Rajasthan Board Praveshika Question Paper 2020 Mathematics

Zm_m§H$ Roll No.

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Sl.No. :

No. of Questions – 30 P–09–Mathematics
No. of Printed Pages – 11

àdo{eH$m narjm, 2020
PRAVESHIKA EXAMINATION, 2020

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J{UV
MATHEMATICS

àíZ nÌ H$mo ImobZo Ho$ {bE `hm± \$m‹S>|
g_` : 3¼ KÊQ>o
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| &
Candidates must write first his / her Roll No. on the question paper
compulsorily.
2) g^r àíZ 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 5320 [ Turn Over

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5) àíZnÌ 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) ^mJ> àíZ g§»¶m A§H$ à˶oH$ àíZ
A 1 - 10 1

~ 11 - 15 2

g 16 - 25 3

X 26 - 30 6

Part Q. Nos. Marks per question

A 1 - 10 1

B 11 - 15 2

C 16 - 25 3

D 26 - 30 6

7) àíZ H«$‘m§H$ 27 d 29 ‘| AmÝV[aH$ {dH$ën h¢&
There are internal choices in Question Nos. 27 and 29.

8) AnZr CÎma-nwpñVH$m Ho$ n¥ð>m| Ho$ XmoZm| Amoa {b{IE& ¶{X H$moB© a’$ 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$a CZ na "a’$ 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«$‘m§H$ 26 H$m boIm{MÌ J«m’$ nona na ~ZmBE&
Draw the graph of Question No.26 on graph paper.

P–09–Mathematics 5320

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^mJ> - A
PART - A

1) gyÌ {Z{Ib‘² H$m à¶moJ H$a 105 H$m dJ© kmV H$s{OE& [1]

Find the square of 105 by using ‘Sutra Nikhilam’.

2) {ZåZ g‘rH$aU H$m hb kmV H$s{OE& [1]

2 (x + 2) = 7 (x + 2)

Solve the following equation:

2 (x + 2) = 7 (x + 2)

3) Xmo g§»¶mAm| H$m JwUZ’$b 12960 h¡ VWm ‘hÎm‘ g‘mndV©H$ 18 hmo Vmo bKwÎm‘ g‘mnd˶© kmV H$s{OE&[1]
If product of two numbers is 12960 and HCF is 18 then find their LCM.

4) ‘mZ kmV H$s{OE …- 3 cos 30° – 4 cos3 30° [1]

Find the value :- 3 cos 30° – 4 cos3 30°

sec 36 ° sec 54 °
5) − H$m ‘mZ kmV H$s{OE& [1]
cosec 54 ° cosec 36 °

sec 36 ° sec 54 °
Find the value of cosec 54 ° − cosec 36 ° .

P–09–Mathematics 5320 [ Turn Over

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6) {H$gr {Ì^wO Ho$ erfm] go g‘XÿañW {~ÝXþ {b{IE& [1]

Write the point equidistant from the vertices of the triangle.

7) 5 go‘r. {ÌÁ¶m dmbo d¥Îm Ho$ Ho$ÝÐ go 13 go‘r. Xÿar na pñWV {~ÝXþ go ItMr JB© ñne© aoIm H$s bå~mB© kmV
H$s{OE& [1]

Find the length of tangent of circle with radius 5 cm drawn from the point 13 cm
away from the centre of the circle.

8) EH$ nmgo H$mo ’|$H$Zo na ‘4’ go N>moQ>m A§H$ AmZo H$s àm{¶H$Vm kmV H$s{OE& [1]

In a throw of a dice, find the probability of getting a number less than ‘4’.

9) dmhZm| Ho$ {b¶o Amdí¶H$ nr. ¶y. gr. H$m nyam Zm‘ {b{IE& [1]

Write the full name of P.U.C. which is essential for vehicles.

10) EH$ H$ma 3 {‘ZQ> ‘| nhbm, 6 {‘ZQ> ‘| Xÿgam, 9 {‘ZQ> ‘| Vrgam ¶mVm¶mV {g¾b nma H$aVr h¡, Vmo dh 13 dm±
{g¾b {H$VZo g‘¶ ‘| nma H$aoJr? [1]

A car passes through first signal in 3 minutes, second in 6 minutes, third in 9
minutes. In how much time it passes through 13th signal?

P–09–Mathematics 5320

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^mJ> - ~

PART - B

11) gyÌ namd˶© AmYm[aV {d{Y go {ZåZ H$mo hb H$s{OE& [2]

14885 ÷ 123

Solve the following by using ‘Sutra Paravartya’.

14885 ÷ 123

7
12) n[a‘o¶ g§»¶m H$m Xe‘bd àgma gm§V h¡ ¶m Agm§V AmdVu& {~Zm {d^mOZ à{H«$¶m H$m Cn¶moJ H$a kmV
80
H$s{OE& [2]

7
State whether the decimal expansion of a rational number is terminating or non
80
terminating recurring. Without performing the long division method.

