Odisha HSC Paper 2014 Maths Part I

No. of Questions : 50
Booklet Sl. No. : ......................... PART – I
No. of Printed Pages : 16
OBJECTIVE
Roll No. of the Candidate 2014
AH Time : 1 Hour 15 Minutes
Full Marks : 50

REGULAR SET : A MTH
AR – 15 OBJECTIVE QUESTION BOOKLET MATHEMATICS
THE CANDIDATES SHALL TAKE THIS QUESTION BOOKLET (PART - I) AFTER
THE EXAMINATION OF THIS SUBJECT IS OVER AND HANDOVER THE OMR
ANSWER SHEET TO THE INVIGILATOR WHEN INSTRUCTED.
DNÿ ¨Àÿêäæ ÓÀÿç¯ÿæ¨{Àÿ FÜÿç ¨÷ɨ § †ÿ÷ ¨ëÖLç ÿæsç (¨æsö - I)Lÿë ¨Àÿêäæ$öêþæ{œÿ Óæ$ç{Àÿ {œÿ{¯ÿ >
DˆÿÀÿ üÿ”ösLç ÿë œÿçÀÿêäLÿZÿë œÿç{”öÉæœÿëÓæ{Àÿ ÜÿÖæ;ÿÀÿ LÿÀÿç{¯ÿ >
œÿç{”öÉæ¯ÿÁÿê INSTRUCTIONS
1. This question booklet contains 50 (fifty)
1> FÜÿç ¨÷ɧ¨†ÿ÷ ¨ëÖçLÿæ{Àÿ 50sç ¯ÿÜÿë¯ÿçLÿÅÿ DˆÿÀÿ ¯ÿçÉçÎ ¨÷ɧ Multiple Choice Questions (MCQ).
ÀÿÜÿçd>ç 2. Each question has four (4) answer choices,
2> ¨÷{†ÿ¿Lÿ ¨÷ÉÀ§ ÿ `ÿæ{Àÿæsç Ó»æ¯ÿ¿ DˆÿÀÿ ’ÿçAæ¾æBdç, {Ó$# out of which only one is correct.
3. Select the correct answer and darken the
þšÀÿë {SæsçF vÿçLÿú> appropriate circle completely in OMR sheet
3> ¨÷{†ÿ¿Lÿ ¨÷ɧÀÿ vÿçLÿú DˆÿÀÿsçLÿë ¯ÿædç OMR DˆÿÀÿ üÿ”ö{Àÿ with Blue/Black ball point pen only. Darken
$#¯ÿæ Óó¨õNÿ ¯ÿõˆÿsçLÿë LÿÁÿæ/œÿêÁÿ ¯ÿàÿ ¨F+ Lÿàÿþ ’ÿ´æÀÿæ only one circle and darkening two or more
circles shall lead to rejection of the answer.
Ó¸í‚ÿö µÿæ{¯ÿ LÿÁÿæ LÿÀÿ> {Lÿ¯ÿÁÿ {SæsçF ¯ÿõˆÿLÿë LÿÁÿæ LÿÀÿ> 4. Partial / incomplete darkened circles shall
’ÿëBsç ¯ÿæ A™#Lÿ ¯ÿõˆÿLÿë LÿÁÿæ Lÿ{àÿ †ÿæÜÿæ œÿæLÿ`ÿ {ÜÿæB¾ç¯ÿ> not be evaluated by the computer.
4> AæóÉçLÿ œÿêÁÿ/LÿÁÿæ LÿÀÿæ¾æB$#{àÿ †ÿæÜÿæ þš þíàÿ¿æߜÿ 5. The OMR answer sheets shall be evaluated
by the computer.
{ÜÿæB¨æÀÿç¯ÿ œÿæÜÿ] > 6. In case the OMR sheet is stained, torn,
5> OMR DˆÿÀÿ üÿ”öSÝë Lç ÿë Lÿ¸ë¿sÀÿ ’ÿ´æÀÿæ þíàÿ¿æߜÿ LÿÀÿæ¾ç¯ÿ> crumpled, mutilated, distorted, not properly
6> OMR üÿ”ö{Àÿ {Lÿò~Óç ’ÿæS àÿæSç${# àÿ, `ÿçÀÿæ üÿsæ $#{àÿ, printed in any manner or otherwise appears
defective, the same shall be returned imme-
{þæÝç þLÿ`ÿç {ÜÿæB$#{àÿ Lÿçºæ d¨æ AØÎ$#{àÿ †ÿæÜÿæLÿë diately to the invigilator and another correct
†ÿ†ÿúä~æ†ÿú ¨Àÿêäæ ’ÿæßç†ÿ´{Àÿ $#¯ÿæ œÿçÀÿêäLÿZÿë {üÿÀÿæB OMR sheet be obtained.
AæD {SæsçF vÿçLÿú OMR DˆÿÀÿ üÿ”ö þæSçœÿçA> 7. Verify carefully whether the No. of printed
pages, No. of questions, Set code etc. printed
7> FÜÿç ¨÷ɨ § †ÿ÷ ¨ëÖLç ÿæ D¨Àÿ ¨õÏæ{Àÿ þë’ÿ÷†ç ÿ $#¯ÿæ ¨õÏæÓóQ¿æ, on the cover page matched with this booklet.
¨÷ɧÓóQ¿æ, {Ósú{Lÿæxÿú Aæ’ÿç ¨÷†ÿç¨õÏæ{Àÿ vÿçLÿú Adç Lÿç In case of any defect/discrepancy, exchange
œÿæÜÿ] þçÁÿæBœÿçA> ¾’ÿç {Lÿò~Óç †ÿ÷ësç $æF {†ÿ{¯ÿ †ÿæÜÿæLÿë the defective one immediately to obtain
{üÿÀÿæB AæD {SæsçF vÿçLÿú ¨÷ɨ § †ÿ÷ Ó{èÿ Ó{èÿ þæSçœÿçA> another correct question booklet.
8. Write your Roll No. in the space provided. Do
8> ¨÷ɨ § †ÿ÷ ¨ëÖLç ÿæÀÿ D”çÎ ×æœÿ{Àÿ {Lÿ¯ÿÁÿ {Àÿæàÿ œÿºÀÿ {àÿQ> not write/scribble anything on any part of this
Àÿüÿ LÿÀÿç¯ÿæ×æœÿ ¯ÿ¿†ÿê†ÿ Aœÿ¿ {Lÿò~Óç ¨õÏæ{Àÿ {àÿQæ{àÿQ# booklet except the space provided for doing
LÿÀÿæ¾ç¯ÿœÿæÜÿ] > the rough work.
9. Discipline must be maintained in the
9> HÝçÉæ ¨Àÿêäæ ¨Àÿç`ÿæÁÿœÿæ AæBœÿú 1988 AœÿëÓæ{Àÿ examination hall as per the provisions of the
¨Àÿêäæ SõÜÿ{Àÿ Éæ;ÿçÉõ\ÿÁÿæ Àÿäæ LÿÀÿç¯ÿæ Aæ¯ÿÉ¿Lÿ> Odisha Conduct of Examination Act, 1988.
10> ¨Àÿêäæ {ÉÌ œÿ {Üÿ¯ÿæ ¨í¯ÿöÀÿë ¨Àÿêäæ$öêþæ{œÿ ¨Àÿêäæ 10. No candidate shall be allowed to leave the
examination hall before the examination is
SõÜÿ dæÝç¨æÀÿç{¯ÿ œÿæÜÿ]> œÿç{”öÉLÿ÷{þ DˆÿÀÿ LÿÀÿç$¯# ÿæ OMR over. The candidates must hand over the OMR
üÿ”ösçLÿë œÿçÀÿêäLÿZÿë ÜÿÖæ;ÿÀÿ LÿÀÿç{¯ÿ> sheet to the invigilator when instructed.

