Question. 1

The sum of perimeters of an equilateral triangle and a rectanmgle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T2. If the sides of the rectangle are in the ratio 1 : 3, then the length, in cm, of the longer side of the rectangle, is

(a) (b) (c) (d)
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Question. 2

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of teh sheet left unpainted is two-thirds of teh painted area tehn the perimeter of the rectangle in inches is

(a) (b) (c) (d)
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Question. 3

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

(a) (b) (c) (d)
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Question. 4

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

(a) (b) (c) (d)
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Question. 5

A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is

(a) (b) (c) (d)
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Question. 6

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is

(a) (b) (c) (d)
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Question. 7

If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 3 : 15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

(a) (b) (c) (d)
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Question. 8

If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 3 : 15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

(a) (b) (c) (d)
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Question. 9

Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

(a) (b) (c) (d)
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Question. 10

A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?

(a) (b) (c) (d)
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Question. 11

The area of a rectangle and the square of its perimeter are in the ratio 1 : 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

(a) (b) (c) (d)
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Question. 12

From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is

(a) (b) (c) (d)
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Question. 13

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

(a) (b) (c) (d)
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Question. 14

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

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Question. 15

A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is

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Question. 16

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to:

(a) (b) (c) (d)
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Question. 17

A regular polygon has an even number of sides. If the product of the length of its side and the distance between two opposite sides is ¼ th of its area, find number of sides it has

(a) (b) (c) (d)
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Question. 18

A field is in the form of a rectangle of dimension 24 m × 56 m. There is 2700 m of fencing that is available. The field has to be divided into many identical smaller square plots, having integral sides (in metres), each of which is to be fenced. Find the side of each of the square plots such that the fencing material that is left out is minimum

(a) (b) (c) (d)
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Question. 19

All reputed B-schools place their students. One-sixth of those B-schools that place their students are reputed and one-fourth of all B-schools that are recognised, place their students. There are exactly 6 reputed B-schools that are recognised too and there are 39 B-schools that are recognised but do not place their students. If there is a total of 78 B-schools that place their students, then how many of these B-schools are neither recognised nor reputed but place their students?

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Question. 20

Through point P, lines are drawn parallel to the sides of triangle ABC. The areas of the DPED, DPFG and DPHI are 9, 16 and 49 sq. cm respectively. Find the area (in sq. cm) of triangle ABC.

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Question. 21

ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units and CD = 14 units. The mid-points of the sides of the trapezium are joined to form a quadrilateral PQRS. Find the ratio of the area of the circle inscribed in the quadrilateral PQRS to the area of trapezium ABCD

(a) (b) (c) (d)
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Question. 22

The smallest possible circle touching two opposite sides of a rectangle is cut-out from a rectangle of area 60 sq. units. If the area of this circle is 3/2 times the area left out in the rectangle, find the length of the smaller side of the rectangle

(a) (b) (c) (d)
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Question. 23

How many rectangles with integral sides are possible where the area of the rectangle equals the perimeter of the rectangle?

(a) (b) (c) (d)
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Question. 24

The top and bottom radii of a frustrum of a solid cone are 3 cm and 6 cm respectively. Its height is 8 cm. There is a conical cavity of height 3 cm and radius 6 cm at the bottom. The amount of material in the solid is

(a) (b) (c) (d)
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Question. 25

The length of the hypotenuse of a right-angled triangle is 240 units. The perimeter of the given triangle is a perfect square. If the perimeter of the given triangle is greater than 550 units, then which of the following can be the length of a side of the given right-angled triangle?

(a) (b) (c) (d)
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Question. 26

A spherical ball of the maximum possible volume is placed inside a right-circular cone of height ‘h’ units. If the radius of the base of the cone is equal to h/root3 units, then the ratio of the volume of the sphere to that of the cone is

(a) (b) (c) (d)
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Question. 27

How many triangles can be drawn by joining any three vertices of a pentagon?

(a) (b) (c) (d)
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Question. 28

(a) (b) (c) (d)
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Question. 29

A rectangle with perimeter 88 m is partitioned into 5 congruent rectangles, as shown in the diagram given below. The perimeter of each of the congruent rectangles is

(a) (b) (c) (d)
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Question. 30

In the regular hexagon shown below, what is the ratio of the area of the smaller circle to that of the bigger circle?

