Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that PTQ 2 OPQ. IÊS> - X SECTION - D 21) {ZåZ a¡{IH$ g_rH$aU `w½_ H$mo AmboIr` {d{Y Ûmam hb H$s{OE … x y 14 x y4 Solve the following pair of linear equations graphically : x y 14 x y4 AWdm/OR EH$ H$jm Ho$ 10 {dÚm{W©¶m| Zo J{UV H$s nhobr à{V¶mo{JVm ‘| ^mJ {b¶m& ¶{X bS>{H$¶m| H$s g§»¶m bS>H$m| H$s g§»¶m go 2 A{YH$ hmo, Bg pñW{V H$m ~rOJ{UVr¶ Ed§ J«m’$s¶ {Zê$nU H$s{OE& 10 students of a class took part in a mathematics quiz. If the number of girls is 2 more than the number of boys, represent the situation algebraically and graphically. 22) {gÕ H$s{OE {H$ : 1 cos A cosec A cot A 1 cos A Prove that : 1 cos A cosec A cot A 1 cos A AWdm/OR P–09–Mathematics 1222 15 {gÕ H$s{OE {H$ : sin A cosec A cos A sec A 7 tan 2 A cot 2 A 2 2 Prove that : sin A cosec A cos A sec A 7 tan 2 A cot 2 A 2 2 23) {ZåZ ~maå~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : dJ© 10-25 25-40 40-55 55-70 70-85 85-100 ~maå~maVm 6 20 44 26 3 1 Find the mode of the following frequency distribution : Class 10-25 25-40 40-55 55-70 70-85 85-100 Frequency 6 20 44 26 3 1 AWdm/OR {ZåZ ~maå~maVm ~§Q>Z H$m ‘mܶ kmV H$s{OE : dJ© 0-20 20-40 40-60 60-80 80-100 ~maå~maVm 6 10 13 7 4 Find the mean of the following frequency distribution : Class 0-20 20-40 40-60 60-80 80-100 Frequency 6 10 13 7 4 P–09–Mathematics 1222 E ER H NG I TH NY A TE RI W O T N DO