P.T.O.

Time : 1 Hour 15 Minutes Full Marks : 50
22 22
π Àÿ þíàÿ¿ œÿçA (Take π = )
7 7
FÜÿç ¯ÿçµÿæS{Àÿ 50sç ¨÷ɧ ’ÿçAæ¾æBdç > ¨÷{†ÿ¿Lÿ ¨÷ɧ ¨æBô `ÿæ{Àÿæsç ¯ÿçLÿÅÿ DˆÿÀÿ ’ÿçAæ¾æBdç >
{Ó$# þšÀÿë vÿçLÿú DˆÿÀÿsç ¯ÿædç OMRDˆÿÀÿ üÿ”ö{Àÿ $#¯ÿæ Ó¸õNÿ ¯ÿõˆÿsçLÿë
LÿÁÿæ/œÿêÁÿ ¯ÿàÿ ¨F+ Lÿàÿþ ’ÿ´æÀÿæ Ó¸í‚ÿöµÿæ{¯ÿ LÿÁÿæ LÿÀÿ>
In this Part 50 questions are given. Each question has four alternative
answers. Choose the correct answer from them and darken the
appropriate circle completely in the OMR Sheet with
the Blue/Black ball point pen.
¨÷{†ÿ¿Lÿ ¨÷ÉÀ§ ÿ þíàÿ¿ 1 A{s >
Each question carries 1 mark.
ÓþÖ ¨÷ÉÀ§ ÿ DˆÿÀÿ ’ÿçA >
Answer all questions.

