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Crack The Iim Indore Ipm Entrance Examination 2nd Edition North Academics (Author) - Solutions

Find the radius of the circle x2 + y2 – 2x –4y – 20 = 0.(a) 10 (b) 5(c) 2.5 (d) None of these.
Number of points on the lines 4x – 3y + 7= 0 or x – y + 3 = 0, which are at a distance 5 units from the point (2, 5) are:(a) 1 (b) 2(c) 3 (d) 4
Points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y –10 = 0 are(a) (3, 1) and (–7, 11)(b) (–3, 7) and (2, 2)(c) (–3, 7) and (–7, 11)(d) None of these.
If three vertices of a rhombus taken in order are (2, -1), (3, 4) and (-2, 3), then the fourth vertex is(a) (-3, -2) (b) (3, 2)(c) (2, 3) (d) (1, 2)
Nearest point on the line 3x - 4y = 25 from the origin is(a) (-4, 5) (b) (3, -4)(c) (3, 4) (d) (3, 5)
Area of the triangle with vertices at the point (a, b + c), (b, c + a), (c, a +b) is(a) 0 (b) a + b + c(c) ab + bc + ca (d) None of these.
The triangle with vertices at (2, 4) (2, 6)and (2 + 3, 5) is(a) right angled(b) right angled and isosceles(c) equilateral(d) obtuse angled
In-centre of the triangle whose vertices are(-36, 7), (20, 7) and (0, -8) is(a) (0, -1) (b) (-1, 0)(c) (1/2, 1) (d) None of these.
Find the area enclosed by the graph y = |X +3| with the coordinate axes in square units.(a) 9 (b) 4.5(c) 0 (c) 12
The points (0, -1), (-2, 3), (6, 7) and (8, 3) are(a) colline(b) vertices of a parallelogram which is not a rectangle(c) vertices of a rectangle, which is not a square (d) None of these.
The points (-a, -b), (0, 0), (a,b) and (a2, ab) are(a) collinear(b) vertices of a parallelogram(c) vertices of a rectangle(d) None of these.
Find out thje area enclosed by the x-axis, y-axis and the graph y = |x| - 4 in the first quadrant (in sq. units).(a) 8 (b) 16(c) 14 (d) None of these.
If each of the point (x1, 4), (-2, y1) lies on the line joining the points (2, -1), (5, -3), then the point p(x1, y1) lies on the line(a) 6(x + y) - 25 = 0 (b) 2x + 6y + 1 = 0(c) 2x + 3y - 6 = 0 (d) 6(x + y) + 25 = 0
Coordinates of the diagonals of a square are (2, 0) and (0, 5). What is the area of the square?(a) 29 sq. units (b) 29 2 sq.units(c) 29 4 sq.units (d) 14.5 sq. units
Ten horses are running in a race, the chance that A will win is 30%, that B will win is 20% and C will win is 10%. What is the probability that one of them will win?(a) 0.689 (b) 0.598(c) 0.498 (d) 0.398
A and B are mutually exclusive events:(a) 0.6 (b) 0.3(c) 0.2 (d) 0.5
How many numbers greater than four million (40,00,000) can be formed with the digits 2, 3, 0, 3, 4, 2, 5, ?(a) 280 (b) 380(c) 360 (d) None of these.
How many words can be formed out of the letters of the word ‘ARTICLE’ so that the vowels occupy the even places?(a) 72 (b) 144(c) 288 (d) 36
In how many ways can the letters of the word ‘LUCKNOW’ be arranged so that the two vowels do not come together?(a) 720 (b) 1,440(c) 3,600 (d) None of these.
How many different words can be formed with the letters of the word ‘VICECHANCELLOR’ so that the vowels are to-gether?(a) 10 × 5! (b) 10! × 5!(c) 5 × 10!/2 (d) 5 × 10!
How many new words can be formed from the letters of the word ‘CIRCLE’ taken all together?(a) 720 (b) 719(c) 360 (d) 359
In how many ways can 15 I.Sc. and 13 B.Sc. candidates be arranged in a line so that no two B.Sc. candidates may occupy consecutive positions?(a) 15! × 13! (b) 15! × 16P12 (c) 13! × 16P12 (d) 2! × 15! × 13!
