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14-430(B) Page 1 P.T.O.
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$
_wI-n¥ð >na Adí` {bIo§ &
Candidates must write the Q.P. Code on the title page of the answer-book.
Series #CDBA SET~
àíZ - nÌ H$moS> amob Z§. Q.P. Code Roll No.
ZmoQ> / NOTE : (i) (^) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 23 h¢ & Please check that this question paper contains 23 printed pages.
(ii) (^) H¥$nm Om±M H$a b| {H$ Bg àíZ-nÌ _| > 38 àíZ h¢ & Please check that this question paper contains 38 questions. (iii) (^) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ- nÌ H$moS H$mo narjmWu CÎma - nwpñVH$m Ho$ _wI - n¥ð> na {bI| & Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (iv) (^) H¥$nm àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma - nwpñVH$m _| àíZ H$m H«$_m§H$ Adí{bI| & Please write down the serial number of the question in the answer-book before attempting it. (v) (^) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ >H$m g_ {Xm Jm h¡ & àíZ-nÌ H$m {dVaU nydm©• _| 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a Bg Ad{Y Ho$ Xm¡amZ do CÎma- nwpñVH$m na H$moB© CÎma Zht {bI|Jo & 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.
J{UV (~w{Z`mXr)$
(Ho$db Ñ{ï>~m{YV narjm{W©`m| Ho$ {bE)
MATHEMATICS (BASIC) ( FOR VISUALLY IMPAIRED CANDIDATES ONLY) {ZYm©[aV g_` : 3 KÊQ>o A{YH$V_ A§H$ : 80 Time allowed : 3 hours Maximum Marks : 80
430(B)
14-430(B) Page 2
gm_mÝ` {ZX}e :
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m g™Vr go nmbZ H$s{OE :
(i) Bg àíZ - nÌ _| 38 àíZ h¢ & g^r àíZ A{Zdm`© h¢ &
(ii) `h àíZ- nÌ nm±M IÊS>m| _| {d^m{OV h¡ – H$, I, J, K Ed§ L> &
(iii) IÊS> H$ _| àíZ g§»m 1 go 18 VH$ ~hþ{dH$ënr (MCQ) VWm àíZ g§»`m 19 Ed§
20 A{^H$WZ Ed§ VH©$ AmYm[aV 1 A§H$ Ho$ àíZ h¢ &
(iv) IÊS> I _| àíZ g§»m 21 go 25 VH$ A{V bKw - CÎmar (VSA) àH$ma Ho$ 2 A§H$m| Ho$
àíZ h¢ &
(v) IÊS> J _| àíZ g§»m 26 go 31 VH$ bKw - CÎmar (SA) àH$ma Ho$ 3 A§H$m| Ho$ àíZ h¢ &
(vi) IÊS> K _| àíZ g§»m 32 go 35 VH$ XrK© - CÎmar (LA) àH$ma Ho$ 5 A§H$m| Ho$ àíZ h¢ &
(vii) IÊS> L> _| àíZ g§»`m 36 go 38 VH$ àH$aU AÜ``Z AmYm[aV 4 A§H$m| Ho$ àíZ h¢ &
àËoH$ àH$aU AÜ``Z _| Am§V[aH$ {dH$ën 2 A§H$m| Ho$ àíZ _| {Xm J`m h¡ &
(viii) àíZ- nÌ _| g_J« {dH$ën Zht {Xm Jm h¡ & `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J
Ho$ 2 àíZm| _|, IÊS> K Ho$ 2 àíZm| _| VWm IÊS> L> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {Xm Jm h¡ &
(ix) Ohm± Amdí`H$ hmo p = 7
(^22) br{OE, {X AÝWm Z {Xm Jm hmo &
(x) H¡$ëHw$boQ>a H$m Cn`moJ d{O©V h¡ &
IÊS> H$