1. 9x + y + 12 = 0 F¯ÿó 18x + ky + 24 = 0 ÓÜÿ ÓþêLÿÀÿ~ ’ÿ´ß Óèÿ†ÿ H œÿçµÿöÀÿÉêÁÿ
{Üÿ{àÿ k Àÿ þæœÿ {Lÿ{†ÿ ?
If the simultaneous equations 9x + y + 12 = 0 and 18x + ky + 24 = 0 are
consistent and dependent, then what is the value of k ?
(A) –1 (B) +1
(C) +2 (D) –2
2. œÿçþק xÿçsÀÿþçœÿæ+Àÿ þíàÿ¿ {Lÿ{†ÿ ?
What is the value of the following determinant ?

2 −1
3 2
(A) 7 (B) –7
(C) 4 (D) –4

AR -15 / P - I / MTH 2 Contd.

3. 3x + 4y = 10 H 2x – 2y = 3 ÓÜÿ ÓþêLÿÀÿ~ ’ÿ´ß ¨÷†ÿçLÿÅÿœÿ ¨÷~æÁÿê{Àÿ Óþæ™æœÿ LÿÀÿç¯ÿæ
¨æBô Lÿ'~ LÿÀÿç¯ÿ ?
What is to be done for solving the simultaneous equations 3x + 4y = 10
and 2x – 2y = 3 by the method of substitution ?
(A) ¨÷$þ ÓþêLÿÀÿ~Lÿë 2 ’ÿ´æÀÿæ H ’ÿ´†ç ÿêßLÿë 3 ’ÿ´æÀÿæ Së~œÿ LÿÀÿç¯ÿ
Multiply the first equation by 2 and the second one by 3
(B) ¨÷$þsçÀÿë x Àÿ þíàÿ¿ œÿç‚ÿöß LÿÀÿç ’ÿ´†ç ÿêßsç{Àÿ {àÿQ#¯ÿ
Determine the value of x from the first one and write it in the second
one
(C) ’ÿ´†ç ÿêß ÓþêLÿÀÿ~Lÿë ¨÷$þÀÿë ¯ÿç{ßæS LÿÀÿç¯ÿ
Subtract the second one from the first one
(D) Dµÿß ÓþêLÿÀÿ~Lÿë þçÉæB¯ÿ
Add both the equations together
4. x + y = 0 H x – y = 0 ÓÜÿ ÓþêLÿÀÿ~ ’ÿ´ßÀÿ S÷æüÿú AZÿœÿ Lÿ{àÿ {LÿDô ¯ÿç¢ÿë{Àÿ ¨ÀÿØÀÿLÿë {bÿ’ÿ
LÿÀÿç{¯ÿ ?
What is the point of intersection of the simultaneous equations x + y = 0
and x – y = 0 on a graph paper ?
(A) (0, 1) (B) (1, 0)
(C) (1, 1) (D) (0, 0)
5
5. ç æ†ÿ ÓþêLÿÀÿ~Àÿ þíÁÿ’ÿ´ßÀÿ ÓþÎç H Së~üÿÁÿ ¾$æLÿ÷{þ 4 H – æ ÓþêLÿÀÿ~sç
{SæsçF ’ÿ´W
2
{Lÿ{†ÿ ?
5
The sum and product of the roots of a quadratic equation are 4 and –
2
respectively. What is the equation ?
(A) 2x2 + 8x + 5 = 0 (B) 2x2 – 8x + 5 = 0
(C) 2x2 + 8x – 5 = 0 (D) 2x2 – 8x – 5 = 0

AR -15 / P - I / MTH 3 P.T.O.

6. x + x = 6 Lÿë FLÿ ’ÿ´W
ç æ†ÿ ÓþêLÿÀÿ~{Àÿ ¨÷LÿæÉ Lÿ{àÿ {Lÿ{†ÿ {Üÿ¯ÿ ?
What is x + x = 6 when expressed as a quadratic equation ?
(A) x2 – 13x + 36 = 0 (B) x2 + 13x + 36 = 0
(C) x2 + 12x + 36 = 0 (D) x2 – 12x + 36 = 0
7. 2x2 + kx + 3 = 0 ÓþêLÿÀÿ~{Àÿ k Àÿ þæœÿ {Lÿ{†ÿ {Üÿ{àÿ þíÁÿ ’ÿëBsç ¯ÿæÖ¯ÿ H Óþæœÿ
{Üÿ{¯ÿ ?
What should be the value of k show that the roots of the equation 2x2 + kx
+ 3 = 0 are real and equal ?

