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

Mid-points of an irregular quadrilateral are joined to form a quadrilateral (irregular quadrilateral cannot have all four sides of the same length). Name the quadrilateral formed as a result.(a) Trapezium(b) Rhombus(c) Parallelogram(d) Square
Sides of a board consecutively measure 9 feet, 5 feet, 9 feet and 5 feet. Without any further information, you can determine that board is a:(a) Rectangle (b) Rhombus(c) Parallelogram (d) Square
Find the area of a cyclic quadrilateral whose sides are 10 cm, 12 cm, 16 cm and 20 cm.
Three sides of a parallelogram are 17 cm, 15 cm and 10 cm. Length of the fourth side must be less than:(a) 32 cm (b) 42 cm(c) 27 cm (d) 25 cm
ABCD is a square of side 13 cm. K is a point on CD such that CK:KD = 1:2. CP is perpendicular to AK produced. Find the length of CP.
ABCD is a parallelogram. M is the mid-point of BD and BM bisects ∠B. Find the value of∠AMB.
Two parallelograms stand on equal bases and between the same parallel lines. What is the ratio between their areas?
If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
The bisectors of any two adjacent angles of a parallelogram intersect at what angle?
In a quadrilateral ABCD, if AO and BO be the bisectors of ∠A and ∠B, respectively,∠C = 70° and ∠D = 30°, then find ∠AOB.
Length of diagonals of a rhombus are 16 cm and 12 cm. What is the side of the rhombus?
In parallelogram KLMN, if diagonal KM measures 30 inches, then:(a) KL measures 18 inches(b) LM measures 24 inches(c) Diagonal LN is perpendicular to diagonal KM(d) None of these.
Find the area of a trapezium whose shorter and longer parallel sides have the length 10 cm and 14 cm and are 8 cm apart from each other.
If two adjacent sides of a parallelogram are 6 cm and 8 cm and angle between them is 60°, then find:(a) Perimeter (b) Area
Find all the angles of parallelogram ABCD in which ∠B is 60° (points are in order).
If sides of a rectangle are 10 cm and 8 cm, then find:(a) Length of the diagonal(b) Perimeter(c) Semi perimeter(d) Area
The area of a field in the shape of a trapezium measures 1,440 m2. The perpendicular distance between its parallel sides is 24 m.If the ratio of the parallel sides is 5:3, the length of the longer parallel side is:(a) 45 m (b) 60 m(c) 75 m (d) 120 m
The two parallel sides of a trapezium are 1.5 m and 2.5 m, respectively. If the perpendicular distance between them is 6.5 metres, the area of the trapezium is:(a) 10 m2 (b) 13 m2(c) 20 m2 (d) 26 m2
If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:(a) Greater than 1 (b) equal to 1(c) equal to 1/2 (d) equal to 1/4
The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the other diagonal?(a) 4/5 (b) 2/5(c) 3/4 (d) 1/4
Each side of a rhombus is 26 cm and one of its diagonals is 48 cm long. The area of the rhombus is:(a) 240 cm2 (b) 300 cm2(c) 360 cm2 (d) 480 cm2
The perimeter of a rhombus is 56 m and its height is 5 m. Its area is:(a) 64 m2 (b) 70 m2(c) 78 m2 (d) 84 m2
One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq cm. The sum of the diagonals is:(a) 10 cm (b) 12 cm(c) 15 cm (d) 16 cm
The area of a rhombus is 150 cm2. The length of one of its diagonals is 10 cm. The length of the other diagonal is:(a) 25 cm (b) 30 cm(c) 35 cm (d) 40 cm
If a parallelogram with area P, a rectangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then which of the following statements is false?(a) P = R (b) P + T = 2R(c) P = 2T (d) T = (1/2) R
A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:(a) 10 2 m (b) 100(c) 100 2 m (d) 200 m
A parallelogram has sides 30 m and 14 m and one of its diagonals is 40 m long. Then, its area is:(a) 168 m2 (b) 336 m2(c) 372 m2 (d) 480 m2