Bg IÊS> _| ~hþ{dH$ënràíZ h¢, {OZ_| àËoH$ àíZ 1 A§H$ H$m h¡ &
- EH$ A^mÁg§»m Ho$ Hw$b JwUZIÊS>m| H$s g§»`m h¡ :
(A) 1 (B) 0
(C) 2 (D) 3
14-430(B) Page 4
- {X ~hþnX x^2 + ax + 2 H$m EH$ eyÝH$ 1 h¡, Vmo ‘a’ H$m _mZ h¡ :
(A) 5 (B) 3 (C) – 3 (D) – 5
- {X ~hþnX (k – 2)x^2 – 10x + 3 H$m EH$ eyÝH$ CgHo$ Xÿgao eyÝ`H$ H$m
ì`wËH«$_ h¡, Vmo ‘k’ H$m _mZ h¡ : (A) 3 (B) 5 (C) – 5 (D) – 3
- ‘k’ H$m dh _mZ {OgHo$ {bE g_rH$aUm| 3x + 5y = 2 VWm 9x + 15y = 2k
Ûmam {Zê${nV aoImE± nañna g§nmVr h¢, h¡ : (A) 3 (B) – 3 (C) 6 (D) – 6
- {X 3 Hw${g©m| VWm 1 _oμO H$m _yë₹ 900 h¡ VWm 5 Hw${g©m| Am¡a 3 _oμOm| H$m
_yë₹ 2100 h¡, Vmo EH$ Hw$gu H$m _yë h¡ : (A) ₹ 100 (B) ₹ 110 (C) ₹ 150 (D) ₹ 450
14-430(B) Page 5 P.T.O.
- If 1 is a zero of the polynomial x 2 + ax + 2, then ‘a’ is :
(A) 5 (B) 3 (C) – 3 (D) – 5
- If one zero of the polynomial (k – 2)x 2 – 10x + 3 is reciprocal of
the other, then the value of ‘k’ is : (A) 3 (B) 5 (C) – 5 (D) – 3
- The value of ‘k’ for which the lines represented by the
equations 3x + 5y = 2 and 9x + 15y = 2k coincide, is : (A) 3 (B) – 3 (C) 6 (D) – 6
- If 3 chairs and 1 table cost ₹ 900 and 5 chairs and 3 tables
₹ 2100, then the cost of one chair is : (A) ₹ 100 (B) ₹ 110 (C) ₹ 150
(D) ₹ 450
14-430(B) Page 7 P.T.O.
- The discriminant of the quadratic equation 8x 2 + 2x – 3 = 0,
is : (A) 100 (B) 92 (C) – 92 (D) 96
- The 30th^ term of the AP 10, 7, 4, ... is :
(A) 87 (B) 77 (C) – 77 (D) – 87
- The distance between the points A(0, – 1) and B(0, – 9) is :
(A) 6 (B) 8 (C) 4 (D) 2
- If (a, 6) is the mid-point of the line segment joining the points
A(– 7, 7) and B(– 3, 5), then the value of ‘a’ is : (A) 5 (B) – 4 (C) 2 (D) – 5
- The distance of the point P(3, – 5) from x-axis is :
(A) 3 units (B) 5 units (C) – 5 units (D) 34 units
14-430(B) Page 8
- Xmo g§H|$Ðr` d¥Îmm|^ _|, ~‹S>o d¥Îm H$s^ 24 cm b§~r Ordm, Am§V[aH$ d¥Îm, {OgH$s
{ÌÁm >5 cm h¡, H$s ñne© aoIm h¡ & ~mø d¥Îm H$s {ÌÁm h¡ :
(A) 13 cm
(B) 26 cm
(C) 601 cm
(D) 551 cm
- (^) `{X cos q = p q h¡, Vmo sin^ q^ ~am~a h¡ :
(A)
2 2
q q – p
(B) q p
(C)
q^2 – p^2 q
(D) 2 2
p q – p
- cos 60º – cosec 30º + tan 45º H$m _mZ h¡ :
(A) 1
(B) – 1 2
(C) 1 2
(D) – 1
14-430(B) Page 10
- {ZåZ ~§Q>Z _| ~hþbH$ dJ© H$s {ZMbr gr_m h¡ :
dJ© A§Vamb (^1) – 10 11 – 20 21 – 30 31 – 40 41 – 50
~ma§~maVm (^10 12 20 5 )
(A) 21
(B) 30·
(C) 21·
(D) 20·
- EH$ nmgm CN>mbZo na, 3 go ~‹S>r {df_ g§»m àmá hmoZo H$s àm{H$Vm h¡ :
(A) 1 6
(B) 1 3
(C) 1 2 (D) 0
- EH$ mÑÀN>m ê$n go MwZo JE brn df© _| 53 _§Jbdma hmoZo H$s àm{`H$Vm h¡ :
(A) 1 7
(B) 2 7
(C) 3 7
(D) 4 7
14-430(B) Page 11 P.T.O.