(A) 4 6 (B) 2 6

6
(C) 6 (D)
2
8. {SæsçF Aæ߆ÿ `ÿç†ÿ÷Àÿ {’ÿðW¿ö ¨÷×vÿæÀÿë 8 {Ó.þç. ¯ÿÝ H FÜÿæÀÿ {ä†ÿ÷üÿÁÿ 240 ¯ÿSö {Ó.þç.>
Aæ߆ÿ `ÿç†ÿ÷Àÿ {’ÿðW¿ö H ¨÷× œÿç‚ÿöß LÿÀÿç¯ÿæ ¨æBô œÿç{þ§æNÿ ÓþêLÿÀÿ~ þšÀÿë {LÿDôsç ¨÷¾fë ¿ ?
The length of a rectangle is greater than its breadth by 8 cm and its area
is 240 sq. cm. Which of the following equations is applicable to find its
sides ?
(A) x2 + 16x = 240 (B) 2x2 – 8x = 240
(C) 2x2 + 16x = 480 (D) 2x2 + 8x = 480
9. œÿçþৠÿçQ†# ÿ AœÿëLÿ÷þ þšÀÿë {LÿDôsç Óþæ;ÿÀÿ ¨÷S†ÿç{Àÿ œÿæÜÿ] ?
Which one of the following series is not in Arithmetic progression ?
1 2 3 4
(A) 1, 2, 3, 4, 5, ... (B) , , , , ...
3 3 3 3
(C) 1.1, 2.3, 3.5, 4.7, ... (D) – 3, –1, 0, 2, 4, ...

AR -15 / P - I / MTH 4 Contd.

10. {SæsçF Óþæ;ÿÀÿ ¨÷S†ÿçÀÿ ¨÷$þ ¨’ÿ – 3 H Óæ™æÀÿ~ A;ÿÀÿ 2 {Üÿ{àÿ, FÜÿæÀÿ ¨÷$þ 11sç
¨’ÿÀÿ ÓþÎç {Lÿ{†ÿ ?
The first term of an arithmetic progression is – 3 and common
difference is 2. What is the sum of its first 11 terms ?
(A) 154 (B) 77
(C) 44 (D) 20
11. (a + b), x H (a – b) A.P.{Àÿ $#{àÿ x Àÿ þæœÿ {Lÿ{†ÿ ?
If (a + b), x and (a – b) are in A.P. What is the value of x ?
(A) 2a (B) a
(C) b (D) 2b
12. Óþæ;ÿÀÿ ¨÷S†ÿç{Àÿ $#¯ÿæ {SæsçF AœÿëLÿ÷þÀÿ ¨÷$þ ¨’ÿ 4 H {ÉÌ ¨’ÿ 76 > F$#{Àÿ †ÿç{œÿæsç
þšLÿ $#{àÿ, ’ÿ´†ç ÿêß þšLÿsç {Lÿ{†ÿ ?
The first term of a series in arithmetic progression is 4 and last term is
76. In between them there are three arithmetic means. What is the
second arithmetic mean ?
(A) 18 (B) 22
(C) 36 (D) 40
13. {SæsçF þë’ÿ÷æLÿë 30 $Àÿ sÓú LÿÀÿç¯ÿæÀÿë ‘H’ {¾{†ÿ $Àÿ AæÓçàÿæ ‘T’ †ÿæÀÿ ’ÿëBSë~ $Àÿ AæÓçàÿæ>
P (T) Àÿ þíàÿ¿ {Lÿ{†ÿ ?
A coin was tossed 30 times. The number of times ‘T’ appeared was twice
the number of times ‘H’ appeared. What is the value of P (T) ?
(A) 20 (B) 10
2 1
(C) (D)
3 3

AR -15 / P - I / MTH 5 P.T.O.

14. {SæsçF xÿ¯ÿæ{Àÿ 5sç ’ÿÉ ¨BÓç, 3sç 25 ¨BÓç H 4sç ¨`ÿæÉ ¨BÓç Adç > {Ó$#Àÿë ¾’ÿõbÿæ
{SæsçF þë’ÿ÷æ DvÿæS{àÿ {SæsçF ¨`ÿæÉ ¨BÓç ¨æB¯ÿæÀÿ Ó»æ¯ÿ¿†ÿææ {Lÿ{†ÿ ?
There are 5, 10 paise coins, 3, 25 paise coins and 4, 50 paise coins in a
box. If one of these coins is lifted at random, then what is the probability
of getting a 50 paise coin ?
1 1
(A) (B)
12 6
1 1
(C) (D)
4 3
15. {SæsçF àÿëxÿë{SæsçLÿë ${Àÿ SÝæ Sàÿæ > ¾’ÿç E Ws~æsç ""üÿÁÿ FLÿ ¾ëS½ ÓóQ¿æ''Lÿë ¯ÿëlæF,
{†ÿ{¯ÿ E Ws~æsç Wsç¯ÿæÀÿ Ó»æ¯ÿ¿†ÿæ {Lÿ{†ÿ ?
A ludo die was thrown once. If the event E indicates ‘‘result is an even
number’’ then what is the probability of occurrence of the event E ?
1 1
(A) (B)
6 3
1 2
(C) (D)
2 3
16. {SæsçF àÿëxÿë{SæsçLÿë ’ÿëB$Àÿ SÝæB’ÿçAæSàÿæ > FÜÿæ ’ÿ´æÀÿæ ÓóQ¿æ ’ÿëBsçÀÿ {¾æSüÿÁÿ 6 ¨æB¯ÿæÀÿ
Ó»æ¯ÿ¿†ÿæ Lÿ{{†ÿ ?
A ludo die was thrown twice. What is the probability of getting the sum of
the numbers as 6 ?
5 2
(A) (B)
6 3
1 5
(C) (D)
9 36

AR -15 / P - I / MTH 6 Contd.

