LEVEL - 2
Year 2011-12
2 | 5 th IMO | LevelII | Class 10
SECTION I : LOGICAL REASONING
1. There are six persons A, B, C, D, E and F. C is the sister of F. B is the brother of E's husband. D is the father of A and grandfather of F. There are two fathers, three brothers and a mother in the group. Which of the following is a group of brothers?
(A) ABF (B) ABD (C) BFC (D) BDF
2. Anita, Mahima, Rajan, Lata and Deepti are five cousins. Anita is twice as old as Mahima. Rajan is half the age of Mahima. Anita is half the age of Deepti and Rajan is twice the age of Lata. If Mahima is 16 years old, then what is the age of Lata ?
(A) 4 years (B) 5 years (C) 7 years (D) 14 years
3. If second Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in that month?
(A) 25 (B) 22 (C) 24 (D) 23
4. If the same function is applied to reach the results in each of the three sets of numbers given then which number will replace the question mark in the third set of numbers?
(A) 24 (B) 30 21 5 17 7 24 28 13 16 2 25 7 10 8 30 ? (C) 36 (D) 40 5. If the first and the second letters of the word UNPRECEDENTED are interchanged with the last and the second last letters and similarly the third and the fourth letters are interchanged with the third and the fourth letters from the last respectively and so on, then what will be the seventh letter to the right of the third letter from the left end ?
(A) C (B) E (C) P (D) R
6. Ravi wants to go to the university. He starts from his home which is in the East and comes to a crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction is the university if all the four places are in different directions ?
(A) North (B) South (C) East (D) West
7. Find out the wrong term in the number series.
105, 85, 60, 30, 0, – 45, – 90
(A) 105 (B) 60 (C) 0 (D) – 45
8. Choose the numberletter group which is different from the others.
(A) M5S (B) B9L (C) T4Y (D) F4J
9. Select a figure from amongst the options which will continue the series established by the five problem figures.
Problem Figures
?
3 5 th IMO | LevelII | Class 10 | 10. In the question, there are seven figures, the first and last of which are unmarked and the remaining
are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five marked figures does not fit into the series. Select that figure from the options.
P Q R S T
(A) P (B) Q (C) R (D) T
11. In the given figure, if the triangle represents girls, the circle represents athletes, the rectangle represents boys and the square represents disciplined, then the boys who are athletes and disciplined are indicated by which number ? (A) 1 6 2 3 4 5 7 1 9 10 8 (B) 2 (C) 6 (D) 10 12. Five boys took part in a race. Raj finished before Mohit but behind Gaurav. Ashish finished before Sanchit but behind Mohit. Who won the race?
(A) Raj (B) Gaurav (C) Mohit (D) Ashish
13. In a certain coding system,
'816321' means 'the brown dog frightened the cat'; '64851' means 'the frightened cat ran away'; '7621' means 'the cat was brown'; '341' means 'the dog ran'.
What is the code for 'the dog was frightened'?
(A) 5438 (B) 8263 (C) 8731 (D) None of these
14. Choose that set of numbers from the options, that is similar to the given set : (9, 15, 21) (A) (10, 14, 16) (B) (7, 21, 28) (C) (5, 10, 25) (D) (4, 8, 12) 15. Find the missing number? 3C 27A 9B 2B ? 4A 4A 64B 16C (A) 8C (B) 12B (C) 16C (D) 18C
16. Find the odd one out.
(A) (B) (C) (D)
17. The question consists of a set of three figures X, Y and Z
X Y Z
showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of fig. (Z).
4 | 5 th IMO | LevelII | Class 10
18. Group the given figures into three classes using each figure only once.
1 2 3 4 5 6 7 8 9 (A) 1, 2, 5; 3, 7, 8; 4, 6, 9 (B) 1, 7, 2; 3, 9, 6; 4, 5, 8 (C) 2, 3, 8; 4, 6, 9; 1, 5, 7 (D) 5, 6, 9; 3, 4, 1; 2, 7, 8 19. When the given figure is folded to form a cube, how many dots would lie opposite the face bearing five dots?
(A) 1 (B) 2 (C) 3 (D) 4
20. Select a figure from the options which satisfies the same conditions of placement of the dots as in fig. (X).
Fig. (X)
(A) (B) (C) (D)
SECTION II : MATHEMATICAL REASONING
21. A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest. He received yearly interest of `130. But if he had interchanged the amounts invested, he would have received `4 more as interest. How much amount did he invest at different rates ?
(A) ` 700 at 12%, ` 500 at 10% (B) ` 700 at 10%, ` 500 at 12% (C) ` 700 each at 10% and 12% (D) ` 500 each at 10% and 12%
22. In D PQR, PD ^ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then (a + b)(a – b) = _____.
(A) 1 (B) (c + d)(d – c) (C) (c + d)(c – d) (D) 0
23. Two circles with radii a and b respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to these two circles. Then ___. (A) 1 - 1 = 1 a b c (B) 1 1 1 0 a + b + c = (C) + = 1 1 1 a b c (D) None of these 24. DABC is right angled at A. DEFG is a square inscribed in triangle as side DE is on BC and G & F
are two points at AB and AC respectively. Then DE 2 =
(A) BD ´ EC (B) BD = 2EC
A C B (C) 1 2 BD= EC (D) None of these
5 5 th IMO | LevelII | Class 10 | 25. If from twice the greater of two positive numbers 16 is subtracted, the result is half the other number.
If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers ? (A) 16, 8 (B) 12, 10 (C) 6, 8 (D) 10, 8 26. If P and Q are two points whose coordinates are (at 2 , 2at) and 2 2 , a a t t æ ö ç ÷ è ø respectively and S is the point (a, 0), then 1 1 SP+ SQis _____.