One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm.The area of the parallelogram is:(a) 48 cm2 (b) 72 cm2(c) 100 cm2 (d) 144 cm2
The ratio of the area of a square inscribed in a semicircle to that of the area of a square inscribed in the circle of the same radius is(a) 2:1 (b) 2:3(c) 2:5 (d) 2:7
P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?(a) 2 1 r ( ) + 3 (b) 2 2 r ( ) + 3(c) r ( ) 1 5 + (d) 2 3 r +
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 m. 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 1 m of any insect repellent. The minimum
What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?(a) 1 or 7 (b) 2 or 14(c) 3 or 21 (d) 4 or 28
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
In ΔABC, base side BC is parallel to Side DE(D point is on side AB and E point on AC).AC = 5.6 cm, AD = 3 cm and BD = 5 cm.Find the length of AE.(a) 2.1 cm (b) 1.2 cm(c) 5.60 cm (d) 2.4 cm
A horizontal pipe for carrying water has diameter 1 m when water in it is 10 cm deep. What is the breadth of the water surface?(a) 80 cm (b) 120 cm(c) 60 cm (d) 24 cm
What is the length of the common chord of the two circles of radii 6 cm and 8 cm with their centres 10 cm apart?(a) 8.4 cm (b) 9.6 cm(c) 10 cm (d) 12 cm
Two circles of radius 10 cm and 8 cm, respectively, touch each other internally.What is the distance between their centres?(a) 8 cm (b) 2 cm(c) 18 cm (d) None of these.
What is the length of the tangent to a circle of radius 5 cm from a point at a distance of 13 cm from the centre of the circle?(a) 8 cm (b) 12 cm(c) 18 cm (d) 24 cm
A chord of length 14 cm is at a distance 6 cm from the centre of a circle. Find the length of another chord at a distance of 2 cm from the centre.(a) 18 cm (b) 24 cm(c) 21 cm (d) 12 cm
Two circles touch internally. The sum of their areas is 116π sq cm and the distance between their centres is 6 cm. Find the radius of the larger circle.(a) 10 cm (b) 22 cm(c) 7 cm (d) 11 cm
Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. Find the radius of the larger circle.(a) 10 cm (b) 22 cm(c) 7 cm (d) 11 cm
In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, find the radius of the circle.(a) 30 cm (b) 3 50 cm(c) 70 cm (d) 20 cm
AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD= 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. What is the radius of the circle?(a) 3 cm (b) 3 5 (c) 7 5 (d) 5 cm
If the ratio of areas of two circles is 4:9, then the ratio of their circumferences will be:(a) 2:3 (b) 3:2(c) 4:9 (d) 9:4
The sum of areas of two circles A and B is equal to the area of a third circle C, whose diameter is 30 cm. If the diameter of circle A is 18 cm, then the radius of circle B is:(a) 10 cm (b) 12 cm(c) 15 cm (d) 18 cm
If the circumference and the area of a circle are numerically equal, then the diameter is equal to:(a) π/2 (b) 2π(c) 2 (d) 4
A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle?(a) 88 cm2 (b) 154 cm2(c) 216 cm2 (d) None of these.
What is the area (in cm2 upto two decimal points) of a triangle whose sides and the angle between them are given as:a = 5 cm and b = 7 cm and angle C = 45°?(a) 12(b) 12.37(c) 2.88 km(d) Cannot be determined.
Four villages lie at the vertices of a squares of side 1 km. What is the smallest length of road needed to link all villages together?(a) 3 km(b) 2.73 km(c) 2.88 km(d) 4 km
Two sides of a plot in the form of a quadrilateral measure 32 m and 24 m and the angle between them is a right angle.The other two sides measure 25 m each.Find the area of the plot (Fig. 12.49):(a) 684 (b) 342 (c) 748 (d) None of these.
