each term of an A.P., then the resulting pattern of numbers is also an A.P.
A. Both statement I and statement II are true and statement II is the correct explanation of statement I.
B. Both statement I and statement II are true but statement II is not the correct explanation of statement I.
C. Statement I is true but statement II is false. D. Statement I is false but statement II is true. 50. For the following grouped frequency distribution,
which of the following options is INCORRECT? Class 3-6 6-9 9-12 12-15 15-18 18-21 21-24
Frequency 2 5 10 23 21 12 3
A. Lower limit of modal class is 12
B. Frequency of the class preceding the modal class = 10
C. Mode = 14.6 and width of the modal class is 4 D. All of these
Year 2014
8th
Class 10
8th IMO - Set A 2
1. Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations of numbers progress from left to right.
Rules:
(i) If an even number is followed by another even number, they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.
36 13 39 77 30 7
Which will be the outcome if the resultant of the second row is divided by the resultant of the first row? A. 12
B. 16 C. 8 D. 6
2. The given square grid shows the plan of a playground. The bench is North of the toy car.
See-saw Swing S Toy-car Bench R Slide Q P
The town council wants to plant a tree in the playground. The location of the tree is to be North of the swing and South-West of the slide. Identify the position where the tree will be planted.
A. P B. Q
C. R D. S
3. A dealer sold six cars – M, N, O, P, Q and R– during a period of Monday to Saturday, one car on each day.
(i) The car O was sold at least before three cars. (ii) The car R was sold on Tuesday.
(iii) Both the cars N and Q were sold at least before one car.
(iv) The car P was sold immediately after the car O. (v) At least four cars were sold after the car Q. If Mr. Jindal is purchased a car sold on Wednesday, then the car purchased by him is
A. M B. N C. O D. P
4. 'X + Y means 'Y is brother of X'; 'X × Y' means 'Y is husband of X'; 'X – Y' means 'X is mother of Y'; and 'X ÷ Y' means 'X is father of Y'. Then which of the following expressions indicates 'P is grandmother of T'?
A. Q – P + R ÷ T B. P × Q ÷ R – T C. P × Q ÷ R + T D. P + Q ÷ R – T
5. A trader in order to code the cost price of an article used the letters of PSIChOlAzY in the form of '0 to 9' respectively. If an article was sold for ` 1015.58 to earn the 16% gain, then which of the following code stands for cost price?
A. AIl.hP B. AIl.hS C. zYA.hO D. zAO.OP
6. Find the missing figure from the options which will continue the series in given Problem Figures.
A. B.
C. D.
7. An enterprising businessman earns an income of ` 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of
business, his income is _______. A. ` 29
B. ` 210
C. ` 10 D. ` 102
8. There is a certain rule followed in all the three figures. Identify the rule and find the missing number.
A. 6 B. 90
C. 540 D. 60
9. Identify the wrong figure in the given series.
A. Q B. S
C. R D. T
10. In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above tins of chocolates but below the rows of packets of chips, cakes are at the bottom and the bottles of peppermints are below the chocolates. The topmost row had the display of jam bottles. Where exactly are the bottles of peppermints from the top?
A. 2nd B. 3rd
C. 4th D. 5th
11. There is a certain relationship between figures P and Q. Identify the same relationship between figures R and S and find the missing figure from the options.
A. B.
C. D.
12. Count the number of circles used to draw the given figure.
A. 20 B. 21
C. 25 D. 17
13. Select the figure from the options in which Fig.(X) is exactly embedded as one of its part.
A. B.
C. D.
14. There are three figures X, Y and z showing a sequence of folding of a sheet of paper. Figure (z) shows the manner in which the folded sheet has been cut. Select the figure from the options which would resemble the unfolded form of paper.
A. B.
C. D.
15. A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smallest cubes of equal size. how many cubes have at least two green faces?
A. 8 B. 27 C. 44 D. 63
8th IMO - Set A 4
16. The given figure is created by using the arcs of quadrants with radii 1 cm, 2 cm and 3 cm. Find the total area of the shaded region. (Take p = 3.14)
A. 31.93 cm2 B. 15.96 cm2 C. 63.84 cm2 D. 13.68 cm2
17. In the given figure (not drawn to scale), AG is parallel to CD and AG= 2CD
7 . The point B on AC is such that BC= 2AC
7 . If the line BG meets AD at F and the line through C is parallel to BG which meets AD at E, then find the value of FG
EC. A. 1 7 B. 3 7 C. 4 7 D. 27
18. In the given figure (not drawn to scale), BD is a diameter of the circle with centre O. C and A are two points on the circle. BA and CD, when produced, meet at E. If ∠DOC = 60° and ∠ABD = 23°, then find ∠OBC.