(A) Dependent of t (B) Independent of t (C) Independent of a (D) None of these
27. If T 1 , T 2 , T 3 , ..., T n are consecutive terms of an A.P., then
1 2 2 3 1 1 1 1 ... - + + + = n n T T T T T T ____. (A) 1 1 n n T T - × (B) 1 n n T T × (C) 2 1 ( 1) n T n T T - × (D) None of these 28. In the given figure, the diameters of two wheels have measures 2 cm and 4 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angle. (A) 4 cm each B A O C P D O¢ (B) 3 cm each (C) 5 cm each (D) 6 cm each
29. In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the approximate value of R.
(A) 5.4 cm A C B (B) 5.0 cm (C) 4.0 cm (D) 4.3 cm
30. A number is selected at random from the numbers :
5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46. Find the probability that the selected number is their average.
(A) 0 (B) 1 (C) 1
6 (D)
1 12
31. A cone is cut into two parts by a horizontal plane passing through the midpoint of its axis. The ratio of the volume of the upper part to the volume of lower part is ____.
(A) 1 : 7 (B) 1 : 8 (C) 7 : 1 (D) 7 : 8
32. The ratio of the areas of the right angled triangles ABC and DEF in which ÐA = 30°, ÐB = 90°, AC = 4 cm, ÐD = 60°, ÐE = 90° and DE = 4 cm is ___.
(A) 1 : 2 (B) 4 : 1 (C) 1 : 4 (D) 2 : 1
33. If (x + a) is a factor of the polynomial x 2 + px + q and x 2 + mx + n, then a = ___.
(A) - - n q m p (B) - - m q n p (C) - - n p m q (D) None of these
6 | 5 th IMO | LevelII | Class 10
34. If A is the area of a rightangled triangle and b is one of the sides containing the right angle, then the length of altitude on the hypotenuse is ____.
(A) + 4 2 2 4 Ab b A (B) 4+ 2 2 4 A b A (C) + 2 4 2 2 4 A b A (D) 4+ 2 2 4 b b A
35. Find the interrelationship of the variables for the quadratic equation y = ax 2 + bx + c from given
graph. (A) a + b + c = 0 x y (–1, 0) (2, 0) –x¢ y¢ (B) a – b + c = 0 (C) 2a + b + c = 0 (D) 4a – 2b + c = 0
36. The houses of a row are numbered consecutively from 1 to 49. If there is a x such that the sum of the numbers of the house preceding the house numbered x is equal to the sum of the numbers of the house following it. Find the value of x.
(A) 35 (B) 34 (C) 30 (D) 33
37. If sin cos andsin cos , then sin cos a q q b q q q q + + = = ____. (A) 2 2 1 a b a = - (B) 2 2 1 b a b = - (C) ab = b 2 – 1 (D) a + b = 1 38. In the given figure, PT is a tangent to the circle at T. If PA = 4cm and AB = 5 cm, find PT.
(A) 7 cm A B P T (B) 6 cm (C) 8 cm (D) 2 cm
39. Consider a cylinder of height n cm and radius 3 cm.
p A string of width h cm, when wound around the cylinder without keeping any space between two turns, covers the lateral surface of the cylinder completely. What is the required length of the string ?
(A) 6 n cm h (B) 12 cm h n (C) 36 cm n h (D) None of these
40. If a and b are roots of the equation A(x 2 + m 2 ) + Amx + cm 2 x 2 = 0, then A(a 2 + b 2 ) + Aab + ca 2b 2 =
____.
(A) 0 (B) 1 (C) –1 (D) None of these
SECTION III : EVERYDAY MATHEMATICS
41. Piyush gave onefourth of the amount he had to Mahesh. Mahesh in turn gave half of what he received from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount received by Suraj is ` 500, how much money did Mahesh receive from Piyush ?
(A) ` 100 (B) ` 200 (C) ` 400 (D) Data inadequate
42. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is ____.
7 5 th IMO | LevelII | Class 10 | 43. A, B and C start cycling around a circular path in the same direction at same time. Circumference
of the path is 1980 m. If the speed of A is 330 m/min, speed of B is 198 m/min and C is 220 m/min and they start from the same point, then after what time interval will they be together at the starting point?
(A) 30 mins (B) 9 mins (C) 90 mins (D) 60 mins
44. A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is ` 250 per quintal, the total monthly expenses are ` 1000 and when it is ` 240 per quintal, the total monthly expenses are ` 980. Find the total monthly expenses of the family when the cost of wheat is ` 350 per quintal.
(A) ` 1100 (B) ` 1200 (C) ` 1300 (D) ` 1500
45. In the Maths Olympiad at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes :
(i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) The other committed an error in the coefficient of x and he got the roots as 12 and 4. In the meantime, they realised that they were wrong and together they managed to get it right. Find the quadratic equation.
(A) x 2 + 4x + 14 = 0 (B) 2x 2 + 7x – 24 = 0 (C) x 2 – 14x + 48 = 0 (D) 3x 2 – 17x + 52 = 0 46. Hari wishes to determine the distance between two objects A and B, but there is an obstacle between
these two objects which prevents him from making a direct measurement. He devises an clever way to overcome this difficulty.
First he fixes a pole at a convenient point O so that from O, both A and B are visible. Then he fixes another pole at the point D on the line AO (produced) such that AO = DO. In a similar way he fixes a third pole at the point C on the line BO (produced) such that BO = CO. Then he measures CD which is equal to 170 cm. The distance between the objects A and B is ____.
A B D C O (A) 170 cm (B) 340 cm (C) 85 cm (D) None of these
47. A, B, C are three points on the same horizontal line and CT is a vertical pole. The angle of elevation of T, as seen from A, is x° and the angle of elevation of T, as seen from B is y°(y° > x°). If AB = d, then the height of the pole is ____.
(A) cos cos
sin( ) d x y y x ° ° ° - ° (B) tan tan tan tan d x y y x ° ° ° - ° (C) cos cos cos( ) d x y y x ° ° ° - ° (D) sin sin cos( ) d x y y x ° ° ° - °
48. A bucket is 40 cm in diameter at the top, 28 cm in diameter at the bottom and 21 cm deep. The cost of tin sheet used in making the bucket, if the cost of tin is ` 1.50 per sq. dm is ____.