In a dinner party there are 10 Indians, 5 Americans and 5 Englishmen. In how many ways can they be arranged in a row so that all persons of the same nationality sit together?(a) 10! × 5! × 5!(b) 20!(c) 3! × 10! × 5! × 5!(d) 20! 3!
There are 20 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions then the maximum number of students who appeared in the examination is:(a) 20C9 (b) 20C11(c) 20C10 (d) None of these.
If mC4, mC5 and mC6 are in AP then m is:(a) 8 (b) 9(c) 14 (d) 9
The number of positive integral solutions of x + y + z = n, n ∈ N, n > 3, is:(a) n–1C2 (b) n–1P2(c) n(n – 1) (d) None of these.
The greatest possible number of points of intersection of 8 straight lines and 4 circles is:(a) 32 (b) 64(c) 76 (d) 104
The total number of integral solutions for(x, y, z) such that xyz = 24 is:(a) 36 (b) 90(c) 120 (d) None of these.
The number of all 4-digit numbers which are divisible by 4 that can be formed from the digits 1, 2, 3, 4 and 5 is:(a) 125 (b) 30(c) 95 (d) None of these.
The total number of 9-digit numbers of different digits is:(a) 10 (9!) (b) 8 (9!)(c) 9 (9!) (d) None of these.
From 4 gentlemen and 6 ladies a committee of 5 is to be formed. Then number of ways in which the committee can be formed so that gentlemen are in majority is:(a) 66 (b) 156(c) 60 (d) None of these.
The total number of selections of at most n things from (2n + 1) different things is 63.Then the value of n is:(a) 3 (b) 2(c) 4 (d) None of these.
Let A be the set of 4-digit numbers a1 a2 a3 a4 where a1 > a2 > a3 > a4 then how many values of A are possible?(a) 126 (b) 84(c) 210 (d) None of these.
The number of 6-digit numbers that can be made with the digits 0, 1, 2, 3, 4 and 5 so that even digits occupy odd places, is:(a) 24 (b) 36(c) 48 (d) None of these.
A committee is to be formed comprising of 7 members such that there is a majority of men and at least 1 woman in every committee.The shortlist consists of 9 men and 6 women.In how many ways can this be done?(a) 3,724 (b) 3,630(c) 3,526 (d) 4,914
At a get-together, it was found that a total of 66 handshakes took place at the conclusion of the party. If each guest shook hand only once will with all the others, how many people were present.(a) 33 (b) 22(c) 12 (d) 13
For the BCCI, a selection committee is to be chosen consisting of 5 ex-cricketers.Now there are 10 representatives from four zones. It has further been decided that if Kapil Dev is selected, Sunil Gavaskar will not be selected and vice versa. In how many ways can this be done?(a) 140 (b) 112(c) 196
From a group of persons the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is(a) 13 (b) 40(c) 3.18 (d) 21
In a group of boys, the number of arrangements of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group is:(a) 10 (b) 8(c) 6 (d) None of these.
Hoppers’ Stop stocks 4 styles of trousers.For each style, there are 10 different possible waist sizes, 6 different trousers lengths and 4 colour choices. How many different types of trousers could the store have?(a) 1,024 (b) 960(c) 921 (d) 924
There are 8 different locks, with exactly one key for each lock. All the keys have been mixed up. What is the maximum number of trials required in order to determine which key belongs to which lock?(a) 44 (b) 28(c) 24 (d) 32
A joint student-teacher committee of 5 members is to be formed from among 4 teachers, 3 male students and 5 female students. How many different committees can be formed if the committee must consist at least 2 teachers, 1 male student and 2 female students?(a) 170 (b) 152(c) 180 (d) 104
How many different license plates of 6 entities involving 3 letters and 3 digits are there if 3 letters appear together, either at the beginning or at the end of the license?(a) 2 × 263 × 103 (b) 54,102(c) 4 × 252 × 104 (d) None of these.
In the above question, what is the number of ways such that the first card is a spade and the second is not a Queen?(a) 611 (b) 612(c) 164 (d) None of these.