17. 8, 5, 6, 7, x H 4 àÿ²æZÿþæœÿZÿÀÿ þæšþæœÿ 6.5 {Üÿ{àÿ x Àÿ þæœÿ {Lÿ{†ÿ ?
If the mean of the scores 8, 5, 6, 7, x and 4 is 6.5, then what is the value
of x ?
(A) 9 (B) 10
(C) 11 (D) 12
18. ¨÷$þ 10sç S~œÿ ÓóQ¿æÀÿ þšþæ, ¨÷$þ 9sç S~œÿ ÓóQ¿æÀÿ þšþævÿæÀÿë {Lÿ{†ÿ {¯ÿÉê ?
By how much the median of the first 10 counting numbers is greater than
the median of the first 9 counting numbers ?
(A) 0 (B) 0.5
(C) 1 (D) 1.5
19. œÿçþק þšÀÿë {LÿDôsç SÀÿçÏLÿ œÿç‚ÿöß LÿÀÿç¯ÿæ ¨æBô vÿçLÿú Óí†ÿ÷ ?
Which one of the following is the correct formula for finding mode ?

þæšþæœÿ + þšþæ
(A) SÀÿÏ
ç Lÿ =
2
Mean + Median
Mode =
2
(B) SÀÿçÏLÿ = 2 þšþæ – 3 þæšþæœÿ
Mode = 2 Median – 3 Mean
(C) SÀÿçÏLÿ = 3 þšþæ – 2 þæšþæœÿ
Mode = 3 Median – 2 Mean
(D) SÀÿçÏLÿ = 2 (þšþæ – þæšþæœÿ)
Mode = 2 (Median – Mean)

AR -15 / P - I / MTH 7 P.T.O.

20. œÿçþ§ àÿ²æZÿþæœÿZÿÀÿ SÀÿçÏLÿ {Lÿ{†ÿ ?
What is the mode of the following scores ?
5, 6, 7, 7, 8, 9, 9, 9, 10, 10, 11, 12, 12, 12
(A) SÀÿçÏLÿ œÿæÜÿ] (No mode)
(B) 9

(C) 12

(D) Dµÿß 9 H 12 (Both 9 and 12)
n n
21. x1, x2, x3, ..., xn Àÿ þæšþæœÿ M A{s > ∑ ( xi − 5 ) = 60 F¯ÿó ∑ ( xi − 8 ) = 24 {Üÿ{àÿ,
i =1 i =1
n Àÿ þæœÿ {Lÿ{†ÿ ?
n
The mean of the scores x1, x2, x3, ..., xn is M. If ∑ ( xi − 5 ) = 60 and
i =1
n
∑ ( xi − 8 ) = 24, then what is the value of n ?
i 1
=

(A) 5 (B) 8

(C) 10 (D) 12

22. ’ÿëBsç ¯ÿç¢ÿë A H BÀÿ ×æœÿæZÿ ¾$æLÿ÷{þ (–1, –2) H (5, – 2) > {ÓþæœÿZÿ þš{Àÿ ’ÿíÀÿ†ÿæ
{Lÿ{†ÿ ?
The co-ordinates of two points A and B are (–1, – 2) and (5, – 2)
respectively. What is the distance between them ?

(A) 6 (B) 4 2

(C) 4 (D) 3 2

AR -15 / P - I / MTH 8 Contd.

23. ∆ ABCÀÿ A, B H C ¯ÿç¢ÿëþæœÿZÿÀÿ ×æœÿæZÿ ¾$æLÿ÷{þ (1, 2), (2, 4) H (3, 5) > AD FLÿ
þšþæ {Üÿ{àÿ D ¯ÿç¢ÿëÀÿ ×æœÿæZÿ {Lÿ{†ÿ ?
The co-ordinates of the points A, B, C of the ∆ ABC are (1, 2), (2, 4) and
(3, 5) respectively. If AD is a median then what is the co-ordinates of the
point D ?
(A) (5, 9) (B) (2.5, 4.5)
(C) (1.5, 3) (D) (2, 3.5)
24. {SæsçF {ÀÿQæQƒÀÿ þš¯ÿç¢ÿëÀÿ ×æœÿæZÿ (0, 0) > FÜÿæÀÿ FLÿ ¨÷æ;ÿ¯ÿç¢ÿëÀÿ ×æœÿæZÿ (2, 3) > Aœÿ¿
¨÷æ;ÿ¯ÿç¢ÿëÀÿ ×æœÿæZÿ {Lÿ{†ÿ ?
The co-ordinates of the mid-point of a line-segment is (0, 0). The co-
ordinates of one of the end-point is (2, 3). What is the co-ordinates of the
other end-point ?
(A) (– 3, –2) (B) (– 2, –3)
(C) (2, 3) (D) (3, 2)
25. (2, 10), (2, 5) H (a, – 2) ¯ÿç¢ÿë†ÿ÷ß FLÿ ÓÀÿÁÿ{ÀÿQæ{Àÿ A¯ÿ×ç†ÿ > a Àÿ þæœÿ {Lÿ{†ÿ ?
The three points (2, 10), (2, 5) and (a, – 2) are in one straight line. What
is the value of a ?
(A) 0 (B) 2
(C) 3 (D) – 2
4
26. ’ÿˆÿ `ÿç†ÿ÷{Àÿ P Q || BC > AP = AB, QC = 1.8 cm >
A 7
AC Àÿ {’ÿðW¿ö {Lÿ{†ÿ {Ó.þç. ?
P Q 4
In the given figure P Q || BC . AP =AB, QC = 1.8
7
B C
cm. What is the length of AC in cm ?