(A) ` 32.25 (B) ` 40.25 (C) ` 44.25 (D) None of these
49. There are 100 transistors in a box. 20 of them are defective. At random two transistors are taken one by one consecutively without replacement. What is the probability that both of them are good ? (A) 316 495 (B) 19 495 (C) 16 99 (D) 32 99
8 | 5 th IMO | LevelII | Class 10
50. A boy is standing on the ground and flying a kite with 100 m length of string at an elevation of 30°. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.
(A) 50 3 m (B) 40 2 m (C) 50 m (D) 100 m
LEVEL - 2
Year 2012-13
2
| 6th IMO | Level-II | Class 10
Section-i : LogicaL ReaSoning
1. Study the following information carefully to answer the given question.M K K i D n e t t Q o B F H a a g t U U X W L S R i
each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for i and so on.
Value of a is exactly equal to the total value of which of the following pairs ?
(i) Do (ii) Qe (iii) MH
(a) Only (i) (B) Only (ii) (c) Only (iii) (D) Both (i) and (ii) 2. Seven villages a, B, c, D, e, F and g are situated as follows:
e is 2 km to the west of B. F is 2 km to the north of a. c is 1 km to the west of a. D is 2 km to the south of g. g is 2 km to the east of c. D is exactly in the middle of B and e.
How far is e from F (in km)?
(a) 4 (B) 20 (c) 5 (D) 26
3. in the given diagram, the circle stands for educated, square for hard-working, triangle for urban and the rectangle for honest people. Different regions in the diagram are numbered from 1 to 12. Region 4 is best described as consisting of ______.
(a) People who are non-urban, honest, uneducated and hard-working. (B) People who are uneducated, urban, honest and hard-working. (c) People who are uneducated, urban, hard-working and dishonest. (D) People who are urban, hard-working, honest and educated.
4. Read the following information carefully to answer the given question.
Fifty books belonging to different subjects, viz. History (8), geography (7), Literature (13), Psychology (8) and Science (14), are placed on a shelf. they are arranged in an alphabetical order subject to the condition that no two books of the same subject are placed together so long as books of other subjects are available. Unless otherwise mentioned, all counting is done from the left. Counting from the right end, the fifth book from the right of 39th book is ______.
(a) History (B) Psychology (c) Geography (D) Science
5. if the word teRMination is coded as 12345671586, what should be the code for the word Motion?
(a) 438586 (B) 458586 (c) 481586 (D) 485186
6. Read the following information carefully and answer the question given below it .
(i) A, B, C, D and E are five friends. (ii) B is elder to E, but not as tall as C. (iii) c is younger to a, and is taller to D and e. (iv) a is taller to D, but younger than e. (v) D is elder to a but is shortest in the group.
Which of the following statements is correct about B? (i) B is not the tallest.
(ii) B is shorter to e.
(iii) When they are asked to stand in ascending order with respect to their heights, B is in the middle.
3 6th IMO | Level-II | Class 10 | 7. Pointing to a photograph, a person tells his friend, "She is the grand daughter of the elder brother
of my father." How is the girl in the photograph related to this man?
(a) Niece (B) Sister (c) Aunt (D) Sister-in-law
8. Study the following information and answer the question given below it .
the admission ticket for an exhibition bears a password which is changed after every clock hour based on set of words chosen for each day. the following is an illustration of the code and steps of rearrangement for subsequent clock hours. The time is 9 a.m. to 3 p.m.
Batch I (9 a.m. to 10 a.m.) : is not ready cloth simple harmony burning Batch II (10 a.m. to 11 a.m.) : ready not is cloth burning harmony simple Batch iii (11 a.m. to 12 noon) : cloth is not ready simple harmony burning Batch iV (12 noon to 1 p.m.) : not is cloth ready burning harmony simple Batch V (1 p.m. to 2 p.m.) : ready cloth is not simple harmony burning Batch Vi (2 p.m. to 3 p.m.) : is cloth ready not burning harmony simple
if the password for Batch i was – 'rate go long top we let have', which batch will have the password–'go rate top long have let we'?
(a) II (B) III (c) IV (D) V
9. N ranks fifth in a class. S is eighth from the last. If T is sixth after N and just in the middle of N and S, then how many students are there in the class?
(a) 23 (B) 24 (c) 25 (D) 26
10. Which one of the four interchanges in signs and numbers would make the given equation correct? 4 × 6 – 2 = 14
(a) × to ÷, 2 and 4 (B) – to ÷ , 2 and 6 (c) – to +, 2 and 6 (D) × to +, 4 and 6 11. A total of 324 coins of 20 paise and 25 paise make a sum of ` 71. the number of 25 paise coins
is _______.
(a) 120 (B) 124 (c) 144 (D) 200
12. Select a figure from amongst the options which will continue the same series as established by the five Problem Figures.
(a) (B) (c) (D)
13. In the given question, there are seven figures, the first and last of which are unnumbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. The number of that figure is the answer.
M ES UH LU EE SP HS UE NN EU SB SY EU EJ B
L S U P Y U S
1 2 3 4 5
4
| 6th IMO | Level-II | Class 10
14. There is a set of five figures labelled P, Q, R, S and T called the Problem figures. Fig. (R) contains a question mark. Select a suitable figure from the options which will substitute this question mark so that a series is formed by the figures P, Q, R, S and T taken in order.
(a) (B) (c) (D)
15. There is a definite relationship between figures P and R. Establish a similar relationship between figures Q and S by selecting a suitable figure from the options that would replace the question mark (?) in fig. (S).
(a) (B) (c) (D)
16. Which term comes next in the given series?
ac, FH, KM, PR, ?
(a) UW (B) VW (c) UX (D) TV
17. Count the number of pentagons in the given figure.
(a) 16 (B) 12 (c) 8 (D) 4
18. choose the correct mirror-image of the Fig. (X) from amongst the four options given along with it, if the mirror is placed along M1 M2.