How many ways are there to pick 2 different cards from a deck of 52 cards such that the first card is an Ace and the second is not a Queen?(a) 188 (b) 198 (c) 164 (d) None of these.
A committee of 5 is to be chosen from among 6 men and 4 ladies. In how many ways can this be done in order to include at least 1 lady?(a) 252 (b) 246(c) 244 (d) 152
If 6 persons are selected out of 10, in how many ways will a particular person be found among those 6?(a) 124 (b) 126(c) 144 (d) 84
How many words can be formed using the letters of the word ‘CORRESPONDENCE’if the consonants are always written together?(a) 182 (b) 184(c) 216 × 9! (d) None of these.
A cricket team of 11 is to be chosen from among 8 batsmen, 6 bowlers and 2 wicketkeepers. In how many ways can the team be chosen if there must be at least 4 batsmen, at least 4 bowlers and exactly 1 wicketkeeper?(a) 1,681 (b) 5,304(c) 1,652 (d) None of these.
In the above question, in how many ways can he invite one or more of five friends and seat them at a circular table with him?(a) 325 (b) 205(c) 265 (d) 320
Akshay is planning to give a birthday party at his place. In how many ways can he invite one or more of five friends and seat them at a circular table?(a) 84 (b) 89(c) 78 (d) 81
The Governing Council of an institute has 15 members and wants to hold its annual meeting. In how many ways can the council be seated around a round table if the Chairman and the Vice-Chairman of the council are always seated together?(a) 10 × 12! (b) 14 × 10!(c) 13! (c) None of these.
From 3 different soft drinks, 4 different Chinese dishes and 2 different ice creams, how many different menus can be planned if at least one of each of the three items is to be included?(a) 315 (b) 282(c) 864 (d) 345
A certain code consists of 5 variables, with each variable having 4 different constant values possible. What is the total number of coded messages that can be sent with 5 constants one from each variable?(a) 1024 × 5! (b) 1024 × 4!(c) 1024 × 3! (d) None of these.
In a letter lock, each of three rings is marked with 15 letters. What is the maximum number of unsuccessful attempts that one has to make before the lock is opened?(a) 3,374 (b) 5,284(c) 315 (d) 3,375
Two out of six papers set for an examination are of mathematics. What is the number of ways in which the papers can be set so that the two mathematics papers are not together?(a) 480 (a) 2.520(c) 492 (d) 512
How many numbers between 100 and 1,000 can be formed using the digits 0, 2, 4, 6, 8, 5, if repetition of digits in a number is allowed?(a) 164 (b) 180(c) 192 (d) 100
How many numbers between 100 and 1,000 can be formed using the digits 0, 2, 4, 6, 8, 5, if repetition of digits in a number is not allowed?(a) 99 (b) 82(c) 100 (d) 120
A cylindrical well of depth 12 m with internal ratio 1.75 m is dug up. The mud that came out from it is spread evenly to form a platform 10.5 m × 8.8 m. What is the height of the platform?(a) 2.25 m (b) 3.25 m(c) 1.25 m (d) 4.25 m
A cube of side length 4 cm is cut into cubes of side 1 cm. Find the ratio of sum of surface area of all the small cubes to that of the large cube.(a) 1:16 (b) 2:3 (c) 4:1 (d) 6:1
A cube of side length 3 cm weighs 12 kg.What is the weight of similar cube of same material whose side length is 12 cm?(a) 768 kg (b) 678 kg(c) 964 kg (d) 864 kg
A rectangular tank is of dimension 30 m ×20 m. Water is being flown into it through a square pipe of side length 5 cm. Find the speed of water if the level of water in the tank rises by 1 m in 8 hours?(a) 30 km/hr (b) 36 km/hr(c) km/hr (d) None of these.