13) 14 go‘r. {ÌÁ¶m Ho$ d¥Îm Ho$ {ÌÁ¶IÊS> Ûmam Ho$ÝÐ na AÝV[aV H$moU 90° h¡& d¥Îm Ho$ bKw {ÌÁ¶IÊS> Ho$ Mmn H$s
bå~mB© kmV H$s{OE& [2]

Angle subtended at the centre by the sector of a circle with radius 14 cm is 90°.
Find the length of the arc of the minor sector of the circle.

P–09–Mathematics 5320 [ Turn Over

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14) EH$ e§Hw$ Ho$ AmYma H$m ì¶mg 14 ‘rQ>a Am¡a {V¶©H$ D±$MmB© 25 ‘rQ>a h¡ Vmo e§Hw$ H$m gånyU© n¥ð>r¶ joÌ’$b kmV
H$s{OE& [2]
Find the total surface area of cone whose diameter of base is 14 m and slant height
is 25 meter.

15) EH$ grYo d 8 ‘rQ>a D±$Mo Iå^o Ho$ erf© na gr gr Q>r dr H¡$‘am Bg àH$ma bJm¶m J¶m h¡ {H$ 10 ‘rQ>a Xÿa Ñ{ï>
aoIm Ho$ AmJo ¶mVm¶mV XoIm Om gH$Vm h¡& Iå^o Ho$ Mmam| Amoa naN>mB© Ûmam {Z{‘©V d¥ÎmmH$ma joÌ H$m joÌ’$b kmV
H$s{OE& (π = 3.14 ) [2]
A CCTV camera has installed on the top of a straight pole of 8 meter height such
that forward traffic can be seen from the line of sight of 10 meter. Find the area of
circular path formed by shadow around the pole. (π = 3.14 )

^mJ> - g
PART - C

16) {ÛKmV ~hþnX x2 – 2x – 15 Ho$ eyݶH$ kmV H$s{OE Am¡a Bg ~hþnX Ho$ eyݶH$m| VWm JwUm§H$m| Ho$ ‘ܶ gå~ÝY
H$s g˶Vm H$s Om±M H$s{OE& [3]
Find the zeros of a quadratic polynomial x2 – 2x – 15 and verify the relationship
between the zeros and the coefficients of this polynomial.

17) ¶{X {H$gr g‘mÝVa lo‹T>r Ho$ Xÿgao Am¡a Vrgao nX H«$‘e… 24 VWm 28 hm| Vmo, lo‹T>r Ho$ nhbo 61 nXm| H$m ¶moJ’$b
kmV H$s{OE& [3]
If second and third terms of an A.P. are 24 and 28 respectively, then find the sum
of first 61 terms.

18) EH$ 12 ‘rQ>a D±$Mm no‹S> VoO hdm go Bg àH$ma Qy>Q> OmVm h¡ {H$ CgH$m erf© O‘rZ H$mo Ny>Zo bJVm h¡ Am¡a O‘rZ
Ho$ gmW 30° H$m H$moU ~ZmVm h¡& VoO hdm go no‹S>, O‘rZ go {H$VZr D±$MmB© go Qy>Q>m>, kmV H$s{OE& [3]
A vertical straight tree 12 meter high is broken by strong wind in such a way that its
top touches the ground and makes an angle of 30° with the ground. Find at what
height from the ground did the tree break.

P–09–Mathematics 5320

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19) EH$ hr AmYma BC na Xmo {Ì^wO ΔABC Ed§ ΔDBC ~Zo h¢& ¶{X AD d BC nañna O na à{VÀN>oX H$a|
Vmo {gÕ H$s{OE {H$ -

Δ ABC H$m jÌo’$b AO
= [3]
Δ DBC H$m jÌo’$b DO

ΔABC and ΔDBC are at the same base BC. If AD and BC intersect each other at
O then prove that -

area of Δ ABC AO
= .
area of Δ DBC DO

20) Xr JB© AmH¥ $ {V ‘| MVw ^ w © O ABCD ‘| AB = AC = AD hmo , Vmo {gÕ H$s{OE {H$
∠ BAD = 2( ∠ BDC + ∠CBD) . [3]

A

B

D

C
In the given figure a quadrilateral ABCD have AB = AC = AD, then prove that
∠ BAD = 2 ( ∠ BDC +∠CBD)

A

B

D

C

P–09–Mathematics 5320 [ Turn Over

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21) ΔABC H$s ^wOm BC H$mo EH$ d¥Îm {~ÝXþ P na ~mø ñne© H$aVm h¡ VWm Aݶ Xmo ^wOmAm| AB d AC H$mo
1
~‹T>mZo na H«$‘e… {~ÝXþ Q d R na ñne© H$aVm h¡, Vmo {gÕ H$s{OE {H$ AQ = ( AB + BC + CA )
2
[3]

A circle touches the side BC of ΔABC at point P externally and touches other two
sides AB and AC when produced at point Q and R respectively, then prove that
1
AQ = ( AB + BC + CA ) .
2

22) ΔABC Ho$ n[aJV d¥Îm H$s aMZm H$s{OE, O~{H$ BC = 6 go‘r., AB = 5 go‘r. Am¡a ∠ B = 60° hmo&
[3]

Construct a circumcircle of ΔABC, such that BC = 6 cm, AB = 5 cm and
∠ B = 60° .