(a) (B) (c) (D)
19. A cube, painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only ?
5 6th IMO | Level-II | Class 10 | 20. Find out which of the options will complete the figure matrix.
(a) (B)
?
(c) (D)
Section-ii : MatHeMaticaL ReaSoning
21. the value of 3 15 2 7 11 4 710 11722 5 11 7 8 52 4 5 8 13 + − ÷ + + − − is _______. (a) 78 (B) 0 (c) 1611 (D) 1 22. if ax – 1 = bc, by – 1 = ca and cz – 1 = ab then xy + yz + zx = ______.(a) xyz (B) x2y2z2 (c) 2xyz (D) 1/(xyz)
23. a railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs ` 216 and one full and one half reserved first class tickets cost ` 327. What is the cost of basic first class full fare and the reservation charge?
(a) ` 105 and ` 6 (B) ` 216 and ` 12 (c) ` 210 and ` 12 (D) ` 210 and ` 6
24. if pand qare the roots of the equation x2 – bx+ c = 0, then what is the equation if the roots are (pq + p +q)
and (pq – p – q)?
(a) x2 – 2cx + (c2 – b2) = 0 (B) x2 – 2bx + (b2 + c2) = 0 (c) 3cx2 – 2(b + cx + c2) = 0 (D) x2 + 2bx – (c2 – b2) = 0 25. Given intersecting chords, find x.
(a) 20° B C E x 40° 80° O D A (B) 40° (c) 60° (D) 80°
26. if ABC is a right angled triangle with ∠A = 90° and 2s = a + b + c, where a > b > c and notations have their usual meanings, then which one of the following is correct?
(a) (s – b) (s – c) > s(s – a) (B) (s – a) (s – c) > s(s – b)
(c) (s – a) (s – b) < s(s – c) (D) 4s(s – a) (s – b) (s – c) = bc
27. Six fruit baskets contain peaches, apples and oranges. three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?
6
| 6th IMO | Level-II | Class 10
28. A is three times as old as B. Four years ago, C was twice as old as A. in four years time, A will be 31. What are the present ages of B and C respectively?
(a) 9, 46 (B) 9, 50 (c) 10, 46 (D) 10, 50
29. If a, b and g are in a.P., then cotb = _______.
(a) cossinag−−cossinga (B) cossingg−−cossinaa (c) 2(cossinaa−−sincos )gg (D) 2(sincosgg−−cossin )aa 30. Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.
How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
(a) 60 mins 15 secs (B) 50 mins 15 secs (c) 51 mins 12 secs (D) 49 mins 8 secs 31. Points A, B, C and D are midpoints of the sides of square JETS. if the area of JETS is 36 sq. cm,
then the area of ABCD is ________.
J A E B T C S D (a) 3 sq. cm (B) 7.5 sq. cm (c) 9 sq. cm (D) 18 sq. cm
32. the mean of 1, 3, 4, 5, 7 and 4 is m. the numbers 3, 2, 2, 4, 3, 3 and p have mean m – 1 and median q, then p + q = ______.
(a) 7 (B) 6 (c) 5 (D) 4
33. What approximate value should come in place of the question mark (?) in the following equation?
158.25 × 4.6 + 21% of 847 + ? = 950.935045
(a) 35 (B) 44 (c) 50 (D) 45
34. If the ratio of mean and median of a certain data is 2 : 3, then find the ratio of its mode and mean.
(a) 2 : 5 (B) 3 : 2 (c) 5 : 2 (D) 1 : 2
35. in the given diagram, ABCD is a square, diagonal BD is extended through D to E. AD = DE and AE is drawn. What is m∠DAE?
(a) 22.5° (B) 45° E D B C A (c) 112.5° (D) 135°
36. What is the probability of getting at least one six in a single throw of three unbiased dice?
(a) 16 (B) 125216 (c) 361 (D) 21691
37. ABC is a right angled triangle, right angled at A. a circle is inscribed in it and the lengths of the two sides containing the right angle are 12 cm and 16 cm. Find the area of the circle.
7 6th IMO | Level-II | Class 10 | 38. a person of height 2 m wants to get a fruit which is on the top of a pole of height 10
3 m if he stands at distance of 4 3
m from the foot of the pole, then the angle at which he should throw the stone, so that it hits the fruit is _____.
(a) 15° (B) 30° (c) 45° (D) 60°
39. The point (–4, –2) lies on a circle. What is the length of the radius of this circle, if the centre is located at (–8, –10)?
(a) 48 (B) 80 (c) 108 (D) 288
40. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is ______.
(a) 15360 (B) 153600 (c) 30720 (D) 307200
Section-iii : eVeRYDaY MatHeMaticS
41. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. the length of the garden is ______.
(a) 20 m (B) 22 m (c) 24 m (D) 26 m
42. 3 years ago, the average age of a family of 5 members was 17 years. a baby having been born, the average age of the family is the same today. the present age of the baby is _____.
(a) 1 year (B) 11
2 years (c) 2 years (D) 3 years
43. Rajan got married 8 years ago. His present age is 65 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's sister is ______.
(a) 32 years (B) 36 years (c) 38 years (D) 40 years
44. In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class?
(a) 65.5 (B) 72.5 (c) 75 (D) 85
45. Padma purchased 30 kg of rice at the rate of ` 17.50 per kg and another 30 kg rice at a certain rate. She mixed the two and sold the entire quantity at the rate of ` 18.60 per kg and made 20% overall profit. At what price per kg did she purchase the lot of another 30 kg rice?
(a) `12.50 (B) `13.50 (c) `14.50 (D) `15.50
46. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
(a) 5 : 7 : 8 (B) 28 : 49 : 64 (c) 38 : 28 : 21 (D) None of these
47. Simi can do a work in 3 days, while Meeta can do the same work in 2 days. Both of them finish the work together and get ` 150. What is the share of Simi?