- For the following distribution, the lower limit of modal class is : Class Interval
Frequency 10 12 20 5 3
(A) 21 (B) 30· (C) 21· (D) 20·
- When a die is thrown, the probability of getting an odd number
greater than 3 is :
(A) 1 6
(B) 1 3
(C) 1 2 (D) 0
- The probability for a leap year (selected at random) will
contain 53 Tuesdays is :
(A) 1 7
(B) 2 7
(C) 3 7
(D) 4 7
14-430(B) Page 13 P.T.O.
- If the volumes of two spheres are in the ratio 125 : 64, then the
ratio of their surface areas is :
(A) 5 : 4 (B) 25 : 16
(C) 125 : 64
(D) 16 : 5
- Two cubes each of volume 64 cm 3 are joined end to end to form
a cuboid. The total surface area of the resulting cuboid is :
(A) 192 cm 2
(B) 160 cm 2 (C) 128 cm 2
(D) 176 cm 2
Questions number 19 and 20 are Assertion and Reason based
questions. Two statements are given, one labelled as Assertion (A)
and the other is labelled as Reason (R). Select the correct answer to
these questions from the codes (A), (B), (C) and (D) as given below.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
14-430(B) Page 14
- A{^H$WZ (A) : {ÌÁm 7 cm VWm D±$MmB© 12 cm dmbo EH$ e§Hw$ H$m AmVZ
616 cm^3 h¡ &
VH©$ (R) : {ÌÁm r VWm D±$MmB© h dmbo EH$ e§Hw$ H$m AmVZ 1 3
pr^2 h
hmoVm h¡ &
- A{^H$WZ (A) : EH$ nmgo H$mo EH$ ~ma |$H$Zo na, Cg na g_ g§»`m AmZo H$r
àm{`H$Vm 1 2
h¡ &
VH©$ (R) : EH$ nmgo H$mo |$H$Zo na Hw$b g§^m{dV n[aUm_m| H$s g§»m 6 h¡ VWm g_ g§»mE± 2, 4 d 6 h¢ &
IÊS> I
Bg IÊS> _| A{V bKw - CÎmar(VSA) àH$ma Ho$ àíZ h¢, {OZ_| àËoH$ àíZ 2 A§H$m| H$m h¡ &
- {ZåZ a¡{IH$ g_rH$aU `w½_ H$m hb kmV H$s{OE :
2x – 3y – 17 = 0 Am¡a 4x + y – 13 = 0
- nyUmªH$m| 1 go 50 _| go EH$ nyUmªH$ mÑÀN>m MwZm J`m & MwZo JE nyUmªH$ Ho$ 6 go
^mÁhmoZo H$s àm{H$Vm kmV H$s{OE &
- (a) `{X cosec q = 10 h¡, Vmo tan q VWm sec q Ho$ _mZ kmV H$s{OE &
AWdm
(b) {gÕ H$s{OE {H$ cos^4 A – sin^4 A = 2 cos^2 A – 1.
