IMO - Mock Test...

What will be the next term in the following series?

256, 1280, 8960, 80640, 887040,

Rohit moved 8 km towards north before turning to his right and walking 11 km straight. He then took a left turn and walked straight for 1 km before taking another left turn and then walking straight for 5 km. From there, he took a left turn and walked straight for 1 km to reach a shop. Find the shortest distance between the shop and the starting point.

Find out the wrong term in the given series:

2, 8, 38, 220, 1301, ....

If '×' stands for 'addition', '÷' stands for 'subtraction', '+' stands for 'multiplication' and '-' stands for 'division', then which of the following equations is correct?

Count the number of cubes in the following figure:

How many faces are there in the following figure?

Directions: In the following question, a set of three figures X, Y and Z shows a sequence in which a paper is folded and finally cut from a particular section. Below these figures, a set of answer figures marked (a), (b), (c), (d) shows the design which the paper actually acquires when it is unfolded. You have to select the answer figure that most closely resembles the unfolded piece of paper.

Directions: In the following question, there are two sets of figures - the Problem figures and the Answer figures. The Problem figures are presented in two units. The first unit has two figures and the second unit has one figure and a question mark. Find out which one of the Answer figures marked (A) to (D) should come in place of the question mark.

In a joint family, there is a father, a mother, three married sons and one unmarried daughter. Out of the sons, two have two daughters each and one has a son. How many female members are there in the family?

How many edges are there in the given figure?

Directions: The following question is based on letter analogy. There are two pairs of letter combinations in the question. The first (left hand side) pair has some relation between its members. In the second pair, one member is missing. Find the answer from the options (1), (2), (3), and (4) such that this pair has a similar relation as the first pair.

BCD : CEG : : LMN : ?

Directions: Find the odd one out from the given options.

Directions: Study the following arrangement carefully and answer the question given below.

B M % R 3 J @ K © D F 6 9 W 4 N E P 2 $ A Y 5 I Q Z # 7 U G

If all the symbols and all the vowels are dropped from the above arrangement, then which of the following will be twelfth from the right end?

Directions: The first figure in the first unit of the problem figures bears a certain relationship to the second figure. Similarly, one of the figures in the answer figures bears the same relationship to the second figure of the second unit of the problem figures. Identify the figure which would fit in place of the question mark.

Directions: In the question below are given four statements, followed by three conclusions numbered I, II and Ill. You have to take the given statements to be true, even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of them logically follow(s) from the given statements disregarding commonly known facts.

Statements:
Some ropes are walls.
Some walls are sticks.
All sticks are chairs.
All chairs are tables.
Conclusions:
I. Some tables are walls.
ll. Some chairs are ropes.
Ill. Some sticks are ropes.

An A.P. consists of 53 terms. If the last term and the first term be 216 and 8 respectively, then find the value of 48^th term.

If ^_, where R is a point on the line segment P(2, 1) and Q(- 2, 3), then find out the ordinate of the point R.

Evaluate tan² θ - sec² θ (1 - sin² θ)

A wall around a circular park needs to be build. The cost of building the wall around the park is Rs. 1.76/cm. If the area of the park is 962.5 m², then find the total cost to build the wall around the park.

If , then find the value of ^.

Find the area of the shaded region from the given figure in which AB = 24 cm, AC = 7 cm, and O is the centre of the circle. BC is the diameter of the circle.

If the length of AO is 5 cm, A is the centre of the bigger circle and O is the centre of the smaller circle, then find the area of the remaining portion if the smaller circle is taken out of the bigger one.

The Y-axis divides the line joining points (- 3, - 2) and (5, 4) in the ratio 3 : 5. Find the coordinates of Y axis.

What will be the H.C.F of three numbers which are in ratio of 3 : 5 : 7 and their L.C.M is 1575?

Find the centroid of the triangle whose vertices are (2, 1), (5, 2), (3, 4).

Find the area of the shaded portion in the given figure, if the radius of each small circle is 14 cm.

In triangle PQR, UV || QR, PU : UQ = 3 : 7. Find the ratio of area of triangle PUV to area of PQR.