(a) (b) (c) (d)
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Question. 31

A circle of radius 6.5 cm is circumscribed around a rightangled triangle with the sides a, b and c cm where a, b and c are natural numbers. What is the perimeter of the triangle?

(a) (b) (c) (d)
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Question. 32

A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is

(a) (b) (c) (d)
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Question. 33

From a square piece of card-board measuring 2a on each side of a box with no top is to be formed by cutting out from each corner a square with sides b and bending up the flaps. The value of b for which the box has the greatest volume is

(a) (b) (c) (d)
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Question. 34

Suresh, who runs a bakery, uses a conical shaped equipment to write decorative labels (e.g., Happy Birthday etc.) using cream. The height of this equipment is 7 cm and the diameter of the base is 5 mm. A full charge of the equipment will write 330 words on an average. How many words can be written using three fifth of a litre of cream?

(a) (b) (c) (d)
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Question. 35

An unsharpened cylindrical pencil consists of a layer of wood surrounding a solid cylinder of graphite. The radius of a pencil is 7 mm, the radius of the graphite cylinder is 1 mm and the length of the pencil is 10 cm. Find the cost of the material (in Rs.) used in a pencil, if the cost of wood is Rs. 0.70/cm3 and that of graphite is Rs. 2.10/cm3

(a) (b) (c) (d)
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Question. 36

(a) (b) (c) (d)
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Question. 37

A cube of edge 12 cm is cut into 64 equal cubes. All the cubes are now arranged on a table such that one face of each cube touches the table. The resulting figure is a solid cuboid whose length and breadth are in the ratio 4 : 1 respectively. What is the total surface area of the table occupied by the cuboid?

(a) (b) (c) (d)
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Question. 38

A conical vessel, with a circular base, is filled with water to two-thirds of its volume. The pointed end of the cone is snipped off and replaced with a lid. The lid is kept open for 10 hours every day during which some water evaporates. The volume of the water that evaporates on a day is directly proportional to the area of the water surface at the beginning of the day. The volume of the water left in the container after evaporation on the 1st day is half the volume of the original cone. If V is the volume of the original cone, then what is the volume of the water that evaporates on the 2nd day?

(a) (b) (c) (d)
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Question. 39

A 20 litre vessel is filled with alcohol. Some of the alcohol is poured out into another vessel of an equal capacity, which is then completely filled by adding water. The mixture thus obtained is then poured into the first vessel to capacity. Then 6.67 litres is poured from the first vessel into the second. Both vessels now contain an equal amount of alcohol. How much alcohol (in litres) was originally poured from the first vessel into the second ? 

(a) (b) (c) (d)
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Question. 40

The area of the circle circumscribing three circles of unit radius touching each other is

(a) (b) (c) (d)
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Question. 41

The area of a regular polygon of side ‘x’ units is ‘10x’ sq units and the length of its inradius is an integer. How many such polygons would be there?

(a) (b) (c) (d)
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Question. 42

The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio 9 : 8. If the length of the first wire is 162 cms., find the length of the other.

(a) (b) (c) (d)
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Question. 43

Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height

(a) (b) (c) (d)
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Question. 44

Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region

(a) (b) (c) (d)
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Question. 45

Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABC

(a) (b) (c) (d)
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Question. 46

Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinde

(a) (b) (c) (d)
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Question. 47

A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq.cm) will be:

(a) (b) (c) (d)
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Comprehension. 1

Directions for Questions: Answer the questions on the basis of the information given below

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

Question. 1

Find the area of the part of the circle (round punch) falling outside the square shee

(a) (b) (c) (d)
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Question. 2

The proportion of the sheet area that remains after punching is:

(a) (b) (c) (d)
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Question. 48

The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

(a) (b) (c) (d)
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Question. 49

Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is

(a) (b) (c) (d)
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Question. 50

Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD and the length of AB is 1 meter. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one meter of any insect repellent. The minimum distance in meters the ant must traverse to reach the sugar particle is

(a) (b) (c) (d)
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Question. 51

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of the white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) (b) (c) (d)
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Question. 52

In the X-Y plane, the area of the region bounded by the graph |x + y| + |x – y| = 4 is

(a) (b) (c) (d)
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Question. 53

A jogging park has two identical circular tracks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

(a) (b) (c) (d)
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Question. 54

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is

(a) (b) (c) (d)
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Question. 55

Let C be a circle with center P0 and AB be a diameter of C. Suppose P1 is the mid-point of the line segment P0 B, P2 is the mid-point of the line segment P1 B and so on. Let C1 , C2 , C3 , ............. be circles with diameters P0 P1 , P1 P2 , P2 P3 , ............... respectively. Suppose the circles C1 , C2 , C3 , ............. are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is

(a) (b) (c) (d)
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Question. 56

A rectangular sheet of paper, when halved by folding it at mid-point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

(a) (b) (c) (d)
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Comprehension. 2

Directions for questions: Read the information given below and answer the questions that follow

Consider a cylinder of height h cms and radius r =π/2 cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns).