- D PQR H$s ^wOmAm| PQ VWm PR H$mo EH$ aoIm l , H«$_e: L VWm M na Bg
àH$ma H$mQ>Vr h¡ {H$ LM ½½ QR h¡ & `{X PQ = 12 cm, PR = 10 cm VWm PL = 7·2 cm h¢, Vmo PM H$s b§~mB© kmV H$s{OE &
14-430(B) Page 16
- (a) A^mÁ` JwUZIÊS>Z Ûmam 6, 72, 120 H$m _.g. (HCF) VWm b.g.
(LCM) kmV H$s{OE & AWdm
(b) {H$gr Iob Ho$ _¡XmZ Ho$ Mmam| Amoa EH$ d¥ÎmmH$ma nW h¡ & Bg _¡XmZ H$m EH$ MŠH$a bJmZo _| VrZ gmB{H$b gdmam| H$mo H«$_e: 30 {_ZQ>, 40 {_ZQ> VWm 48 {_ZQ> bJVo h¢ & {X do VrZm| EH$ hr ñWmZ go Am¡a EH$ hr g_ na àma§^ H$aHo$ EH$ hr {Xem | OmVo h¢, Vmo {H$VZo g` ~mX do nwZ: àma§{^H$ ñWmZ na {_b|Jo? IÊS> J
Bg IÊS> _| bKw - CÎmar(SA) àH$ma Ho$ àíZ h¢, {OZ_| àËoH$ Ho$ 3 A§H$ h¢ &
- (a) dh AZwnmV kmV H$s{OE, {Og_| q~Xþ (– 6, y), q~XþAm| A(– 3, – 1)
VWm B(–^ 8, 9)^ H$mo {_bmZo dmbo aoImIÊS> H$mo {d^m{OV H$aVm h¡ & y^ H$m _mZ ^r kmV H$s{OE & AWdm (b) `{X A(2, – 2), B(7, 3), C(11, – 1) VWm D(6, – 6) EH$ MVw^w©O ABCD Ho$ erf© h¢ Vmo kmV H$s{OE {H$ ABCD H¡$gm MVw^w©O h¡ &
- {gÕ H$s{OE {H$ 3 + 2 5 EH$ An[a_og§»m h¡, O~{H$ {X`m h¡ {H$ 5
EH$ An[a_og§»m h¡ &
- (a) `{X^ cos q + sin q = 2 cos q h¡, Vmo Xem©BE {H$
cos q – sin q = 2 sin q. AWdm
(b) {gÕ H$s{OE : (^) t
t a
an (^) + cot = 1 + tan + cot 1 – c to 1 – n
- {H$amE na nwñVH|$ XoZo dmbo {H$gr nwñVH$mbH$m àW_ VrZ {XZm| H$m EH$ {ZV {H$amm h¡ VWm CgHo$ ~mX àËoH$ A{V[aº$ {XZ H$m {H$amm AbJ h¡ & g[aVm Zo gmV {XZm| VH$ EH$ nwñVH$ aIZo Ho$ {bE ₹ 27 AXm {H$E, O~{H$ a{d Zo EH$ nwñVH$ N>: {XZm| VH$ aIZo Ho$ ₹ 24 AXm {H$E & {ZV {H$amm VWm àËoH$ A{V[aº$ {XZ H$m {H$am`m kmV H$s{OE &
14-430(B) Page 17 P.T.O.
- (a) Using prime factorization, find the HCF and LCM of 6, 72 and 120. OR (b) There is a circular path around a sports field. Three cyclists start from the same point and at the same time and go in the same direction. If they take 30 minutes, 40 minutes and 48 minutes respectively to complete one round of the field, after how many minutes will they meet again at the starting point?
SECTION C
This section comprises Short Answer (SA) type questions of 3 marks each.