A solid cone kept on its base is cut at 2/3rd of its height along a plane parallel to its circular base. The base radius and the slant height are 14 cm and 50 cm, respectively.What is the ratio of the portion cut-out from the solid to the volume of remaining solid?(a) 1:20 (b) 1:25 (c) 1:36 (d)
The height of a right circular cylinder is 6 m. Three times the sum of the areas of its two circular faces is twice the area of its curved surface. The radius of the base is:(a) 4 m (b) 2 m(c) 6 m (d) 1.5 m
A cylindrical structure standing on its base with radius 1.5 m and height 5 m is cut with a saw in such a way that the cutting planes go through all the points at a distance of 0.625 m from the base. Find volume of the remaining piece.(a) 5.62 (b) 9.24(c) 9.04 (d) None of these
A cone and a cylinder have their height in the ratio 3:2 and the radii of their bases in the ratio 4:3. Find the ratio of their volumes.(a) 9:1 (b) 9:2(c) 8:9 (d) 3:1
A classroom is to be built to accommodate 70 students. It should be done in such a way that for every student there is 2.2 m2 of floor and 11 m3 of space. If the length of the room is 14 m, then find the breadth and height of the room.(a) 12 m, 5.5 m(b) 11 m, 5 m(c) 13 m, 6 m(d) 11 m, 4 m
Three equal cubes of unit side length are placed adjacent to each other in a row. Find the ratio of the total surface area of the new cuboid to that of the sum of the surface areas of all the three cubes.(a) 3:5 (b) 4:5(c) 6:7 (d) 7:9
Total area of four walls of a room is 150 m2.If the area of the floor is 50 m2 and the width of the floor is 3 m, then find the height of the room.(a) 2.6 m (b) 3.8 m (c) 5.42 m (d) 7.32 m
A cylindrical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, the what is the radius of its base?(a) 12 cm (b) 24 cm(c) 36 cm (d) 48 cm
The height of a room is 1 5of the sum of its length and breadth. Cost of preparing its wall at the rate ` 4 per m2 is ` 640.What is the height of the room?(a) 4 m (b) 5 m(c) 6 m (d) 7 m
A vessel 2 m long, 1 m wide and 1.5 m deep contains 2 m3 water. How many bricks 20 cm × 10 cm × 7.5 cm can be put in it so that water does not overflow provided that a brick is supposed to absorb 1/7 of its own volume of water?(a) 666 (b) 111(c) 555 (d) None of these.
Within a rectangular courtyard of length 60 feet, a gravelled path 3 feet wide is laid down along all the four sides. The cost of gravelling the path is ` 2 per feet2. If the path had been twice as wide, the gravel would have cost ` 984 more. The width of the courtyard is:(a) 24 feet (b) 40 feet
A man by walking diametrically across a circular grass plot, finds that he has taken 45 seconds less than if he had kept to the path round the outside, if he walks at the rate of 80 m per minute. The diameter of the grass plot is:(a) 35 m (b) 65 m(c) 105 m (d) 145 m
Dimension of a room is thrice as long as it is high, but only twice as long as it is wide.Total cost of painting its walls at the rate` 2.50 m2 is ` 360.What is the cost of laying carpet on its floor at the rate ` 3/m2?(a) ` 81 (b) ` 125(c) ` 216 (d) ` 260
A rectangular field is of the dimension 15.4 m× 12.1 m. A circular well of 0.7 m radius and of 3 m depth is dug in the field. The mud dug out from the well is spread in the field. By how much would the level of the field rise?(a) 1 cm (b) 2.5 cm(c) 3.5 cm (d) 4 cm
A 20 m long, 3 m high and 40 cm thick brick wall is to se built. It has a door 3 m by 2 m.Supposing each brick is 15 cm long, 7 1 2cm broad and 5 cm thick, how much will be the cost of bricks at the rate of ` 800 per thousand of bricks?(a) ` 55,270 (b) ` 66,230(c) ` 30,720 (d) ` 15,750
A solid wooden toy is in the shape of a right circular cone mounted on base of a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wood needed to construct another such toy.(a) 104 cm3 (b) 162 cm3(c) 427 cm3 (d) 266 cm3
