IMO - Mock Test...

In the given 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 is to be answered. The operations of numbers progress from left to right.

Rules:
(i) If an even number is followed by another even number, they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.

A child went 90 m in the East to look for his father and then he turned right and went 20 m. Then he turned right and after going 30 m, he reached his uncle's house. His father was not there. From there, he went 100 m to his North and met his father in the shop. How far did he meet his father from the starting point?

Priya starts her trip from a fixed point. She moves towards East and walks 25 metres. She then turns to her left and walks 30 metres. Next she moves 25 metres to her right. She then turns to her right again and walks 55 metres. Finally she turns to her right and moves 75 meters. In which direction is she now from her starting point?

Choose from the options, the correct water image of the given word.

CARING

Choose from the given options which satisfies the same conditions of placement of the dots as in Fig. (X).

Select a figure from the options which will continue the series as established by the Problem Figures.

A, B, C, D, E, F, G, H and K are sitting around a circle facing the centre. F is fourth to the right of A, who is third to the right of B, K is fourth to the left of B and third to the right of D, C is third to the right of H. E is second to the left of G. What is E's position with respect to B?

Select a figure from the options which when placed in the blank space of Fig. (X) would complete the pattern.

If the code of SENSITIVE is QHLVGWGYC, then what will be the code of MICROSOFT?

Find the missing number, if a certain rule is followed row-wise or column-wise.

Which of the following Venn diagrams best represents the relationship among State, Country and Village?

If it is possible to make a meaningful word with the second, fourth, eight and tenth letters of the word CONFIDENCE, which of the following will be the second letter of that word? If more than one such word can be made, give 'S' as the answer. If no such word can be made, give 'P' as the answer.

Three different positions of a dice are shown below. Which of the following colours will be opposite to the face having red colour?

A goldsmith has five gold rings, each having a different weight;

Statement 1: Ring D is weighing twice as much as ring E.
Statement 2: Ring E is weighing four times as much as ring F.
Statement 3: Ring F is weighing half as much as ring G.
Statement 4: Ring G is weighing half as much as ring H.
Statement 5: Ring H is weighing less than ring D but more than ring F.

Which of the following represents the descending order of weights of the rings?

A sheet of paper has been folded (either once or twice) and then it has been cut. You have to select a figure from the options that would most closely resemble the unfolded form of Fig. (X).

The term containing the highest power of x in the polynomial f(x) is 2x⁴. Two of the roots of the equation f(x) = 0 are -1 and 2. Given that x² - 3x + 1 is a quadratic factor of f(x), find the remainder when f(x) is divided by 2x - 1.

PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal SQ is joined. Find the ratio ar(||gm XQRY) : ar(△QSR)

Select the correct option.

The numbers 7.478478... and 1.101001000100001... are:

If x = , find the value of x³ - 2x² - 7x + 5.

The base of an isosceles triangle is 4 cm and its area is 16 cm². If one of the two equal sides of the triangle is k cm, then the approximate value of k - 1.24 is _________.

The given figure is not drawn to scale. Find the values of QPS and TRQ respectively.

Study the given graph and answer the following question.



Calculate the area enclosed by the lines I, x = -3, y = -2 and y = -x + 2.

Find the ratio of the shaded area to the area of the quadrilateral ABCD.

Three statements are given below:

(i) In a ||gm, the angle bisectors of two adjacent angles enclose a right angle.
(ii) The angle bisectors of a ||gm form a rectangle.
(iii) The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which of the options is true?

Solve for x:

Simplify:

The weight, in kg, of 50 students is given below:

The figure below is made up of a square ABCD and two rhombuses ATCP and DRBV.



Given that BVD = 135° and AT = BR, find PCT and ABD respectively.

Water flows in a tank 150 m × 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time, will the water be 3 metres deep?

Directions: Study the graph carefully to answer the question that follows.

Number of Players Participating in three different games in five different schools


25% of the numbers of the players participating in hockey from School-5 are females. What is the number of the hockey players who are males in School-5?

Sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.

Study the figure shown here (not drawn to scale), If ABG is a straight line, then find ABH and reflex ABC respectively.

The value of up to 35 decimal places is given below:

3.14159265358979323846264338327950288

Find the probability of occurring 8 in it.

In the figure shown, square 2 is formed by joining the mid-points of square 1; square 3 is formed by joining the mid-points of square 2 and so on. In this way, total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares?

Two men and three women finish 25% of a work in 4 days, while six men and fourteen women can finish the whole work in 5 days. In how many days will 20 women finish it?

The length of the longest pole that can be placed on the floor of a room is 12 m and the length of the longest pole that can be placed in the room is 15 m. The height of the room is

The price of rice is reduced by 2% per kg. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?

The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?

A well with 10 m inside-diameter is dug 14 m deep. The earth taken out of it is spread all around to a width of 5 m to form an embankment. The height of the embankment is ________.

In a mixture of 60 litres, the ratio milk to water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is __________.

Suresh travelled 1200 km by air which was (2/5) of his trip. He travelled one-third of the whole trip by car and the rest of the journey by train. Find the distance travelled by train. Also, find the speed of the train if the time taken for the train to travel the whole distance was 8 hr.

There are four bells. They ring after every one minute, two and a half minutes, 50 seconds and 5 seconds, respectively. If all the four bells rang together last time at 8:20 p.m., then at what time will they all next ring simultaneously?

Roma took a loan of Rs. 16,000 against her insurance policy at the rate of 12% per annum. Calculate the total compound interest that will be paid by Roma after 3 years.

A fruit seller has 24 kg of apples. He sells a part of these at a gain of 20% and the balance at a loss of 5%. If on the whole he earns a profit of 10%, the amount of apples sold at a loss is ______.

Select the correct option.

Statement 1: If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is not isosceles.
Statement 2: If the bisector of the vertical angle of a triangle bisects the base, then the triangle is not isosceles.

Which of the following statements is correct?

Fill in the blanks.

In coordinate geometry, the coordinate axes divide the plane into four parts called _P_. The point of intersection of the axes is called _Q_. The sign of abscissa and ordinate will be same in _R_ and _S_ quadrants.

In the given figure (not drawn to scale), ABC and BDE are two equilateral triangles such that BD = CD and AE intersects BC at F. Now match the columns given below.

Column - I	Column - II
(i) Area(BDE) =	(p) 2 × Area(FED)
(ii) Area(FED) =	(q) × Area(ABC)
(iii) Area(BFE) =	(r) × Area(AFC)

Which of the following statements is INCORRECT for a parallelogram?