GENERAL INSTRUCTIONS Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 1. The question paper consists of 40 Objective Questions, for each question you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) marks will be awarded. 2. It is mandatory to fill the required informations on the OMR Sheet. 3. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form are not allowed. 4. All rough work should be done only in the extra blank papers provided by the invigilator with the question paper. 5. Use Black or Blue Ball Pen to fill the bubbles on OMR Sheet. NAME OF THE CANDIDATE FATHER’S NAME SCHOOL NAME CLASS ROLL NO. MOBILE NO. Sign. of Student : ______________________ Sign. of Invigilator : ____________________ Siktaur Chauraha, Deoria Bypass Gorakhpur-273010, Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected] Time : 2 Hours. Maximum Marks : 120 Total Number of Questions : 40 HIGHER FOR CLASS-IX & X Ramanujan Olympiad by
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GENERAL INSTRUCTIONSPlease read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
1. The question paper consists of 40 Objective Questions, for each question you will be awarded 3 marks ifyou have darkened only the bubble corresponding to the correct answer and zero mark if no bubble isdarkened. In case of bubbling of incorrect answer, minus one (–1) marks will be awarded.
2. It is mandatory to fill the required informations on the OMR Sheet.3. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any
form are not allowed.
4. All rough work should be done only in the extra blank papers provided by the invigilator with the questionpaper.
5. Use Black or Blue Ball Pen to fill the bubbles on OMR Sheet.
NAME OF THE CANDIDATE
FATHER’S NAME
SCHOOL NAME
CLASS ROLL NO.
MOBILE NO.
Sign. of Student : ______________________
Sign. of Invigilator : ____________________
Siktaur Chauraha, Deoria Bypass Gorakhpur-273010,Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected]
Time : 2 Hours.Maximum Marks : 120Total Number of Questions : 40
HIGHER FOR CLASS-IX & X
Ramanujan Olympiad
by
Siktaur Chauraha, Deoria Bypass Gorakhpur-273010,Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected] 2
Class-IX & X1. 28 rose plants, 56 marigold plants 108 Shoeflower planted in rows such that each rowcontain the same numbes of trees of one variety only. Minimum number of rows in whichthe above trees may be planted is:(A) 24 (B) 48 (C) 21 (D) 56
2. The price of butter has increased by 50%. The percentage of reduction that a family should affect in the useof butter so as not to increase the expenditure on this account is :(A) 30% (B) 50% (C) 33.33% (D) 25%
3. If ,5.0x then which of the following has the smallest value?
(A) x/12 (B) x/1 (C) 2/1 x (D) x2
4. If 3d/e1/2,c/d2,b/c1/3,a/b and 1/4,e/f then what is the value of abc/def?(A) 3/8 (B) 27/8 (C) 3/4 (D) 27/4
Answer questions 5 and 6 on the basis of the information given below:A punching machine is used to punch acircular hole of diameter two units from asquare sheet of aluminium of width 2 units,as shown below. The hole is punchedsuch that the circular hole touches onecorner P of the square sheet and thediameter of the hole originating at P is inline with a diagonal of the square. P
5. The propotion of the sheet area that remains after punching is :(A) 8/)2( (B) 8/)6( (C) 4/)4( (D) 2/)2(
6. Find the area of the part of the circle (round punch) falling outside the square sheet.(A) 4/ (B) 2/)1( (C) 4/)1( (D) 2/)2(
Answer questions 7 and 8 on the basis of the information given below:An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Twopassengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs.2400respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggagecharge would have been Rs.5400.
7. What is the weight of Praja’s luggage?(A) 20 kg (B) 25 kg (C) 30 kg (D) 35 kg
8. What is the free luggage allowance?(A) 10 kg (B) 15 kg (C) 20 kg (D) 25 kg
9. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun atthe same instant, how many hours after Arun did Kiranmala start?(A) 3 (B) 3.5 (C) 4 (D) 4.5
10. When you reverse the digits of the number 13, the number increases by 18. How many other two-digitnumbers increase by 18 when their digits are reversed?(A) 5 (B) 6 (C) 7 (D) 8
11. A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawnmeeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of thesemi-circle (in sq. cm) will be :(A) 32 (B) 50 (C) 5.40 (D) 81
Siktaur Chauraha, Deoria Bypass Gorakhpur-273010,Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected] 3
Class-IX & X12. If 1,
ab
ba
then ?)b(a 33
(A) –1 (B) –3 (C) –2 (D) 013. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?
