Mathematics (Regular) (Part - I) Sample Question Paper For HSC Examination, 2014
Mathematics (Regular) (Part - I) Sample Question Paper For HSC Examination, 2014
Mathematics (Regular) (Part - I) Sample Question Paper For HSC Examination, 2014
1. 50 multiple choice questions (MCQ) are given in part (A). All the questions are compulsory.
Each question carries 1 mark.
2. For each question select the correct alternative from four given alternatives to answer the
question and darken the circle O as l by ball pen (Blue / Black) against the alphabet
corresponding to that alternative in the given OMR sheet.
1 1
(A) 1 (B) (C) – (D) – 1
2 2
2
12. ~\ò ùMûUòG A.P. e Sn = 2n2 + 3n jêG ùZùa A.P. e iû]ûeY @«e .............ö [Space for rough work]
If Sn of an A.P. is 2n2 + 3n then the common difference of the A.P. is
.............I
(A) 13 (B) 4 (C) 9 (D) – 2
1 3 3 4
(A) (B) (C) (D)
3 7 4 7
2 1 1 1
(A) (B) (C) (D)
9 4 3 6
24. ‘a’ e ùKCñ cû^ _ûAñ P(3,a) Gaõ Q(4,1) aò¦ê c¤ùe \ìeZû 10 GKK ùja ?
For what value of ‘a’, the distance between the points P(3,a) and Q(4,1)
is 10 unit ?
(A) 4 (B) –3 (C) 2 (D) 0
4
25. ABCD PZêbêðRe gúhðaò¦êMêWÿòKe iÚû^ûu A(0,0), B(2,0), C (2,2) Gaõ D(0,2) [Space for rough work]
ùjùf PZêbêðRUò GK .............ö
(A) aMðPòZâ (B) e´iþ
(C) @ûdZPòZâ (D) Uâû_òRòdcþ
If the vertices of ABCD quadrilateral are A(0,0), B(2,0), C (2,2) and
D(0,2) then ABCD quadrilateral is a .............I
(A) square (B) Rhombus
(C) Rectangle (D) Trapezium
28. ùMûUòG aée GK Rýû, aée aýûiû¡ðe 2 MêY ùjùf aée iõ_éq lê\âPû_e
WòMâú _eòcû_ .......ö
If the length of chord of a circle is 2 times of its radius, then the
degree measure of the minor arc is ...............I
(A) 300 (B) 450 (C) 600 (D) 900
29. 10 ùi.cò. aýûiû¡ð aògòÁ ùMûUòG aéùe GK Rýû aée ùK¦âeê 6 ùi.cò. \ìeùe
[ôùf Rýûe ù\÷Nðý.......ö
A chord is at a distance of 6 cm from the centre of a circle of radius
10 cm. Then the length of the chord is .........I
(A) 4 cm. (B) 16 cm. (C) 8 cm. (D) 32 cm.
5
30. ùMûUòG aée A X B e WòMâú _eòcû_ 1400 ö A I B Vûùe @uòZ ÆgðK \ßde [Space for rough work]
ùQ\aò¦ê P ùjùf mÐAPB = ................ö
The degree measure of A X B is 1400 in a circle. If the tangents drawn
at A and B intersect at P then mÐAPB = ................I
(A) 400 (B) 500 (C) 200 (D) 300
31. GK aéùe _eòfòLòZ PZêbêðRe \êA aò_eúZ aûjêe ù\÷Nðýe icÁò 12 ùi.cò.
ùjùf PZêbêðRe _eòiúcû .........ö
The sum of the lengths of the two opposite sides of circumscribing
quadrilateral of a circle is 12 cm. Then the perimeter of the quadrilateral
is ...........I
(A) 48 cm. (B) 24 cm. (C) 12 cm. (D) 36 cm.
D C
32. _ûgßðiÚ PòZâùe AB aýûi Gaõ O aée ùK¦â ö
~\ò mÐADC = 1180 jêG A B
O
ùZùa, mÐBDC = ............. ö
In the given figure ‘O’ is the centre of the circle and AB is the diameter.
If mÐADC = 1180 then mÐBDC = ............. I
(A) 380 (B) 560 (C) 280 (D) 180
33. ùi.cò. aýûiû¡ð aògòÁ GK aéùe @«fòðLòZ icaûjê ZâòbêRe aûjêe ù\÷Nðý
‘r’
ùKùZ ?