A. 60° B. 30°
C. 45° D. 67°
19. Which of the following have non-terminating repeating decimal? A. 25 2 B. 2 7 C. 231 2 5 72× ×2 D. 1323 63×( )352
20. In the given figure (not drawn to scale), OABC is a quadrilateral with ABC on horizontal ground and O is vertically above A. M is the mid-point of BC. If ∠BAC = 90°, AB = AC = 16 cm and OA = 12 cm,
calculate the length of OB.
A. 25 cm B. 15 cm
C. 20 cm D. 28 cm
21. The given figure shows sector OAB with centre O and radius 54 cm. Another circle XYZ with centre P, is enclosed by the sector OAB. If ∠AOB = 60°. Find the area of OXPY.
A. 161 cm2 B. 461 cm2 C. 324 cm2 D. 561.2 cm2
22. If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2− 3and2+ 3, then find all the zeros.
A. –5, 7 B. –7, 5 C. 3, –5 D. 5, –3
23. Solve : (sin4 q – cos4 q + 1) cosec2q A. 1
B. –2 C. 2 D. 0
mathematical reasoning
24. What is the value of the median of the data using the graph in the figure given below, of less than ogive and more than ogive?
A. 8 B. 4
C. 5 D. 17.5
25. The number of zeroes for the given graph is ____.
A. 3 B. 2
C. 4 D. 1
26. Find the mode (approx.) from the given frequency distribution. Expenditure on food (in `) in a month Number of workers 300-309 310-319 320-329 330-339 340-349 350-359 360-369 370-379 10 20 24 38 48 27 17 6 Total 190 A. 336.41 B. 307.20 C. 343.22 D. 342.72
27. If the roots of the quadratic equation x2 + px + q = 0 are tan 30° and tan 15° respectively, then the value of 2 + q – p is ______.
A. 0 B. 1 C. 2 D. 3
28. Swati folded the three corners of a triangle. She managed to measure four of the angles as shown below before breaking her protractor. She needs help to figure out what the named angles are. Help her find f , g and h. f g h A. 52° 44° 47° B. 44° 52° 47° C. 44° 47° 52° D. 47° 44° 52°
29. Kunal arranged some metal blocks at the bottom of a tank as seen in the figure below. Then he filled the 30 cm by 25 cm by 25 cm tank with water. If each block is 4 cm long, 3 cm wide and 5 cm tall, then how much water is needed to fill the tank to 80% of the tank's height?
A. 15000 cm3 B. 2280 cm3 C. 12720 cm3 D. 16470 cm3
30. A number is chosen at random from 1 to 120. The probability of the number chosen being a multiple of 3 and 15 both is _____.
A. 1/15 B. 1/16
C. 1/17 D. 1/19
31. In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ∠OBA = 32°, then find the values of x and y respectively.
A. 32°, 58° B. 58°, 48° C. 58°, 58° D. 42°, 58°
8th IMO - Set A 6
32. In the given graph, line APB meets the x-axis at A and y-axis at B. P is the point (–4, 2) and
AP : PB = 1 : 2. Find the coordinates of A and B
respectively.
A. (–5, 0), (0, 5) B. (–6, 0), (0, 6) C. (–6, 0), (0, 5) D. (6, –6), (–6, 6) 33. let Sn denote the sum of the first 'n' terms of an A.P.
S2n = 3Sn. Then, the ratio S3n/Sn is equal to _____.
A. 4 B. 6 C. 8 D. 10
34. If x2 + px + q = 0 and x2 + qx + p = 0 have a common root, then ______.
A. p = q B. 1 + p + q = 0 C. p + q = 0 D. Both A and B
35. If the area of the triangle given below is 20 sq. units, then what are the co-ordinates of point C?
A. 0 40, a B. (a2 + b2, 0) C. 20 0b , D. 40 0b ,
everyday mathematics
36. A man walks a distance of 48 km in a given time. If he walks 2 km an hour faster, he will perform the journey 4 hours before. Find his normal rate of walking.