(A) 75 (B) 90 (C) 120 (D) 150
14. The value of m3n1m
1n3nmn2m3m
151066532
is equal to :
(A) 0 (B) 1 (C) m2 (D) none of these
15. The area of quadrilateralABCD in the given figure is :(A) 57 cm2
(B) 108 cm2
(C) 114 cm2
(D) 195 cm2
16. Value of 981
871
761
651
541
431
321
211
(A) 2 (B) 3 (C) 4 (D) 5
17. By using appropriate identity the value of 333 )8()17()25( will be :(A) 20480 (B) 25190 (C) 10200 (D) 36140
18. If )( ax is a factor of qpxx 2 and nmxx 2 then the value of a is :
(A) qnpm
(B) pmqn
(C) pmqn
(D) qnpm
19. If ,11914
4 a
a then find the value of .13
3
aa
(A) 20 (B) 56 (C) 36 (D) 7820. The total length of all the edges of a cube is X m. If the surface area of the cube is X m2, what is its volume?
(A) 2m3 (B) 8m3 (C) Xm3 (D) X3 m3
21. A square (shaded) is inscribed in a 3-4-5 right-angled triangle as shown.What fraction of the triangle’s areadoes it occupy?
(A) 2512
(B) 4924
(C) 21
(D) 4925
Siktaur Chauraha, Deoria Bypass Gorakhpur-273010,Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected] 4
Class-IX & X22. It is possible to construct a triangle PQR with :
(A) 00 25PQR,110PRQ3cm,RQPR
(B) 00 301PQR,20QPR5cm,QR4cm,PQ
(C) 00 30PRQ,60PQR6cm,QR3cm,PQ
(D) 6cmPR3cm,QR2cm,PQ
23. A solid cylinder has total surface area of 462 cm2. Its curved surface area is rd31
of the total surface area.
Then the radius of the cylinder is :(A) 7cm (B) 3.5cm (C) 9cm (D) 11cm
24. A 83 rectangle is cut into two piecesalong the dashed line shown. The twopieces are then rearranged to form aright-angled triangle. What is theperimeter of the triangle formed?(A) 22 (B) 23(C) 24 (D) 32
25. The number of integers N for which NN 2 is prime number is :(A) 1 (B) 2 (C) 0 (D) 3
26. The diagram shows an equilateraltriangle (shaded) with its vertices at themid-points of alternate sides of aregular hexagon. What is the ratio ofthe area of the triangle to the area ofthe hexagon?(A) 1 : 2 (B) 1 : 3(C) 4 : 9 (D) 3 : 8
27. If ,323 x then 33 1
xx
(A) 2 (B) 4 (C) 8 (D) 9
28. If ,3 cbax then the value of )()()(3)()()( 333 cxbxaxcxbxax is :
(A) cba (B) )()()( accbba (C) 0 (D) none of these
29. In fig., if chords AB andCD of the circle inter-sect each other at rightangles, then yx
(A) 045 (B) 060(C) 075 (D) 090
Siktaur Chauraha, Deoria Bypass Gorakhpur-273010,Contact no. : 9935703444, 9935585704, Website : www.aatmdeepvidyalaya.com, Email ID : [email protected] 5
Class-IX & XConsider a number N = 2 1 P 5 3 Q 4 (Qu. no. 30 to 31)30. Number of ordered pairs (P, Q) so that the number ‘N' is divisible by 9, is
(A) 11 (B) 12 (C) 10 (D) 8
31. Number of values of Q so that the number ‘N’ is divisible by 8, is(A) 4 (B) 3 (C) 2 (D) 6
32. If a two-digit number is divided by the number having same digits written in reverse order, we get 4 as quotientand 3 as remainder and if the number is divided by the sum of the digits then 8 as a quotient and 7 as aremainder is obtained. Find the number.(A) 71 (B) 51 (C) 17 (D) none
33. If (a2 + b2)3 = (a3 + b3)2 and ab 0 then the numerical value of ab
ba
is equal to ______
(A) 2/3 (B) 1/3 (C) 4/3 (D) 5/3
34. If a, b, c are real and distinct numbers, then the value of )()()()()()(
ac.cb.baaccbba 333
is :
(A) 1 (B) a b c (C) 2 (D) 3
35. Count the number ofcubes in the given figure.
(A) 14 (B) 12(C) 10 (D) 8
36. If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of(A) 0 (B) 1 (C) 69 (D) 35
37. Two identical circles intersect so that their centres, and the points at which they intersect, form a square ofside 1 cm. The area in sq. cm of the portion that is common to the two circles is
(A) 4/ (B) 12
(C) 5
(D) 1
38. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?(A) 1 or 7 (B) 2 or 14 (C) 3 or 21 (D) 4 or 28
39. The digits of a three digit number A are written in the reverse order to form another three digit number B. If B >A and B “ A is perfectly divisible by 7, then which of the following is necessarily true?(A) 100 < A < 299 (B) 106 < A < 305 (C) 112 < A < 311 (D) 118 < A < 317
40. In the following figure, the diameter ofthe circle is 3 cm. AB and MN are twodiameters such that MN isperpendicular to AB. In addition, CG isperpendicular to AB such that AE:EB= 1:2, and DF is perpendicular to MNsuch that NL:LM = 1:2. The length ofDH in cm is
(A) 122 (B) 2/))122((
(C) 2/))123(( (D) 3/))122((
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