(A) 2.4 (B) 3.6

(C) 4.2 (D) 5.4

AR -15 / P - I / MTH 9 P.T.O.

27. A ’ÿˆÿ `ÿç†ÿ÷{Àÿ m ∠ BAD = m ∠ CAD > ∆ ABD H ∆ ACD Àÿ
{ä†ÿ÷üÿÁÿÀÿ Aœÿë¨æ†ÿ LÿæÜÿæ Ó{èÿ Óþæœÿ ?
(
( In the given figure m ∠ BAD = m ∠ CAD. Ratio of the
areas of the ∆ ABD and ∆ ACD is equal to which
B D C one of the following ?

(A) AC : AB (B) AB : DC

(C) BD : AC (D) AB : AC

28. P ’ÿˆÿ `ÿç†ÿ÷{Àÿ ∆ PQR ~ ∆ QRS > m ∠ PQR = 50°, m ∠ QSR
= 100° > m ∠ PRS = {Lÿ{†ÿ ?
S
In the given figure ∆ PQR ~ ∆ QRS. m ∠ PQR = 50°,
(

(
Q R m ∠ QSR = 100°. What is the measure of ∠ PRS ?

(A) 70° (B) 80°

(C) 90° (D) 100°

29. A ’ÿˆÿ `ÿç†ÿ÷{Àÿ XY || BC H AX : XB = 2 : 3 > ∆ AXY H
ç þú XYCB Àÿ {ä†ÿ÷üÿÁÿÀÿ Aœÿë¨æ†ÿ {Lÿ{†ÿ ?
s÷æ¨çfß
X Y
In the given figure XY || BC and AX : XB = 2 : 3.
What is the ratio of the areas of ∆ AXY and trape-
B C
zium XYCB ?

4 4
(A) (B)
25 21

4 2
(C) (D)
9 3

AR -15 / P - I / MTH 10 Contd.

30. ∆ ABC {Àÿ m ∠ A = 90° F¯ÿó AD ⊥ BC > BD = 2 {Ó.þç. H BC = 8 {Ó.þç.
{Üÿ{àÿ, AB = {Lÿ{†ÿ {Ó.þç. ?
In ∆ ABC, m ∠ A = 90° and AD ⊥ BC . If BD = 2 cm and BC = 8 cm,
then what is the length of AB in cm ?

(A) 2 3 (B) 3 2

(C) 4 (D) 4 3

31. {SæsçF {ÀÿQæQƒ Ó¯ÿöæ™#Lÿ {Lÿ{†ÿsç ¯ÿõˆÿÀÿ ¯ÿ¿æÓæ•ö {ÜÿæB¨æÀÿç¯ÿ ?
A line segment can be a radius of how many circles in the maxium ?
(A) 1 (B) 2
(C) 3 (D) 4

32. A
H ’ÿˆÿ `ÿç†ÿ÷{Àÿ O ¯ÿõˆÿÀÿ {Lÿ¢ÿ÷ H m AEB
¼ = 100° > m ∠ BDC =
E
D {Lÿ{†ÿ ?
B O
G In the given figure O is the centre and m AEB
¼ =
F
C 100°. What is the measure of ∠ BDC ?
(A) 40° (B) 50°
(C) 60° (D) 80°
33. {SæsçF ÓëÌþ ÌݵÿëfÀÿ ¨÷{†ÿ¿Lÿ ¯ÿæÜÿë FÜÿæÀÿ ¨Àÿç¯ÿõˆÿÀÿ ¨Àÿç™v# ÿæ{Àÿ AZÿœÿ LÿÀÿë$¯# ÿæ {Lÿæ~Àÿ
¨Àÿçþæ~ {Lÿ{†ÿ ?
What is the measure of the angle subtended by each side of a regular
hexagon at the circumference of its circum-circle ?
(A) 120° (B) 90°
(C) 60° (D) 30°

AR -15 / P - I / MTH 11 P.T.O.