Question. 1

In the setup of the previous two questions, how is h related to n?

(a) (b) (c) (d)
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Question. 2

The same string, when wound on the exterior four walls of a cube of side n cms, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string, in cms, is

(a) (b) (c) (d)
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Question. 3

What is the vertical spacing in cms between two consecutive turns?

(a) (b) (c) (d)
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Question. 57

Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps : the original square of side a is divided into n smaller squares, not necessarily of the same size ; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is

(a) (b) (c) (d)
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Question. 58

(a) (b) (c) (d)
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Question. 59

The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle , and square are c, t, and s, respectively. Then

(a) (b) (c) (d)
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Question. 60

There are two concentric circles such that the area of the outer circle is four times the area of the inner circle . Let A,B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters ) of the triangle ABC would be

(a) (b) (c) (d)
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Question. 61

Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with centre at O. The horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centres at P and R respectively, and S is the centre of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi–circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi circle with diameter AB that cannot be grazed by the horses is nearest to

(a) (b) (c) (d)
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Question. 62

In the figure below , ABCDEF is a regular hexagon and AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

(a) (b) (c) (d)
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Question. 63

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be

(a) (b) (c) (d)
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Question. 64

In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with center at O. The length of side AB is greater than that of side BC. The ratio of the area of the circle to the area of the rectangle ABCD is π : √3 . The line segment DE intersects AB at E such that ∠ODC = ∠ADE. What is the ratio AE : AD?

(a) (b) (c) (d)
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Question. 65

Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?

(a) (b) (c) (d)
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Question. 66

A square tin sheet of side 12 inches is converted into a box with open top in the following steps: The sheet is placed horizontally; Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet; Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?

(a) (b) (c) (d)
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Question. 67

A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle . If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?

(a) (b) (c) (d)
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Comprehension. 3

Directions for questions: Read the information given below and answer the questions that follow :

Answer these questions based on the following diagram.

In the diagram below :  ∠ABC = ∠DCH = ∠DOE = ∠EHK = ∠FKL = ∠GLM = ∠LMN = 90° and AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN

Question. 1

The ratio of the areas of the two quadrangles ABCD and DEFG is

(a) (b) (c) (d)
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Question. 2

The magnitude of ∠FGO =

(a) (b) (c) (d)
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Question. 68

The area of the triangle whose vertices are (a, a), (a + 1, a + 1), (a + 2, a) is

(a) (b) (c) (d)
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Question. 69

In the figure given below, ABCD is a rectangle. The area of the isosceles right traingle ABE = 7 cm² ; EC = 3 (BE). The area of ABCD (in cm² ) is

(a) (b) (c) (d)
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Question. 70

Neeraj has agreed to mow the front lawn, which is a 20 m by 40 m rectangle. The mower mows a 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he has mowed half the lawn?

(a) (b) (c) (d)
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Question. 71

Four horses are tethered at four corners of a square plot of side 14 metres so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m² at the centre. The area left ungrazed is

(a) (b) (c) (d)
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Question. 72

Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?

(a) (b) (c) (d)
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Question. 73

Two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three angles are not right angles.

What is the area of the plot?

(a) (b) (c) (d)
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Question. 74

A ladder leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

(a) (b) (c) (d)
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Question. 75

In the diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the area of the triangle CEF and that of the rectangle?

(a) (b) (c) (d)
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Question. 76

A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the south gate. What is the diameter of the wall that surrounds the city?

(a) (b) (c) (d)
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Question. 77

A square, whose side is 2 metres, has its corners cut a way so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres is

(a) (b) (c) (d)
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Question. 78

A rectangular pool 20 metres wide and 60 metres long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square metres, how wide, in metres, is the walkway?