The length of the side of an equilateral triangle inscribed in a circle of
radius r is .............I
34. 3 ùi.cò. aýûiû¡ð aògòÁ aé _âZò ajòüiÚ P aò¦êeê aé _âZò @uòZ ÆgðK L \ßd
PA Gaõ PB ö mÐAPB = 600 ùjùf PA e ù\÷Nðý ............ ö
PA and PB are the two tangents segments drawn from an external
point ‘P’ to a circle of radius 3 cm. If mÐAPB = 600 then the length of
PA is ....................I
6
35. _ûgßðiÚ PòZâùe aé _âZò T aò¦êùe @uòZ R [Space for rough work]
x
↔
ÆgðK PQ ö y = 2x Gaõ mÐRTP = 800 M y
O
ùjùf, mÐMTR = ...........ö 800
Q T P
↔
In the given figure is a tangent to the circle at T. If y = 2x and
PQ
0
mÐRTP = 80 then mÐMTR = ...........I
(A) 600 (B) 800 (C) 200 (D) 400
36. \êAUò _eÆeùQ\ú aé _âZò iaûð]ôK @uòZ ÆgðK iõLýû ùKùZ ?
The number of tangents can be drawn to two intersecting circles at
most is ............I
(A) 1 (B) 2 (C) 3 (D) G[ôeê ùKøYiòUò ^êùjñ (None of these)
1
37. DABC ~ DDEF Gaõ EF = BC ùjùf,
3
7
r [Space for rough work]
39. ùMûUòG ùKû^þe bìcòe aýûiû¡ð Gaõ aKâ CyZû ~[ûKâùc 2 ùi.cò. Gaõ l ùi.cò.
ùjùf, Gjûe icMâ _éÂZke ùlZâ`k ùKùZ aMð ùi.cò.?
r
If the radius of the base and slant height of a cone is cm and l cm
2
respectively, then the total surface area of the cone in square cm. is
.............I
FG l + r IJ
(A) 2prl (B) pr(l+r) (C) pr H 2 4K (D) 2pr(l + r)
40. \êAUò ùMûfKe @ûdZ^e @^ê_ûZ 64:27 ùjùf, ùicû^ue aýûie @^ê_ûZ
........ ö
If the ratio of the volumes of two spheres is 64:27 then the ratio of their
diameters is ..........I
(A) 16:9 (B) 8 :3 (C) 10 : 7 (D) 4 : 3
41. ~\ò ùMûUòG aéùe GK Pû_e WòMâú _eòcû_ 900 jêG, ùZùa Pû_ Gaõ aée
_eò]ôe @^ê_ûZ .......ö
If the degree measure of an arc of a circle is 900, then the ratio of the arc
to its circumference is ...........I
(A) 3 : 4 (B) 1:3 (C) 1:4 (D) 2 : 3
42. ùMûUòG ZâòbêRûKéZò bìcò aògòÁ _âòRòcþe bìcòe ùlZâ`k 30 aMð ùi.cò. Gaõ @ûdZ^
150 N^ ùi.cò ùjùf _âòRcþe CyZû............. ö
The triangular base area of a prism is 30cm2. If the volume of the prism
is 150 cm3, then its height is ............. I
(A) 10 cm (B) 15 cm (C) 5 cm. (D) 20 cm
5
43. ùMûUòG aéKkûe ùlZâ`k, iõ_ìð aée ùlZâ`ke 18
@õg ùjùf aéKkûe
Pû_e WòMâú _eòcû_ ............. I
5
If the area of a sector of a circle is parts of the area of the circle then,
18
the degree measure of the arc of the sector is .............I
(A) 1200 (B) 900 (C) 600 (D) 1000
8
44. ùMûUòG ùMûfKe _éÂZke ùlZâ`k 154 a.ùi.cò. ùjùf Gjûe aýûiû¡ð ùi.cò.ùe [Space for rough work]
...........ö 22
(p ~ 7 )
If the surface area of a sphere is 154 cm2 then, the radius of the sphere
22
................ cm I (p ~ 7 )
(A) 15 (B) 7.5 (C) 7 (D) 3.5
45. ùMûUòG iòfòeûKéZò ɸe _éÂZke ùlZâ`k 264 a.cò. Gaõ @ûdZ^ 924 N.cò.
ùjùf, ɸe bìcòe aýûi .............ö
The curved surface area of a cylindrical pillar is 264 m2. If the volume
of the pillar is 924 m3 then, diameter of the base is ................I
(A) 14 m. (B) 7 m. (C) 21 m. (D) 10.5 m.
46. (1+tan150) (1+tan300) e cû^ .............ö
The value of (1+tan150) (1+tan300) is ............I
(A) 1 (B) 0 (C) –1 (D) 2
47. cos(480+q) . cos(120 – q) – sin 480+q) . sin (120 –q) e cû^ .............ö
The value of cos(480+q) . cos(120 – q) – sin 480+q) . sin (120 –q)
is ...............I
1 1 3 3
(A) (B) – (C) (D) –
2 2 2 2
sin162 + cos153
0 0
48. e cû^ .............ö
cos72 0 − cos27 0
sin162 0 + cos1530
The value of is ...................I
cos72 0 − cos27 0