34. {SæsçF ¯ÿõˆÿÀÿ FLÿ f¿æ ¯ÿõˆÿÀÿ {Lÿ¢ÿ÷{Àÿ 90° {Lÿæ~ DŒŸ Lÿ{Àÿ > ¯ÿõˆÿÀÿ ¯ÿ¿æÓæ•ö H f¿æÀÿ
{’ÿðW¿ö Àÿ Aœÿë¨æ†ÿ {Lÿ{†ÿ ?
A chord of a circle subtends a right angle at its centre. What is the ratio
of the lengths of the radius of the circle and the chord ?
(A) 2 : 1 (B) 1 : 2
(C) 2 :1 (D) 1 : 2
35. ’ÿëBsç ¯ÿÜÿç ØÉöê ¯ÿõˆÿ ¨÷†ÿç Ó¯ÿöæ™#Lÿ {Lÿ{†ÿæsç Óæ™æÀÿ~ ØÉöLÿ AZÿœÿ LÿÀÿæ¾æB¨æÀÿç¯ÿ ?
In the maximum how many common tangents can be drawn to two
externally tangent circles ?
(A) 1 (B) 2
(C) 3 (D) 4

36. ’ÿˆÿ `ÿç†ÿ÷{Àÿ O ¯ÿõˆÿÀÿ {Lÿ¢ÿ÷ F¯ÿó BA ØÉöLÿ Qƒ > m ∠ ACB =
O
110° {Üÿ{àÿ, m ∠ CAB = {Lÿ{†ÿ ?
C
B
In the given figure O is the centre of the circle and
A
BA is a tangent-segment. If m ∠ ACB = 110°, what
is the measure of ∠ CAB ?
(A) 20° (B) 30°
(C) 55° (D) 70°
37. C ’ÿˆÿ `ÿç†ÿ÷{Àÿ O ¯ÿõˆÿÀÿ {Lÿ¢ÿ÷ > OA || BC F¯ÿó OC || AB
{Üÿ{àÿ, m ∠ C = {Lÿ{†ÿ ?
B
O In the given figure O is the centre of the circle. If
A OA || BC and OC || AB , then what is the measure
of ∠ C ?
(A) 30° (B) 40°
(C) 50° (D) 60°

AR -15 / P - I / MTH 12 Contd.

38. ’ÿˆÿ `ÿç†ÿ÷{Àÿ OA = 8 {Ó.þç., OP = 17 {Ó.þç. > O ¯ÿõˆÿÀÿ {Lÿ¢ÿ÷
A {Üÿ{àÿ, P ¯ÿç¢ÿëÀÿë ¯ÿõˆÿ ¨÷†ÿç AZÿç†ÿ ØÉöLÿ QƒÀÿ {’ÿðW¿ö {Lÿ{†ÿ
{Ó.þç. ?
O P
In the given figure OA = 8 cm, OP = 17 cm. If O is
the centre of the circle then what is the length of the
tangent segment drawn from P to the circle in cm ?

(A) 8 (B) 15

(C) 17 (D) 25

39. A ’ÿˆÿ `ÿç†ÿ÷{Àÿ PA H PB ØÉöLÿ Qƒ > m ∠ PAB = {Lÿ{†ÿ ?
50° (
P In the given figure PA and PB are tangent-
B
segments. What is the measure of ∠ PAB ?
(A) 40° (B) 50°
(C) 65° (D) 75°
40. ’ÿëBsç ¯ÿõˆÿÀÿ ¨Àÿç™À# ÿ A;ÿÀÿ 88 {Ó.þç. H {ÓþæœÿZÿÀÿ ¯ÿ¿æÓæ•ö ’ÿ´ßÀÿ ÓþÎç 78 {Ó.þç. >
¯ÿõÜÿˆÿÀÿ ¯ÿõˆÿÀÿ ¯ÿ¿æÓæ•ö {Lÿ{†ÿ {Ó.þç. ?
The difference of the circumferences of two circles is 88 cm and the sum
of their radii is 78 cm. What is the radius of the bigger circle in cm ?
(A) 92 (B) 83
(C) 46 (D) 32
41. ’ÿëBsç FLÿ-{Lÿ¢ÿ÷Lç ÿ ¯ÿõˆÿÀÿ ¯ÿ¿æÓ ¾$æLÿ÷{þ 32 {Ó.þç. H 18 {Ó.þç. > DµÿßÀÿ ¨Àÿç™# A;ÿSö†ÿ
×æœÿÀÿ {ä†ÿ÷üÿÁÿ {Lÿ{†ÿ ¯ÿSö {Ó.þç. ?
The diameters of two concentric circles are 32 cm and 18 cm. What is
the area of the space included by their circumferences in sq. cm ?
(A) 550 (B) 1100
(C) 1650 (D) 2200

AR -15 / P - I / MTH 13 P.T.O.