8
| 6th IMO | Level-II | Class 10
48. a bicycle can be purchased on cash payment of ` 1500. The same bicycle can also be purchased at the down payment (initial payment, at the time of purchasing) of ` 350 and rest can be paid in 3 equal installments of ` 400 for next 3 months. The rate of SI per annum charged by the dealer is _____.
(a) 23 9
17% (B) 17 923% (c) 13 917% (D) None of these
49. The question given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
a solid metallic cone is melted and recast into a sphere. What is the radius of the sphere? i. the radius of the base of the cone is 2.1 cm.
ii. the height of the cone is four times the radius of its base. iii. the height of cone is 8.4 cm.
(a) Only I and II (B) Only II and III (c) Only I and III (D) Any two of three 50. Yash invested a certain sum of money at 8% p.a. simple interest for ‘n’ years. at the end of ‘n’
years, Yash got back 4 times his original investment. What is the value of n?
(a) 50 years (B) 25 years (c) 12 years 6 months (D) 37 years 6 months SPace FoR RoUgH WoRK
LEVEL - 2
Year 2013-14
7th IMO | Class-10 | Level 2 2
1. There are five persons P, Q, R, S and T. One is a football player, one is a chess player and one is a hockey player. P and S are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which T is the husband. Q is the brother of R and is neither a chess player nor a hockey player. Who is the football player? A. P B. Q C. R D. S 2. How many such pairs of digits are there in the number 95137248 each of which has as many digits between them in the number as when they are arranged in ascending order?
A. None B. One C. Two D. Three
3. In a certain code language, 'bring the white board' is written as 'ka na di pa' and 'white and black board' is written as 'na di sa ra'. How is 'the' written in that code? A. ka B. pa C. ka or pa D. None of these 4. Read the following information and answer the question given below it. (i) L, M, N, O, P, Q, R and S are sitting around a circle facing the centre. (ii) N, who is third to the left of P, is not a neighbour of R and M. (iii) S is the neighbour of ‘O’ and ‘R’ and is third to the right of M. (iv) L is not the neighbour of O, who is second to the left of N. What is the position of Q? A. Immediate right of R B. Immediate left of N C. Third to the right of M D. Second to the left of S
5. Two different positions of the same dice has been shown below. If digit 1 is on the top what will come just below it? 4 3 2 3 5 6 A. 2 B. 3 C. 4 D. 5 6. Figures (i) and (ii) of the Problem Set bears a certain relationship. Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace the question mark in fig.(iv). ? (i) (ii) (iii) (iv)
Problem Set A. B. C. D. 7. If 'tall' is equivalent to 'circle', 'army men' to 'triangle' and 'strong' to 'square', indicate which number will represent only strong army men? A. 3 B. 4 C. 5 D. 6 8. Select a figure from the options which will continue the series established by the Problem Figures. Problem Figures A. B. C. D. 5 4 7 6 32 1
logical reasoning
7th IMO | Class-10 | Level 2 3 9. Three of the following four are alike in a certain way and so form a group. Which is the one that does not belong to that group? A. 215 B. 247 C. 91 D. 65 10. Group the given figures into three classes using each figure only once. A. 1,2,5 ; 3,7,8; 4, 6, 9 B. 1, 7, 2; 3, 9, 6; 4, 5, 8 C. 2, 3, 8; 4, 6, 9; 1, 5, 7 D. 5, 6, 9; 3, 4, 1; 2, 7, 8 11. Choose the option which most closely resembles the water-image of the given combination. GR98AP76ES A. B. C. D. 12. Identify which one of the alternative figures completes the pattern in the given matrix. A. B. C. D.
13. If it is possible to make a meaningful word from the second, fourth, seventh and tenth letters of the word UNDENOMINATIONAL, using each letter only once, third letter of the word would be your answer. If more than one such word can be formed your answer would be ‘X’, whereas if more than two such words can be formed your answer would be ‘Y’, and if no such word can be formed, answer would be ‘Z’. A. X B. Z C. Y D. N
14. The following problem consists of a set of six figures, the first of which is unnumbered and marks the beginning of the series which is continued in the successive figures numbered from 1 to 5. However, the series will be established only if the positions of two of the numbered figures are interchanged. The number of the earlier of the two figures is the answer. If no two figures need to be interchanged, then the answer is 5. A. 1 B. 2 C. 3 D. 5 15. Study the following arrangement carefully and answer the question given below: 4 K @ 1 E F © 2 H D % 3 8 B I M 6 * U W Y 5 $ 9 G J # 7 A How many such consonants are there in the above
arrangement, each of which is immediately preceded by a letter and immediately followed by a number? A. None B. One C. Two D. Three 16. Mohit lives to the North of Rajesh who lives to the West of Tanuj. Arun who lives to the South of Mohit have his house in which direction with respect to Tanuj?
A. North-East B. North C. South-West
7th IMO | Class-10 | Level 2 4 17. Find the suitable alternative to fit into the blank space in Fig. (X) in order to complete the pattern. A. B. C. D. 18. In the following question, 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 operation of numbers progresses from left to right. Rules: (i) If an odd number is followed by another composite odd number, they are to be multiplied. (ii) If an even number is followed by an odd number, they are to be added. (iii) If an even number is followed by a number which is a perfect square, the even number is to be subtracted from the perfect square.