A. 4 km/hr B. 6 km/hr C. 3 km/hr D. 8 km/hr
37. Mohan ate half a pizza on Monday. he ate half of what was left on Tuesday and so on. he followed this pattern for one week. how much of the pizza would he have eaten during the week?
A. 99.22% B. 95%
C. 98.22% D. 100%
38. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2014 the price of commodity X was ` 4.20 and that of Y was ` 6.30, in which year commodity X will cost 40 paise more than the commodity Y?
A. 2024 B. 2021
C. 2022 D. 2023
39. The total monthly salary of 4 men and 2 women is ` 46,000. If a woman earns ` 500 more than a man, what is the monthly salary of a woman?
A. ` 6500 B. ` 7500 C. ` 8000 D. ` 9000
40. The members in a welfare committee decided to collect as many paise from each member of the committee as is the number of members. If the total collection amounts to ` 96.04, then the number of members in the committee is _______.
A. 84 B. 98
C. 102 D. 92
41. A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?
A. 4500 B. 4600
C. 4680 D. 4710
42. A housewife saved ` 2.50 in buying an item on sale. If she spent ` 25 for the item, then how much percent she saved in the transaction approximately?
A. 8% B. 9%
C. 10% D. 11%
43. Rajeev buys goods worth ` 6650. he gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
A. ` 6876.10 B. ` 6999.20 C. ` 6654 D. ` 7000
44. Twenty women can do a work in sixteen days and sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
A. 3 : 4 B. 4 : 3
C. 5 : 3 D. Data inadequate
45. A sum of money is borrowed and paid back in two annual installments of ` 882 each allowing 5% compound interest. The sum borrowed was _______.
A. ` 1620 B. ` 1640 C. ` 1680 D. ` 1700
achievers section
46. Which of the following statements is true?
Statement-1 : The area of the equilateral triangle
described on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles described on the other two sides of the triangle.
Statement-2 : The area of the equilateral triangle
described on the side of right angled isosceles triangle is half of the area of the equilateral triangle described on its hypotenuse.
A. Only statement-1 B. Only statement-2
C. Both statement-1 and statement-2 D. Neither statement-1 nor statement-2 47. Match the columns.
Column-I Column-II
(i) (sec2q + tan2q)2 – 4sec2qtan2q = (p) 9
(ii)
(tan cos
sec cos )
cos sec cot
2 2 2 2 2 60 4 45 3 30 5 90 30 60 30 ° + ° + ° + ° ° + °− ec °° (q) 8/17
(iii) If secq + tanq = 4, then cosq = (r) 4 (iv) tan5°tan85° + tan10°tan80° (s) 1
tan35°tan55° + tan25°tan65° =
A. (i) → (s), (ii) → (p), (iii) → (r), (iv) → (q) B. (i) → (s), (ii) → (p), (iii) → (q), (iv) → (r) C. (i) → (p), (ii) → (r), (iii) → (q), (iv) → (s) D. (i) → (q), (ii) → (p), (iii) → (s), (iv) → (r) 48. Which of the following situations do not form an
A.P.?
(i) The fee charged from a student every month by a school for the whole session when the monthly fee is ` 400.
(ii) The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ` 250 and it increases by ` 50 for the next higher class.
(iii) The amount of money in the account of Sanchi at the end of every year when ` 1000 is deposited at simple interest at the rate of 10% per annum.
(iv) The number of bacteria in a certain food item after each second, when they double themselves in every second.
A. Only (i) B. Only (ii) C. Both (ii) and (iv) D. Only (iv)
49. Find the mean, mode and median respectively of the following data. xi 58 59 60 61 62 63 64 65 66 fi 2 3 6 15 10 5 4 3 2 A. 51.72, 62, 61 B. 61, 62, 61 C. 61, 60, 61 D. 61.72, 61, 61 50. Fill in the blanks.
let a p
q
= be a rational number such that p and q are
P and the prime factorisation of q is not of the
form 2n × 5m, where n and m are whole numbers, then a has a decimal expansion which is Q and
R .