What is the radius of a spherical ball in inches which is formed by melting a cylinder of base diameter 8 inches and height 160 inches, if the conversion wastage results in a 10% weight loss?(a) 6 (b) 8(c) 12 (d) 16
Ratio of diagonals of two cubes is 3:2.What is the ratio of the surface areas of these two cubes, respectively?(a) 27:8 (b) 3:2(c) 9:4 (d) 16:9
A spherical ball was painted black. After getting painted, it was cut into 4 similar pieces. What is ratio of the painted area to the non-painted area?(a) 1:1 (b) 1:2(c) 3:1 (d) 3:2
An open box is made of wood 2 cm thick.Its internal dimension is 86 cm × 46 cm ×38 cm. What is the cost of painting the outer surface of this box at the rate ` 10 per m2?(a) ` 12.35 (b) ` 8.85(c) ` 15.70 (d) ` 16.50
Find the area of the shaded region in the given Fig. 13.14 of square ABCD:(a) 128 cm2 (b) 184 cm2 (c) 154 cm2 (d) 168 cm2
A cylinder circumscribes a sphere. The ratio of their volumes is:(a) 2:1 (b) 3:2(c) 4:3 (d) 6:5
If a regular square pyramid has a base of side 8 cm and height of 10 cm, then what is its volume (in cc)?(a) 360 (b) 480(c) 640 (d) 800
Water flows at the rate of 10 m per minute from a cylindrical pipe of radius 2.5 mm.A conical vessel whose diameter is 40 cm and depth 24 cm is filled with water flowing from this pipe. The time taken to fill the conical vessel is:(a) Less than 30 mins(b) Less than 50 minutes but more than 30
If the right circular cone is cut into three solids of volumes V1, V2 and V3 by two cuts which are parallel to the base and trisect the altitude, then V1:V2:V3 is:(a) 1:2:3 (b) 1:4:6(c) 1:6:9 (d) None of these.
A cone and a hemisphere have equal base radius and equal volumes. The ratio of their heights is:(a) 3:1 (b) 2:1(c) 4:1 (d) None of these.
The radius of base and the volume of right circular cone are doubled. What is the ratio of the length of the larger cone to that of the smaller cone?(a) 1:4 (b) 1:2(c) 1:3 (d) 4:1
In the adjoining Fig. 13.13, PQRS is a rectangle of the dimension 8 cm × 6 cm and is inscribed in a circle. Find the area of the shaded portion.(a) 44 cm2 (b) 34.25 cm2 (c) 32.50 cm2 (d) None of these.
If the diagonals of a rhombus are 18 cm and 24 cm, respectively, then find its perimeter.(a) 15 cm (b) 42 cm(c) 60 cm (d) 68 cm
A spherical metal ball of 6 cm radius is melted and recast into three spherical balls.The radii of two of these balls are 3 cm and 4 cm. What is the radius of the third ball?(a) 4.5 cm (b) 5 cm(c) 6 cm (d) 7 cm
A reservoir is in shape of a frustum of a right circular cone. It is 8 m wide at the top and 4 m wide at the bottom. If it is 6 m deep, then what is its volume?(a) 224 m3 (b) 176 m3 (c) 204 m3 (d) None of these.
The radius of an iron rod is decreased to one-fourth of its actual radius. If its volume remains constant, the length will become:(a) 2 times (b) 12 times(c) 8 times (d) 16 times
If the curved surface area of a cylinder is 1,320 cm2 and its base radius is 21 cm, then what is its total surface area?(a) 4,092 cm2 (b) 2,084 cm2(c) 5,104 cm2 (d) None of these.
The ratio between curved surface area and total surface area is 2:3 and the total surface is 924 cm2. What is the volume of the cylinder?(a) 2,156 cm3 (b) 2,183 cm3 (c) 2,492 cm3 (d) None of these.
Find the height of the cylinder whose volume is 511 cm3 and the area of the base 36.5 cm2.(a) 3.5 cm (b) 10.5 cm(c) 14 cm (d) None of these.
A banquet hall has the dimensions 30 m × 12 m × 6 m. Each person should get 8 m3 of space. Find the number of persons who can be accommodated in this hall.(a) 240 (b) 250(c) 270 (d) 300
If the side of a cube is increased by 100%, find by what percentage the surface area of the cube is increased?(a) 150% (b) 200%(c) 300% (d) 350%
Mid-points of a rectangle are joined to form a quadrilateral. Name the quadrilateral formed as a result.(a) Rectangle (b) Rhombus(c) Parallelogram (d) Square

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