(iv) If an odd number is followed by a prime odd number, the first number is to be divided by the second number. (v) If an odd number is followed by an even number, the second one is to be subtracted from the first one. 58 17 5 85 5 n If n is the resultant of the first row what is the resultant of the second row? A. 255 B. 32 C. 49 D. 34 19. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the option that would replace the question mark (?) in fig. 4. A. B. C. D. 20. Pointing to a woman in a photograph a man says; “She is the only daughter of my father’s mother-in-law”. How is the woman related to the man? A. Daughter B. Mother C. Daughter-in-law D. Mother-in-law
MatheMatical reasoning
21. Determine the value of k so that the following linear equations have no solution. (3k + 1)x + 3y – 2 = 0 (k2 + 1)x + (k – 2)y – 5 = 0 A. –1 B. –2 C. 1 D. 4 22. Find the value of sec39 51 2 3 ° °+ cosec tan17° tan38° tan60° tan52° tan73° – 3(sin231° + sin259°) A. –1 B. 0 C. 1 D. 27th IMO | Class-10 | Level 2 5
23. Let f(x) = x2 + bx + c where b, c are integers. If f (x) is a factor of both x4 + 6x2 + 25 and 3x4 + 4x2 + 28x + 5, then the value of f(1) is _____ A. 1
B. 2 C. 3
D. None of these
24. A, B, C are three towns connected by straight roads from A to B, B to C and C to A. AB = 5 km, BC = 6 km and CA = 7 km. Two cyclists start simultaneously from A and go in different roads with same speed. They meet at D, then BD = _______. A. 2 km B. 4 km C. 6 km D. 8 km 25. Triangle ABC is equilateral of side length 8 cm. Each arc shown in the diagram is an arc of a circle with the opposite vertex of the triangle as its centre. The total area enclosed within the entire figure shown (in cm2) ________. A. 48(p − 3) B. 30 3 p C. 32(p − 3) D. 90 p 26. Solve for x : x2 + x – (a + 1)(a + 2) = 0 A. (a + 1), (– a + 2) B. (a + 1), (a + 2) C. (– a + 1), (a + 2) D. (a + 1), – (a + 2) 27. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD. A. 19 cm B. 20 cm C. 25 cm D. 30 cm 28. The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60°. Find the height of the cloud. A. 100 m B. 120 m C. 60 m D. 125 m 29. A bag contains 12 balls out of which x are white. If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that of drawing a white ball before adding the balls. Find the value of x.
A. 1 B. 6 C. 3 D. 7
30. Find the area of the quadrilateral ABCD whose vertices are respectively A(1, 1), B(7, –3), C(12, 2) and D(7, 21). A. 125 sq. units B. 110 sq. units C. 148 sq. units D. 132 sq. units 31. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling. A. 15.82 km/hour B. 15.84 km/hour C. 15.96 km/hour D. 20 km/hour 32. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in figure. What fraction of water overflows?
A. 3/8 B. 8/3 C. 5/4 D. 6/7
33. The sum of 5th and 9th terms of an A.P. is 72 and the sum of 7th and 12th terms is 97. Find the A.P. A. 5, 10, 15, 20 ...
B. 15, 30, 45, 60 ... C. 6, 11, 16, 21, 26, ... D. 2, 4, 6, 8, 10 ...
7th IMO | Class-10 | Level 2 6
34. Find the median of the following data.
Class 0- 10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 5 3 4 3 3 4 7 9 7 8 A. 64 B. 48.93 C. 63.43 D. 66.43 35. Evaluate :
sec cos ( ) tan cot( )
sin sin tan tan θ ec 90 θ θ 90 θ 55 35 10 20 2 2 ° − − ° − + ° + °
° °°tan60°tan70°tan80° A. 1 3 B. 2 3 C. 3 D. 1 36. The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream. A. 4 km/hr B. 5 km/hr C. 6 km/hr D. 7 km/hr
37. Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 km/h. The second goes at a speed of 8 km/h in the first hour and increases the speed by 1/2 km in each succeeding hour. After how many hours will the second car overtake the first car if both cars go non-stop? A. 9 hours B. 10 hours C. 12 hours D. None of these 38. An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river. A. 115.47 metres B. 200 metres C. 215.47 metres D. 315.47 metres
39. Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize? A. 19 20 B. 1 25 C. 1 20 D. 17 20 40. Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the flow of water is 72 cm per second, how many litres of water are being pumped out in one hour? A. 2772 litres B. 9979 litres C. 9979.2 litres D. 9297.4 litres
41. A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size (in inches) of the tile required that has to be cut and how many such tiles are required respectively? A. 24, 20 B. 20, 24 C. 20, 43 D. 41, 6 42. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils respectively. A. 28, 12 B. 12, 28 C. 27, 13 D. 13, 27 43. Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops. A. 12 m B. 13 m C. 14 m D. 15 m 44. A sum of ` 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ` 20 less than its preceding prize, find the value of each prize.
everyday MatheMatics
7th IMO | Class-10 | Level 2 7
achievers section
A. ` 100, ` 120, ` 140, ` 160, ` 80, ` 40, ` 20 B. ` 160, ` 140, ` 120, ` 100, ` 80, ` 40, ` 20 C. ` 160, ` 140, ` 120, ` 100, ` 80, ` 60, ` 40 D. ` 380, ` 360, ` 340, ` 320, ` 300, ` 280, ` 260 45. In an examination the ratio of the number of successful candidates and unsuccessful candidates is 4 : 1. Had 20 more candidates appeared and 2 more passed, the ratio of successful candidates to unsuccessful candidates would have been 2 : 1. Find the number of candidates who appeared in the examination originally. A. 85 B. 92 C. 34 D. 17 46. CAB is an angle whose measure is 70°. ACFG and ABDE are squares drawn outside the angle. The diagonal FA meets BE at H. Then the measure of the angle EAH is _____. A. 45° A E B 70° C G F D H B. 25° C. 65° D. 70° 47. Study the statements carefully and select the correct option.Statement-1 : The distance between two points (x1, y1) and (x2, y2) is (x x1− 2)2+(y y1− 2)2
Statement-2 : The point(s) on the x-axis which has its distances from the points (7, 6) and (–3, 4) in the ratio 1 : 2 is 35
3 ,0 or (–9, 0). A. Both the statements are true. B. Statement-1 is true but statement-2 is false. C. Statement-1 is false but statement-2 is true. D. Both the statements are false. 48. Fill in the blanks.
A P to a circle is a line that meets the circle at only one point. It is a special case of Q , when the two end points of its corresponding chord R .
There is only one S at a point of circle.