23) EH$ d¥Îm H$s {ÌÁ¶m 21 go‘r. h¡ VWm Ordm Ûmam Ho$ÝÐ na AÝV[aV H$moU 90° h¡& Bg Ordm Ûmam ~Zo bKw d¥ÎmIÊS>
H$m joÌ’$b kmV H$s{OE& [3]

Radius of a circle is 21 cm and angle subtended by a chord at the centre is 90°.
Find the area of the minor segment formed by this chord.

24) EH$ YmVw H$m Jmobm {OgH$s {ÌÁ¶m 9 go‘r. h¡, H$mo {nKbmH$a 3 go‘r. {ÌÁ¶m Am¡a 6 go‘r. D±$MmB© Ho$ {H$VZo
~obZ ~ZmE Om gH$Vo h¢? [3]

How many cylinders of radius 3 cm and height 6 cm can be formed by melting
sphere whose radius is 9 cm?

P–09–Mathematics 5320

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25) EH$ W¡bo ‘| 5 g’o$X, 2 bmb d 3 H$mbr J|Xo h¢& Bg W¡bo ‘| go EH$ J|X ¶mÑÀN>¶m {ZH$mbr OmVr h¡& BgH$s ³¶m
àm{¶H$Vm h¡ {H$ {ZH$mbr JB© J|X ................... hmoJr& [3]

i) g’o$X

ii) bmb

iii) H$mbr

A bag contains 5 white, 2 red and 3 black balls. From this bag one ball is drawn
randomly. What is the probability that the drawn ball is _______.

i) White

ii) Red

iii) Black

^mJ> - X
PART - D

26) {ZåZ a¡{IH$ g‘rH$aU ¶w½‘ H$mo AmboIr¶ {d{Y Ûmam hb H$s{OE& [6]

4x – 5y = 20

3x + 5y = 15

BgH$s ghm¶Vm go ‘m’ H$m ‘mZ kmV H$s{OE O~{H$ 4x + 3y = m h¡&

Solve the following pair of linear equation by graphical method

4x – 5y = 20

3x + 5y = 15

With the help of this find the value of ‘m’ while 4x + 3y = m.

P–09–Mathematics 5320 [ Turn Over

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27) {gÕ H$s{OE& [6]

 1 − sin A  1
i)  =
 1 + sin A  sec A + tan A

( sinθ + cosecθ ) + ( cosθ + secθ ) = 7 + tan 2 θ + cot 2 θ
2 2
ii)

Prove that :

 1 − sin A  1
i)  =
 1 + sin A  sec A + tan A

( sinθ + cosecθ ) + ( cosθ + secθ ) = 7 + tan 2 θ + cot 2 θ
2 2
ii)
AWdm/OR
{gÕ H$s{OE& [6]
i) cos4 θ + sin 4 θ = 1 − 2cos2 θ sin 2 θ

2cos2A −1
ii) cot A− tan A =
sin A cosA

Prove that :
i) cos4 θ + sin 4 θ = 1 − 2cos2 θ sin 2 θ

2cos2A −1
ii) cot A− tan A =
sin A cosA

28) i) x-Aj na dh {~ÝXþ kmV H$s{OE Omo {~ÝXþAm| (–2, 3) Am¡a (–3, 4) go g‘mZ Xÿar na pñWV h¡&
Find the point on x-axis which is equidistant from the point (–2, 3) and (–3, 4).
ii) {~ÝXþAm| (11, 8) Am¡a (1, 3) H$mo {‘bmZo dmbr aoIm H$mo {~ÝXþ (7, 6) {H$g AZwnmV ‘| {d^m{OV H$aVm
h¡?
In which ratio, point (7, 6) divides the line joining the points (11, 8) and (1, 3).
[6]

P–09–Mathematics 5320

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29) {gÕ H$s{OE {H$ EH$ Mmn Ûmam d¥Îm Ho$ Ho$ÝÐ na AÝV[aV H$moU d¥Îm Ho$ eof ^mJ Ho$ {H$gr {~ÝXþ na AÝV[aV
H$moU H$m XmoJwZm hmoVm h¡& [6]

Prove that the angle formed by an arc on the centre of the circle is twice the angle
formed at any point of remaining part of the circle.

AWdm/OR

{gÕ H$s{OE H$s {H$gr MVw^w©O H$s EH$ ^wOm ~‹T>mZo na ~ZZo dmbm ~{hîH$moU AnZo AÝVam{^‘wI H$moU Ho$
~am~a hmo, Vmo dh EH$ MH«$s¶ MVw^w©O hmoVm h¡& [6]

Prove that an exterior angle formed by increasing side of a quadrilateral is equal to
the interior opposite angle, then it is a cyclic quadrilateral.

30) {ZåZ ~maå~maVm ~§Q>Z Ho$ ‘mܶ d ~hþbH$ kmV H$s{OE& [6]

dJ© 0-10 10-20 20-30 30-40 40-50

fi 6 10 13 7 4

Find the mean and mode of the following frequency distribution -

Class 0-10 10-20 20-30 30-40 40-50

fi 6 10 13 7 4



P–09–Mathematics 5320

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