(a) (b) (c) (d)
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Question. 79

What is the area of the region bounded by |x + y| =1 , |x| =1& |y| =1

(a) (b) (c) (d)
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Question. 80

(a) (b) (c) (d)
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Question. 81

There are two tanks, one cylindrical and the other conical. The cylindrical tank contains 500 litres limca more than the conical tank. 200 litres is removed both from the cylindrical and conical tank. Now the cylindrical tank contains double the volume of liquid in the conical tank. What is the capacity of the cylindrical tank in litre?

(a) (b) (c) (d)
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Question. 82

There is a square field of side 500 metres. From one corner of the field a triangular area has to be cordoned off with a straight fence of length 100 metres, using the boundaries of the field as the other two sides. What is the maximum area that can be cordoned of

(a) (b) (c) (d)
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Question. 83

A cow is tethered at A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.

m∠A = 30º

∂(AB) = ∂(AC) = 10 m.

∂(BC) = 6 m

What is the area that can be grazed by the cow if the length of the rope is 12 m?

(a) (b) (c) (d)
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Question. 84

A cow is tethered at A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.

m∠A = 30º

∂(AB) = ∂(AC) = 10 m.

∂(BC) = 6 m

What is the area that can be grazed by the cow if the length of the rope is 8 m?

(a) (b) (c) (d)
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Question. 85

Four identical coins are placed in a square. For each coin the ratio of area to circumference is same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins

(a) (b) (c) (d)
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Question. 86

Four identical coins are placed in a square. For each coin the ratio of area to circumference is same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins

(a) (b) (c) (d)
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Comprehension. 4

Directions for questions: Read the information given below and answer the questions that follow :

A cow is tethered at A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.

Question. 1

What is the area that can be grazed by the cow if the length of the rope is 12 m?

(a) (b) (c) (d)
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Question. 2

What is the area that can be grazed by the cow if the length of the rope is 8 m?

(a) (b) (c) (d)
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Question. 87

In a triangle ABC, points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq. units, find the area of the triangle PQR

(a) (b) (c) (d)
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Question. 88

The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh square, counting from the innermost square

(a) (b) (c) (d)
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Question. 89

In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of the triangle CBE to that of the triangle ADE

(a) (b) (c) (d)
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Question. 90

A cube of side 12 cm. is painted red on all the faces and then cut into smaller cubes, each of side 3cm. What is the total number of smaller cubes having none of their faces painted?

(a) (b) (c) (d)
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Question. 91

A closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is painted inside. The expenses of painting are Rs 70. What is the rate of painting in rupees per sq. cm.?

(a) (b) (c) (d)
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Question. 92

From a circular sheet of paper with a radius 20 cm, four circles of radius 5cm each are cut out. What is the ratio of the uncut to the cut portion?

(a) (b) (c) (d)
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Question. 93

The sum of the areas of two circles which touch each other externally is 153. If the sum of their radii is 15, find the ratio of the larger to the smaller radius

(a) (b) (c) (d)
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Question. 94

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

(a) (b) (c) (d)
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Question. 95

The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ABC

(a) (b) (c) (d)
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Question. 96

The figure shows a rectangle ABCD with a semi-circle and a circle inscribed inside it as shown. What is the ratio of the area of the circle to that of the semi-circle?

(a) (b) (c) (d)
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Question. 97

ABCD is a square of area 4, which is divided into four non overlapping triangles as shown in the fig. Then the sum of the perimeters of the triangles is

(a) (b) (c) (d)
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Question. 98

The sides of a triangle are 5, 12 and 13 units respectively. A rectangle is constructed which is equal in area to the triangle and has a width of 10 units. Then the perimeter of the rectangle is

(a) (b) (c) (d)
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Question. 99

In the adjoining figure, AC + AB = 5 AD and AC – AD = 8. Then the area of the rectangle ABCD is

(a) (b) (c) (d)
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Question. 100

PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR=OS. Then, the ratio of area of the circle to the area of the square is

(a) (b) (c) (d)
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Question. 101

In ΔACD, AD = AC and ∠C = 2∠E . The distance between parallel lines AB and CD is h.

Then

I. Area of parallelogram ABCD

II. Area of ΔADE

(a) (b) (c) (d)
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Question. 102

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and frustum are in the ratio

(a) (b) (c) (d)
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Question. 103

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder are equal to their diameters. Then their volumes are proportional, respectively, to

(a) (b) (c) (d)
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