P Q R S
A. secant tangent intersect tangent B. tangent secant coincide tangent C. tangent chord coincide secant D. line tangent meet tangent 49. Match the columns.
Column I Column II
(i) The 8th term from the end of the
A.P. 7, 10, 13, …, 184 is (p) 108 (ii) The 10th term from the end of the
A.P. 8, 10, 12, …, 126 is (q) –142 (iii) The first term of an A.P. is 5
and its 100th term is – 292. The 50th term is (r) 163 A. (i) → (q), (ii) → (p), (iii) → (r) B. (i) → (r), (ii) → (p), (iii) → (q) C. (i) → (p), (ii) → (q), (iii) → (r) D. (i) → (q), (ii) → (r), (iii) → (p)
50. If the volume of a sphere is increased by 955 16% without changing the shape, what will be the percentage increase in the surface area? A. 56.25% B. 50 % C. 28.56% D. Remains same
LEVEL - 2
Year 2015-16
2 | 9th IMO | Class-10 | Level 2 1. If one of the zeros of a quadratic polynomial of the
form x2 + ax + b is negative of the other, then it
______.
A. Has no linear term and the constant term is negative.
B. Has no linear term and the constant term is positive.
C. Can have a linear term but the constant term is negative.
D. Can have a linear term but the constant term is positive.
2. Solve for x and y :
1+ 1 4 5 0 bb +x +aa = −y b a x,b− ay= ;ab≠ . A. x = –a, y = b B. x = b2, y = a2 C. x = a2, y = b2 D. x = b, y = –a
3. In the given figure, ABC is a triangle right angled at B and BD ^ AC. If AD = 4 cm and CD = 5 cm, find BD and AB respectively. A B C D A. 2 5cm,3 5 cm B. 3 5 cm, 6 cm C. 2 5 cm, 6 cm D. 3 5 cm, 8 cm
4. In DABC right angled at B, BC = 5 cm and AC – AB = 1 cm. Evaluate 1+ sin cos . C C A. 5 13 B. 13 C. 1213 D. 5
5. Which of the following statements is correct ? A. sin (A + B) = sin A + sin B
B. The value of sin q increases as q decreases
C. The value of cos q increases as q increases D. None of these
6. The following table shows the daily pocket allowance given to the children of a multistorey building. The mean of the pocket allowance is ` 18. Find out the missing frequency. Class interval 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Frequency (in `) 3 6 9 13 ? 5 4 A. 8 B. 16 C. 12 D. 4
7. Three years ago, the average age of Latika, Garima and Megha was 27 years and that of Garima and Megha 5 years ago was 20 years. Latika’s present age is _______.
A. 30 years B. 36 years C. 40 years D. 46 years
8. Find the mode of the following frequency distribution : Marks 10-20 20-30 30-40 40-50 50-60 Number of students 12 35 45 25 13 A. 20.33 B. 30.12 C. 33.33 D. 60.43
9. A small scale industry produces a certain number of items per day. The cost of production of each item (in rupees) was calculated to be 74 minus twice the number of articles produced in a day. On a particular day, the total cost of production was ` 540. Which of the following equations represent how to find the number of items produced on that day?
A. 74 + 2x = 540 B. x2 + 74x – 540 = 0
C. 74 – 2x = 540 D. x2 – 37x + 270 = 0
10. The sum of first n terms of an A.P. is given by (n2 + 8n).
Find the 12th term of the A.P. Also find the nth term
of the A.P.
3 9th IMO | Class-10 | Level 2 |
A. 31, 2n + 9 B. 31, 2n + 7 C. 30, 2n + 6 D. 30, 2n + 8
11. In the given figure, PQ is the chord of circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is ________. P Q R T A. 135° B. 150° C. 120° D. 110° 12. In the given figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region. [Use p = 3.14]
A. 39.25 cm2
B. 48.50 cm2
C. 78.50 cm2
D. 28.25 cm2
13. Two cleanliness hoardings are put on two poles of equal heights standing on either side of a roadway 50 m wide between the poles. The elevations of the tops of the poles from a point between them are 60° and 30°. Find the height of the pole.
A. 50 3 m B. 253 3 m C. 25 3 m D. 25
2 3 m
14. Beena gave a simple multiplication question to her students. But one student reversed the digits of both numbers and carried out the multiplication and found that the product was exactly the same as the
one expected by Beena. Which one of the following pairs of numbers will fit in the description of the question?
A. 14, 22 B. 13, 62 C. 19, 33 D. 42, 28
15. For what values of k will the following pair of linear equations have infinitely many solutions? 2x + 3y = 4 and (k + 2) x + 6y = 3k + 2 A. 1 B. –1 C. 2 D. –2
16. The values of l for which the quadratic equation x2 + 5lx + 16 = 0 has no real root is _____.
A. l > 8 B. l < –5 C. − < <8 5 8 5 l D. − ≤ <8 5 l 0
17. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
A. 3 seconds B. 6 seconds C. 9 seconds D. 5 seconds
18. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is odd ? A. 1 2 B. 3 4 C. 3 8 D. 1 4 19. Find the median of the following data :
Marks 0-10 10-20 20-30 30-40 40-50 No. of students 10 18 40 20 12 A. 51.5 B. 25.5 C. 28.5 D. 31
4 | 9th IMO | Class-10 | Level 2 20. A number is selected at random from the numbers :
5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46.
Find the probability that the selected number is a prime number. A. 0 B. 1 8 C. 1 6 D. 1 12
21. The value of expression
( . ) ( ) ( . ) ( . ) ( ) / / / / / / 0 3 1 27 9 0 81 0 9 3 1 3 1 3 1 4 1 6 2 3 2 3 1 2 ⋅ ⋅ ⋅ ⋅ − ⋅ ⋅−2 (243)−1 4/ ÷ − ⋅ + − − − − ( . )0 6 ( . )0 1 3 2 3 2 13 0 1 3 1 3 1 is A. – 0.2 B. 0.9 C. 1.27 D. – 0.06
22. There are two circles intersecting each other. Another smaller circle with centre O, is lying between the common region of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. AB = 16 cm and the radii of the larger circles are 10 cm each. What is the area of the smaller circle ?