A ladder 50 cm long is placed so as to reach a window 48 cm high and on turning the ladder over to other side of the street, it reaches a point on the opposite wall 14 cm high. Find the breadth of the street.(a) 56 m (b) 60 cm(c) 64 cm (d) 62 cm
The sides of a triangle are 5 cm, 7 cm and 10 cm. Find the length of the median to the longest side.(a) 4.5 cm (b) 3.1 cm(c) 3.5 cm (d) 4.2 cm
In a triangle ABC, AB = 6, BC = 8 and AC = 10.A perpendicular dropped from B, meets in side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q, respectively, then AP:QC is equal to:(a) 1:1 (b) 3:2(c) 4:1 (d) 3:8
Ifa, b, c are sides of a triangle and a2 + b2+ c2 = ab + bc + ca then the triangle is:(a) Isosceles(b) Scalene(c) Equilateral(d) Cannot be determined.
In ∆ABC, points P, Q and R are the midpoints of side AB, BC and CA, respectively.If area of ∆ABC is 20 sq units then find the area of ∆PQR.(a) 10 sq units (b) 5 3(c) 5 sq units (d) None of these.
To find the area of a triangle which of the following statements is/are sufficient?A. All the length of the sides of the triangles.B. Any side and the corresponding altitude of the triangle.C. Two sides and the angle between them.(a) A alone is sufficient(b) B alone is sufficient(c) Either A or B
In triangle ABC, ∠B is a right angle. If AC is 6 cm and D is the mid-point of side AC, the length of BD is:(a) 4 cm (b) 6 cm(c) 3 cm (d) 3.5 cm
The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall the upper end of the ladder coincides with the tip of the wall, then the height of the wall is:(a) 12 m
Which one of the following cannot be the ratio of angles in a right-angled triangle?(a) 1:2:3 (b) 1:1:2(c) 1:3:6 (d) None of these.
Under the usual 2-dimensional coordinate system, which structure is represented by the equation | x | + | y | = 1, where x and y are real numbers?
The sides of a regular octagon are extended to form a star. Find the measure of the internal angle at each point of the star.
There are two regular polygons with number of sides in the ratio 4:5 and the interior angles in the ratio 25:26. Number of sides in the first polygon is .
It is given that perimeter of a square = Perimeter of a regular Octagon = Perimeter of a regular Decagon. Area of Square = S,Area of Octagon = O and Area of Decagon = D. What is the order for the areas in ascending order?
What is the number of diagonals in a pentagon?
Ratio between one internal angle and one external angle of a regular polygon is 1:2.Which type of polygon is this?
Ratio between one internal angle and one external angle of a regular polygon is 2:1.Which type of polygon is this?
Two straight lines AB and CD cut each other at O. If Angle BOD = 63°, find angle BOC.
How many degrees are there in an angle, which equals one fifth of its supplement?
If B = 4m and E = m + 2n; D = 3n + 8, find the value of H.
If G = 11n; A = 4m – n and D = 5n + 2m – 20, find the value of H.
If A = m, G = 3m + 20 and F = 2x, find x.
If A + E = 150, find F.
If 2 [log (x + y) - log 5] = log x + log y, then what is the value of x2 + y2?(a) 20xy (b) 23xy(c) 25xy (d) 28xy
Given that x, y and z are three angles of a triangle. Which of the following will be one possible set of value for x, y and z, such that log (x × y × z) = 3 log X + 4 log 2 (x, y and z are integers)?(a) 30°, 70°, 80° (b) 30°, 60°, 90°(c) 20°, 80°, 80° (d) 30°, 50°, 100°
Arrange the following in ascending order:A = log7 2401 B = log7 7 343 C = log 6 216 D = log2 32(a) ABCD (b) BDCA(c) BDAD (d) BADC
What is the value of x in the following expression:log log [ ( ) ] ? 7 5 x x + + 5 0 =(a) 1 (b) 2(c) 3 (d) 4
If [N] = the greatest integer less than or equal to N, then [log10 6730.4] is equal to:(a) 6 (b) 4(c) 3 (d) 7
Evaluate log ( ) 36 6 to the base 6.(a) 1/2 (b) 5/2(c) 3/2 (d) 7/2
What is the value of log ? 3 3 27(a) 2 (b) 3(c) 4 (d) 5
What is the number of digits in the expansion of 520 given that log 5 = 0.698?(a) 12 (b) 13(c) 14 (d) 15
x3n+ y3n is divisible by x + y, if:(a) n is any integer ≥ 0.(b) n is an odd positive integer.(c) n is an even positive integer.(d) n is a rational number.