42. {SæsçF ¨÷fç þúÀÿ µÿíþç FLÿ Óþ{Lÿæ~ê Óþ’ÿ´¯ç ÿæÜÿë †ÿ÷µç ÿëf > FÜÿæÀÿ Lÿ‚ÿöÀÿ {’ÿðW¿ö 8 2 {Ó.þç. >
¨÷fç þúÀÿ Daÿ†ÿæ 10 {Ó.þç. {Üÿ{àÿ, FÜÿæÀÿ Aæ߆ÿœÿ {Lÿ{†ÿ Wœÿ {Ó.þç. ?
The base of a prism is a right angled isosceles triangle whose
hypotenuse is 8 2 cm. If the height of the prism is 10 cm, what is the
volume in cubic cm ?
(A) 1280 (B) 640 2
(C) 640 (D) 320
43. {SæsçF {LÿæœÿúÀÿ Daÿ†ÿæ {SæsçF ÓçàÿçƒÀÿÀÿ Daÿ†ÿæ Ó{èÿ Óþæœÿ F¯ÿó {ÓþæœÿZÿÀÿ Aæ߆ÿœÿ
Óþæœÿ > {LÿæœÿúÀÿ ¯ÿ¿æÓ H ÓçàÿçƒÀÿÀÿ ¯ÿ¿æÓÀÿ Aœÿë¨æ†ÿ {Lÿ{†ÿ ?
The height of a cone is equal to the height of a cylinder and their volumes
are equal. What is the ratio of the diameters of the cone and cylinder ?
(A) 2 3 : 1 (B) 3 :1
(C) 1 : 3 (D) 1 : 2 3
44. ’ÿëBsç ÓþWœÿÀÿ ÓþS÷ ¨õφÿÁÿÀÿ {ä†ÿ÷üÿÁÿÀÿ A;ÿÀÿ 1050 ¯ÿSö {Ó.þç. > {ÓþæœÿZÿÀÿ ¯ÿæÜÿëÀÿ
{’ÿðW¿ö Àÿ Aœÿë¨æ†ÿ 4 : 3 {Üÿ{àÿ, ¯ÿõÜÿˆÿÀÿ ÓþWœÿÀÿ ¯ÿæÜÿëÀÿ {’ÿðW¿ö {Lÿ{†ÿ {Ó.þç. ?
The difference of the total surface areas of two cubes is 1050 sq. cm.
The ratio of the lengths of their sides is 4 : 3. What is the length of the
side of the bigger cube in cm ?
(A) 15 (B) 20
(C) 10 (D) 7.5
45. {SæsçF {SæàÿLÿÀÿ Aæ߆ÿœÿ {¾†ÿçLÿç Wœÿ {Ó.þç. †ÿæÜÿæÀÿ ¨õφÿÁÿÀÿ {ä†ÿ÷üÿÁÿ {ӆÿçLÿç ¯ÿSö {Ó.þç.
{Üÿ{àÿ, {SæàÿLÿÀÿ ¯ÿ¿æÓ {Lÿ{†ÿ {Ó.þç. ?
The volume of a sphere in cubic cm is equal to its surface area in square
cm. What is the diameter of the sphere in cm ?
(A) 8 (B) 6
(C) 4 (D) 3

AR -15 / P - I / MTH 14 Contd.

12
46. sinA = {Üÿ{àÿ, cotA Àÿ þæœÿ {Lÿ{†ÿ ?
13
12
If sinA = , what is the value of cot A ?
13
5 12
(A) (B)
12 5
5 17
(C) (D)
13 13
47. sin120° + tan 150° . cos135° Àÿ þæœÿ {Lÿ{†ÿ ?
What is the value of sin120° + tan 150° . cos135° ?
2 3 2 3
(A) (B)
3+ 2 3− 2
3− 2 3+ 2
(C) (D)
2 3 2 3
48. sec (90° + θ ) – cot (180° – θ ) Àÿ þæœÿ {Lÿ{†ÿ ?
2 2

What is the value of sec2 (90° + θ ) – cot2 (180° – θ ) ?
(A) 0 (B) 1
1
(C) –1 (D) –
2
1
49. tan A = H cot B = 3 {Üÿ{àÿ, A + B Àÿ þæœÿ {Lÿ{†ÿ ?
2
1
If tan A = and cot B = 3, what is the value of A + B ?
2
(A) 120° (B) 60°
(C) 45° (D) 30°
50. tan1° × tan2° × tan3° × ... × tan88° × tan89° = {Lÿ{†ÿ ?
tan1° × tan2° × tan3° × ... × tan88° × tan89° = How much ?
1
(A) (B) 1
3
(C) 3 (D) – 1

AR -15 / P - I / MTH 15 P.T.O.

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AR -15 / P - I / MTH 16 Contd.