A O B A. 4p cm2 B. 2p cm2 C. 4 p cm2 D. p 4 cm2
23. If the points A(– 2, 1), B(a, b) and C(4, –1) are collinear and a – b = 1, find the values of a and b respectively.
A. 1, 0 B. 1, –1 C. 0, 1 D. –1, 1
24. A circular paper is folded along its diameter, then again it is folded to form a quadrant. Then it is cut as shown in the figure, after it the paper was reopened in the original circular shape. Find the ratio of the original paper to that of the remaining paper?
(The shaded portion is cut off from the quadrant. The radius of quadrant OAB is 5 cm and radius of each semicircle is 1 cm)
A. 25 : 16 B. 25 : 9 C. 20 : 9
D. None of these
25. There are 100 apples in a box. 20 of them are rotten. At random, two apples are taken one by one consecutively without replacement. What is the probability that both of them are good ?
A. 316 495 B. 19 495 C. 16 99 D. 32 99
26. Which of the following statements is INCORRECT ? (i) In order to divide a line segment internally in the
ratio m : n, both m and n are real numbers. (ii) A pair of tangents can be constructed to a circle
inclined at an angle of 165°. A. Only (i)
B. Only (ii)
C. Both (i) and (ii) D. Neither (i) nor (ii)
27. If a and b be two zeros of the quadratic polynomial p(x) = 2x2 – 3x + 7, evaluate 1 2 3 1 2 3 a− + b− . A. − 3 14 B. 3 7 C. −5 4 D. 3 14
5 9th IMO | Class-10 | Level 2 |
28. 5 3 2− − is _____. A. A rational number B. A natural number C. Equal to zero D. An irrational number
29. In figure, the line segment LM is parallel to side XZ of DXYZ and it divides the triangle into two parts of equal areas. Find the ratio XL
XY. Y M Z X L A. 2 1 2− : B. 2 1 2+ : C. 1− 2 2: D. 2− 2: 2
30. Two ships are sailing in the sea on the either side of the lighthouse, the angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the ships is 200 3 1 3 +
metres, find the height of the lighthouse. A. 100 3 m B. 100 m C. 200 m D. (1+ 3)m
31. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. A. 4.50 m
B. 2.125 m C. 1.125 m D. 3.25 m
32. In the given figure, if ∠POQ = 130°, then ∠SOR is equal to P Q R S O A. 50° B. 45° C. 35° D. 55°
33. In the given figure, XW is a tangent to the circle with centre O at X and YZW is a straight line. Find the value of y. X W Y Z O y 70° 20° A. 30° B. 35° C. 40° D. 50°
34. If the common difference of an A.P. is 5, then a18 – a13 = _____.
A. 5 B. 20 C. 30 D. 25
35. If the points A(1, –2), B(2, 3), C(–3, 2) and D(–4, –3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram. A. 26 24 units B. 14 13 units C. 24 26 units D. 13 14 units
36. If the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, – 3) in the ratio k : 1, then find the value of x.
A. 8 B. 67
8 C. 67
3 D. 9
37. ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle.
A. 1/2 cm B. 13 cm C. 2 cm D. 10 cm
6 | 9th IMO | Class-10 | Level 2 38. In figure, ABCDEF is any regular hexagon with
different vertices A, B, C, D, E and F as the centres of circles with same radius ‘r’ units are drawn. Find the area of the shaded portion.
A. 2pr2 sq. units
B. 4pr2 sq. units
C. pr2 sq. units
D. 6pr2 sq. units
39. A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 20 m per minute. How long would it take to fill a conical tank, with diameter of base as 80 cm and depth 72 cm ? A. 5 minutes
B. 3 minutes 56 seconds C. 4 minutes 20 seconds D. 4 minutes 48 seconds
40. If sum of the squares of zeros of the polynomial 6x2 + x + k is 25 36, find k. A. 2 B. –2 C. 1 D. –1
41. In the Maths Olympiad in a school, two representatives from two teams, while solving a quadratic equation, committed the following mistakes :
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) The other committed an error in the coefficient of x and he got the roots as 12 and 4.
In the meantime, they realised that they were wrong and together they managed to get it right. Find the right quadratic equation.
A. x2 + 4x + 14 = 0
B. 2x2 + 7x – 24 = 0
C. x2 – 14x + 48 = 0
D. 3x2 – 17x + 52 = 0
42. What must be added to the polynomial 3l4 + 5l3 – 7l2
+ 5l + 3 so that the resulting polynomial is exactly divisible by l2 + 3l + 1 ?
A. –3l + 1 B. –3l – 1 C. 3l + 1 D. 3l – 1
43. In the given figure, DE | | BC. If DE : BC = 3 : 5, find the ratio of the area of DADE to the area of trapezium BCED. A B C D E A. 9 : 16 B. 25 : 9 C. 16 : 9 D. 9 : 25 44. If cos sin cos sin q q q q − + = − + 1 3 1 3 and 0° < q < 90°, then find the angle q. A. 30° B. 60° C. 90° D. 45°
45. Evaluate : 4 (sin4 30° + cos4 60°) – 3 (cos2 45° – sin2 90°)
+ (sin2 60° + sin2 45°) A. 31 4 B. 1 4 C. 3 4 D. 7 16
ACHIEvErS SECTIon
46. Which of the following options hold ?
Statement 1 : If p, q, r and s are real numbers such that pr = 2 (q + s), then atleast one of the equations x2 + px + q = 0 and x2 + rx + s = 0 has real roots.
Statement 2 : If a, b, c are distinct real numbers, then the equation
(x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 has real and distinct roots.
A. Statement 1 is true, Statement 2 is false B. Statement 1 is false, Statement 2 is true C. Both Statement 1 and Statement 2 are true D. Both Statement 1 and Statement 2 are false