- (a) Determine the ratio in which the point (– 6, y) divides the line segment joining the points A(– 3, – 1) and B(– 8, 9). Also, find the value of y. OR (b) If A(2, – 2), B(7, 3), C(11, – 1) and D(6, – 6) are the vertices of a quadrilateral ABCD, then find what type of quadrilateral ABCD is.
- Prove that 3 + 2 5 is an irrational number, given that 5 is an irrational number.
- (a) If cos q + sin q = 2 cos q, then show that cos q – sin q = 2 sin q. OR
(b) Prove that t
t a
an cot
- = 1 + tan + cot 1 – c to 1 – n
- A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Sarita paid ₹ 27 for a book kept for seven days, while Ravi paid ₹ 24 for a book he kept for six days. Find the fixed charge and the charge for each extra day.
14-430(B) Page 19 P.T.O.
- Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that Ð^ APB = 2^ Ð^ OAB.
- A vessel is in the form of a hollow hemisphere surmounted by a hollow cylinder of the same radius. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. SECTION D
This section comprises Long Answer (LA) type questions of 5 marks each.
- (a) The perimeter of a sector of a circle of radius 6·5 cm is 31 cm. Find the area of the sector. OR (b) A chord of a circle of radius 21 cm subtends an angle of 60º at the centre. Find the area of the minor segment of the circle. [Use 3 = 1·73].
- Find the sum of all integers between 50 and 500 which are divisible by 7.
- (a) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then show that the other two sides are divided by this line in the same ratio. OR (b) ABCD is a trapezium with AB ½½ DC and the diagonals intersect each other at the point O. Show that AO (^) =CO BO DO
- From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 30 cm high building are 45° and 60° respectively. Find the height of the transmission tower. [Use 3 = 1·732]
14-430(B) Page 20
IÊS> L>
Bg IÊS> | 3 àH$aU AÜ``Z AmYm[aV àíZ h¢ {OZ| àË`oH$ àíZ 4 A§H$m| H$m h¡ &
àH$aU AÜ``Z – 1
- em§V Ob _| EH$ _moQ>a ~moQ> H$s Mmb 25 km/h h¡ & 40 km H$s Xÿar V` H$aZo
Ho$ {bE `h ~moQ> D$na (Ymam Ho$ à{VHy$b) OmZo _|, ZrMo (Ymam Ho$ gmW) OmZo go 40 {_ZQ> A{YH$ boVr h¡ &
Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :
(i) {X Ymam H$s Mmb x km/h h¡, Vmo x Ho$ nXm| _| _moQ>a ~moQ> Ho$ D$na H$s {Xem _| OmZo H$s J{V ìº$ H$s{OE & 1
(ii) Cnw©º$ pñW{V H$mo x Ho$ ê$n _| {ÛKmV g_rH$aU _| ìº$ H$s{OE & 1
(iii) (a) Ymam H$s Mmb kmV H$s{OE & 2 AWdm
(b) {X Ymam H$s Mmb^ 10 km/h h¡, Vmo^ 40 km D$na H$s {Xem _| OmZo _| ~moQ> {H$VZm g_ boJr? 2
àH$aU AÜ``Z – 2
- ‘ñdÀN> ^maV A{^`mZ’ Ho$ A§VJ©V {Xëbr Ho$ EH$ BbmHo$ Ho$ Hw$N> Kam| Zo AnZo
BbmHo$ Ho$ EH$ ñHy$b _| Hw$N> nm¡Yo bJmH$a Bgo gw§Xa ~ZmZo H$m {ZU©{bm & {d{^Þ Kam| Ûmam {XE JE nm¡Ym| H$s g§»`m {ZåZ gmaUr _| Xr JB© h¡ :
{XE JE nm¡Ym| H$s g§»m 1 –^4 4 –^7 7 –^10 10 –^13 13 –^16 16 –^19 Kam| H$s g§»m 10 8 9 7 12 4
(i) _mÜ`H$ dJ© {b{IE & 1
(ii) ~hþbH$ dJ© {b{IE & 1