The figure given below shows an octagon with each interior angle measuring 135°. What is the area of the octagon?

The point which divides the line joining (1, 2) and (3, 4) internally in the ratio of 1 : 1 lies in which quadrant?

If in ΔABC, DE BC, then what can be the possible value(s) of x?

In a quadrant of radius 6a, two semicircles with centres D and F are cut as shown in the figure. If a circle with centre E is cut as shown in the figure, then what will be the area of the remaining part of the quadrant?

In the figure given below, AB is a diameter of the circle, TD is a tangent to the circle and AB = 2AD. If AHD = 36° and DBA = 30°, then what is the measure of CDT?

x = 17¹² + 10¹² and y = 16⁶ + 9⁶. If x - y is divided by 13, then the remainder is R₁ and if it is divided by 14, then the remainder is R₂. What is (R₁, R₂)?

If the LCM of two whole numbers is twice their HCF, then what is the ratio of the larger number to the smaller number?

On 2^nd July 1985, it was Wednesday. The day of the week on 2^nd July, 1984 was

Rina participated in a quiz which consisted of 30 questions, out of which some were multiple choice questions and the rest were subjective questions. Each multiple choice question carried 2 marks and each subjective question carried 5 marks. The quiz was of 75 marks. Find out the number of multiple choice questions asked in the quiz.

For which of the following values of (p), does the given quadratic equation 2x² + 3x + p = 0 have real roots?

On a busy day, 2000 sweets were sold by a confectionery. Total amount collected on that day was Rs. 9600. If the cost of mint flavoured sweets is Rs. 8/sweet, the cost of chocolate sweets is Rs 4/sweet, then how many mint sweets and chocolates sweets were sold that day?

Liquor is being poured into a vessel with two circular ends of radii 14 cm and 7 cm. The height of the bucket being filled is 60 cm. What is the maximum limit of alcohol which the vessel can hold?

The angles of elevation of a plane flying at a constant altitude of 10,000 ft are found to be 60^o and 30^o at an interval of 1 minute. What is the speed of the plane?

A toy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The base radius of the cone is 3.5 m and its volume is (2/3)^rd of the volume of the hemisphere. Calculate its height.

An acrobat climbs up a rope stretched from a point 120 metres above the ground to a point on the ground. The angle made by the rope with the ground is 60°. Find the length of the rope.

Two cyclists met each other at 10 a.m. on Ferozepur road. After their meeting, one of them proceeded in the north direction and the other proceeded in the east direction. Exactly at noon, they were 60 km apart. If the difference between their speeds was 6 km/hr, then find the speed of the faster cyclist.

Three plots having areas 132, 204 and 228 square metres are to be sub-divided into equal sized flower beds. If the breadth of a bed is 3 metres, find the maximum length that each bed can have.

A pencil is cylindrical in shape with a length of 20 cm and a cross-sectional radius of 1 cm. It is sharpened using a good sharpener on both the sides such that the shape on either end of the cylindrical pencil is that of a right circular cone with a height of 3 cm. If there is no change in the net length of the pencil due to sharpening, what is the volume of the material that was removed from the pencil to sharpen the edges?

Two farmers Ravi and Ram have 40 goats in total. They sell their goats at different prices, but each of them receives the same amount of money. If Ravi had sold his goats at Ram's price, he would have received Rs. 5,400. If Ram had sold his goats at Ravi's price, he would have received Rs. 2,400. How many goats does Ravi have in total?

How many real solutions of the equation = 1 exist?

In the figure, PQ is parallel to BC. If the ratio between the areas of the triangles APQ and ABC is 4 : 9, and ABCD is a parallelogram, then find the ratio between the areas of parallelograms APRD and PRCB.

A cylinder, having a diameter of 27 units and a height of 30 units, contains two lead spheres of radii 6 units and 9 units, with the larger sphere sitting at the bottom of the cylinder, as shown. Water is poured into the cylinder so that it just covers both spheres. Find the volume of water required (in cubic units).

If t_n = 1 + , n = 1, 2, 3, ____, then find the value of t₁ t₂ t₃ ____ t₂₅.