P Q R
A. Prime Non-terminating Non-repeating B. Co-prime Terminating Repeating C. Co-prime Non-terminating Repeating D. Prime Non-terminating Repeating
Year 2014
8th
Class 10
1. In the given letter series, some of the letters are missing which are given in that order as one of the options below it. Choose the correct option.
mnonopqopqrs A. knopq
B. oqrst C. pqrst D. qrstu
2. How many such pair of letters are there in the word PRODUCTION each of which has as many letters between them as in the English alphabet?
A. None B. One C. Two D. Three
3. In a certain code 'a friend of mine' is written as '4 9 1 6', 'mine lot of metal' is written as '3 1 0 9' and 'a piece of metal' is written as '7 1 6 3'. How can '8 7 3' be written in same code?
A. a metal piece B. metal for friend C. piece of advice D. large metal piece
4. Boys and girls are made to sit in 7 rows and 7 columns all of them facing West. P is at the centre of the arrangement, Q is just behind P, R is on the immediate left of Q, and S is to the West of P. Then R is in which direction with respect to S?
A. South-West B. North-West C. South-East D. Data inadequate
5. There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace the question mark in figure (iii).
?
(i) (ii) (iii) (iv)
A. B.
C. D.
6. Read the following information and answer the question given below :
(i) Four persons A, B, C and D eat Mango, Banana, Orange or Peach from Monday to Thursday. No two persons eat the same fruit on a day. Each of them eats only one fruit on a day and does not repeat it on any other day.
(ii) Neither C nor D eats orange or peach on Tuesday.
(iii) B eats banana on Wednesday. (iv) A eats peach on Monday.
(v) C does not eat mango on Thursday. (vi) D eats banana on Monday.
Which fruit does D eat on Thursday? A. Banana
B. Peach
C. Either banana or mango D. Either peach or orange
7. A, B, C, D, E and F are seated in a circle facing the centre. A and C are seated adjacent to each other and E and B are also seated adjacent to each other. B is to the immediate left of F. There are two persons between D and E. A is not seated adjacent to E. Who is to the immediate left of E?
A. C B. B C. F
D. Cannot be determined
8. The six faces of a cube are coloured, each with a different colour.
I. The white face is between yellow and green. II. The red face is adjacent to brown.
III. The green face is opposite the yellow side. IV. The blue face is adjacent to red.
V. The yellow face is the top face of the cube. The faces adjacent to white bear the colours A. Yellow, green, brown and red
B. Yellow, brown, blue and green C. Yellow, green, blue and red D. None of these
9. Find the correct mirror-image of the given word, if the mirror is placed vertically to the right.
d i s t u r b A. d i s t u r b B. b r tu is d C. bru st di D. bi s t u rd
LogicaL Reasoning
8th IMO - Set B 2
10. The given Venn diagram represents the students who study Physics, Chemistry and Mathematics. Identify the region which represents the students who study Physics and Mathematics but not Chemistry. P Q R S T U V X Y Z Physics Chemistry Mathematics A. T B. P + T + S C. V D. P + T + S + R + U + V
11. The given set of figures carry certain characters. Assuming that the characters in each set follow a similar pattern, identify the pattern and find the missing character. 72 27 33 43 29 39 45 73 30 31 44 29 42 43 79 40 10 20 59 ? 39 A. 49 B. 50 C. 60 D. 69
12. Three figures X, Y and Z shows a sequence of folding a sheet of paper. Figure Z shows the manner in which the folded sheet has been cut out. Select a figure from the options which most closely resembles the unfolded form of sheet.
X Y Z A. B. C. D. 13. Select a figure from the options which will continue the series established by the problem figures. A. B. C. D.
14. There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a figure from the options that would replace the question mark in figure (iv).
?
(i) (ii) (iii) (iv)A.
B.
C.
D.