In writing a quadratic equation of the form x2+ bx + c = 0, a student writes the coefficient of x incorrectly and finds the roots as 7 and 8.Another student makes a mistake in writing the constant term and gets the roots as 8 and –3. Find the correct quadratic equation.(a) x2 – 5x + 56 = 0(b)
If the co-efficient of x2 and the constant term of a quadratic equation are interchanged, then which of the following will not get changed?(a) Sum of the roots.(b) Product of the roots.(c) Roots of the equation.(d) None of these.
If x < 0, then what is the maximum value of 9 x 9 x+ ?(a) 2 (b) –2(c) +∝ (d) None of these.
A and B are the roots of the equation x2 – 13x + N = 0.If A – B = 3, what is the value of N?(a) 20 (b) 27(c) 36 (d) None of these.
Five burgers, six pizzas and seven cold drinks cost ` 178 and six burgers, four pizzas and two cold drinks cost ` 124.What is the cost of 3 (pizzas + burgers + cold drinks)?(a) ` 60(b) ` 62.5(c) ` 90(d) Cannot be determined.
For what value of K, the equations 2x +3y = 5 and 4x + Ky = A will not have any solution?(a) 2(b) –2(c) 6(d) More than one value is possible.
Which of the following satisfies the inequality –x2 + 6x – 8 > 0?(a) 3 < x < 5 (b) 2 < x < 4(c) x < 2 and x > 4 (d) x < 3 and x > 5
Present age of a father is eight times the present age of the son. After three years, the father’s age will become five times his son’s age. What is the present age of the father?(a) 24 years (b) 32 years (c) 40 years (d) 48 years
Roots of the quadratic equation ax2 + bx + c= 0 are 1 and 2, for some certain value ofa, b andc. What will be sum of roots of the equation having the roots opposite in sign of this equation ax2 + bx + c = 0?(a) 3 (b) 6(c) –3 (d) None of these.
Which of the following quadratic equations will not have real roots?(a) 3x2 + 2x – 1 = 0(b) x2 + 2x + 1 = 0(c) 3x2 + 2x + 5 = 0(d) 2x2 + 3x + 1 = 0
Roots of the quadratic equation ax2 + bx+ c = 0 are 1 and 2, for some certain value of b andc. If a = 1, what will be the value of (a + b + c)?(a) 2(b) –2(c) –3(d) Cannot be determined.
The cost of 3 apples and 2 guavas is ` 23 and that of one apple and four guavas of the same type is ` 21.What is the cost of 5 guavas?(a) ` 4 (b) ` 20(c) ` 12 (d) ` 25
What is the value of k such that the equation x2 – (k + 6) x + 2 (2k – 1) = 0 has sum of the roots equal to half of their product?(a) –2(b) 7(c) 9(d) 12
Mid-points of adjacent sides of a square are joined. Again, the mid-points of the adjacent sides of the newly formed figure are connected, and this process is repeated again and again. Calculate the sum of areas of all such figures given that the diagonal of outermost square is:(a) 35 cm2 (b) 44
If m times the mth term of an AP is equal to p times the pth term, find the (m + p)th term.(a) 0 (b) a2 – b2(c) a – b (d) 1
If the terms of one geometric progression are multiplied by the corresponding terms of another geometric progression, the sequence obtained will be in(a) AP(b) HP(c) GP(d) Cannot be determined
A GP consists of 1,000 terms. Sum of the terms occupying the odd places is P1 and the sum of the terms occupying the even places is P2. Find out the common ratio of this GP.(a) P2/P1 (b) P1/P2 (c) (P2 – P1)/P1 (d) (P2 + P1)/P2
In an infinite GP every term is equal to the sum of all the terms that follow. Find out the common ratio.(a) 1/2 (b) 1/3(c) 1/4 (d) 1/6
Find out the sum of an AP of 14 terms and whose first and last terms are 8 and 99, respectively.(a) 707 (b) 749(c) 789 (d) 747

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