15. How many such 1's are there in the given arrangement, each of which is immediately preceded by a perfect square? 1 8 5 9 4 7 1 2 5 8 3 6 5 9 2 7 6 4 5 2 9 2 6 4 1 2 3 5 1 4 2 8 3 A. None B. One C. Two D. Three
16. If one of the zeroes of the cubic polynomial
x3 + ax2 + bx + c is –1, then the product of the other
two zeroes is A. b – a + 1 B. b – a – 1 C. a – b + 1 D. a – b – 1
17. Solve for x and y : bx + ay = a + b,
ax a b a b by b a b a a a b 1 1 1 1 2 − − + + − − + = + A. x b a ab b y b a b = + + = + 2 2 2, 2 B. x a a b y b b a = − = − 2 , 2 C. x a b a ab y b a b = + + = −− 2 2 2 , 2 D. x = a2 + b2, y = 2ab + a2
18. If tanq + secq = l, then secq = l2nl+ , find m : n.m A. 1 : 2
B. 2 : 1 C. 4 : 1 D. 1 : 4
19. In DPQR, point M is on side PQ and point S is on the side PR such that QRSM is a trapezium. If MS : QR = 3 : 5, then find area (DPMS) : area (QRSM). A. 9 : 16 B. 10 : 17 C. 3 : 5 D. 9 : 25 20. The median of the given data is 50. Find the values of
p and q respectively, if the sum of all the frequencies
is 90. Marks Frequency 20-30 p 30-40 15 40-50 25 50-60 20 60-70 q 70-80 8 80-90 10 A. 4, 6 B. 7, 5 C. 5, 7 D. 9, 3 21. The given figure is made up of a large circle ABCDE with centre O, a small circle BQOP, two semi-circles and a sector OED. AC is 28 cm. Find the total shaded area of the figure.
A B C E P Q O D A. (198p – 98) cm2 B. (49p + 198) cm2 C. (150p + 100) cm2 D. (147p – 196) cm2
22. The sum of the remainders obtained when 2x3 + (p + 2)x + p – 2 is divided by x – 2 and when
it is divided by x + 1 is 0. Find the value of p. A. 3
B. –2 C. – 4 D. 8
23. Find the values of p and q respectively for which the equation 2x2 + px = q has root –3 and factor
(x – 5). A. –5, –25 B. – 4, 30 C. 5, –25 D. – 4, –30 24. Find the sum from the sixth term to the twelfth term of the arithmetic progression 6, 10, 14, …
A. 266 B. 240 C. 256 D. 276
25. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice.
A. 1/3 B. 11/36 C. 1/4 D. 13/36
MaTHeMaTicaL Reasoning
8th IMO - Set B 4
26. In the given diagram, ST is a tangent to the circle with centre O. Find the value of x. A. 25° B. 35° C. 40° D. 45° P Q R S O T x65° 70°
27. In the arithmetic progression 7, 10, 13, … how many terms will add up to a sum of 920?
A. 25 B. 16 C. 27 D. 23
28. A solid rectangular block has a square base with side ( 3− 2) .m The volume of the block is (3 18 7 3− ) .m 3 Find the height of the block in the form (a 2+b 3)m, where a and b are integers.
A. 3 2+ 3 B. 5 3 4 2+ C. 15 2+ 3 D. 5 5 3 3+ 29. Solve : 3(81)x + 3 = 9x + 1 + 9x. A. 3, 2 B. ±1/2 C. 4, 5 D. ±1
30. For a frequency distribution, mean, median and mode are connected by which of the following relations?
A. Mode = 3 Mean – 2 Median B. Mode = 2 Median – 3 Mean C. Mode = 3 Median – 2 Mean D. Mode = 3 Median + 2 Mean
31. Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is
A B O O A. 7 cm B. 3 7 cm C. 4 7 cm D. (8 + 2 7 ) cm
32. O is the centre of a circle of diameter 4 cm and
OABC is a square. If the shaded area is 1
3area of the square, then the side of the square is
A. p 3 cm B. 3p cm C. 3 p cm D. 3 p cm A B C O
33. Given below are the steps of construction of a pair of tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm. Find which of the following step is wrong?
Step-I : Take a point O on the plane paper and
draw a circle of radius OA = 4 cm. Also, draw a concentric circle of radius OB = 6 cm.
Step-II : Find the mid-point A of OB and draw a
circle of radius BA = AO. Suppose this circle intersects the circle of radius 4 cm at P and Q.
Step-III : Join BP and BQ to get the desired
tangents. A B C O P Q A. Only Step-I B. Only Step-II
C. Both Step-I and Step-II D. Both Step-II and Step-III 34. The value of a a b a a b a a b a a b + − − − + − − + − 2 2 2 2 2 2 2 2 is A. a b 2 2 B. b a 2 2 C. ab D. 2 2( a22 b2) b −
35. If the sums of n, 2n and 3n terms of an A.P. are S1,
S2 and S3 respectively, then SS3S
2 1 ( − ) is A. 0 B. 1 C. 2 D. 3