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 of numbers is to be answered. The operations on numbers progress from left to right.

Rules:
(i) If an odd number is followed by another composite odd number, they are to be multiplied.
(ii) If an even number is followed by an odd number which is not a perfect square, they are to be added.
(iii) If an even number is followed by a number which is a perfect square, the even number is to be subtracted from the perfect square.
(iv) If an odd number is followed by a prime odd number, the first number is to be divided by the second number.
(v) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.

P is the mother of Q and daughter of R. S is the daughter of Q and sister of T. How is P related to T?

P, Q and R are three points on the ground. Point P is north of point Q and PQR is 135° in anticlockwise direction. In which direction is point R from point Q?

Find the water image of Fig. (X).

Select a figure from the options which satisfies the same conditions of placement of the dots as in Fig. (X).

Select a figure from the option figures which will continue the same series as established by the five Problem Figures.

Directions: Study the following information carefully and answer the question.

Eight friends Q, R, S, T, V, W, Y and Z sit around a circular table, facing the centre. There are three males and five females in the group of friends. No two males are immediate neighbours of each other.
(i) V sits second to the right of his wife.
(ii) S sits third to the right of V.
(iii) W sits second to the right of her husband Z. Z is not an immediate neighbour of V's wife.
(iv) T is a male and Y is not an immediate neighbour of V.
(v) R sits second to the right of Q.

Which of the following statements is/are true regarding T?

Vijay is fifteenth from the front in a column of boys. There are thrice as many behind him as there are in front. How many boys are there between Vijay and the seventh boy from the end of the column?

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

Find out which of the options completes the figure matrix.

If 12% people in a village are suffering from cancer and 13% from blood pressure, which of the following diagram best represents the sick population of the village?

If all the consonants starting from B are given sequentially the value of even numbers such as B = 2, C = 4 and so on, and all the vowels are given double the value of the preceding vowel and the value of A is 5, then what is the value of REASONING?

Two positions of a dice are shown below. What number will be opposite to the number 4?

If 2 is subtracted from each odd digit and 3 is added to each even digit in the number 3675249, then how many digits will appear twice in the new number thus formed?

Select the figure in which figure (X) is exactly embedded as one of its part.

Find the value of I, so that y - 2p is a factor of - 2y + lp.

If x⁴ + = 47, then find the value of x³ + .

How many planes can be made to pass through three distinct points?

In the given figure, B < A and C < D.



Which of the following statements is true regarding the relationship between AD and BC?

In the given figure, AB II CD II EF. CE is joined and produced to G. If BAC = 130°, ACE = 140°, then find DCE and FEG respectively.

The graph of line y = 6 is

Directions: The given question is followed by three statements. You have to study the question and all the three statements to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

What is the marked price of the suitcase?

I. When a discount of 15% is offered, the profit earned is 10.5%.
II. The cost price of the suitcase is 1500.
III. The marked price is 30% above the cost price.

The line BE is a diameter of the given circle. If BAC = 33° and EBC = 57°. Then CAE =

ABCD is a field in the form of a quadrilateral whose sides are AB = 40 m, BC = 15 m, CD = 28 m and AD = 9 m. If DAB = 90°, than the area of the field is

If then the value of k is

The number of zeros of the zero polynomial is

The sum of a number and its reciprocal is thrice the difference between the number and its reciprocal. The number is ________.

The probability of selecting a boy in a class is 0.6 and there are 45 students in a class. Find the number of girls in the class.

What percentage of a day is six hours and 45 minutes?

Find the value of a and b respectively, if

In the given figure (not drawn to scale), LMNO is a parallelogram and OPQR is a rhombus. Find NMH given that LMH is a straight line.

In the given figure, 'O' is the center of circle, CAO = 25° and CBO = 35°. What is the value of AOB?

John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram.

Directions: The pie chart below shows the number of fruits sold on a particular day at a fruit stall.



The ratio of the number of mangoes sold to the number of apples sold is 6 : 5. What percentage of the total sales came from the sale of mangoes?

A cuboidal metal block of dimensions 20 cm × 16 cm × 12 cm weighs 6 kg. Find the weight of a block of the same metal of size 10 cm × 8 cm × 8 cm.

Ajay has a certain amount in his account. He gives half of it to his eldest son and one third of the remaining to his youngest son. What fraction of the original amount is left with him now?

The average age of 6 sons of a family is 8 years. The average age of the sons together with their parents is 22 years. If the father is older than the mother by 8 years, then the age of the mother is

A sum of Rs. 1550 is lent in two parts, one at 8% and another one at 6%. If the total annual income is Rs. 106, then find the money lent at each rate.

A train travelling at 48 km/hr. completely crosses another train having half its length and travelling in opposite direction at 42 km/hr in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is ________

Savita has Rs. 27 in the form of fifty-paisa and twenty-five paisa coins. She has twice as many twenty-five paisa coins as she has fifty-paisa coins. How many coins of each kind does she have?

Four runners started running the race in the same direction around a circular path of 7 km. Their speeds are 4 km/hr, 3 km/hr, and 9 km/hr and 3.5 km/hr individually. If they have started their race at 6 o'clock in the morning, then at what time they will be at the starting point?

In a bag, there are coins of 25 paisa, 10 paisa and 5 paisa in the ratio of 1 : 2 : 3. If there are Rs. 30 in all, then how many 5 paisa coins are there?

A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book are

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

The dimensions of a photograph are 4 cm and 1.8 cms. If the breadth of the enlarged photo is 4.5 cm and it was enlarged proportionally, then what is the new length of new photograph?

The polynomial p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7 when divided by x + 1 leaves the remainder 19. Find

(a) The value of a.
(b) The remainder when p(x) is divided by x + 2.

Which of the following options hold(s)?

Statement-1: If any two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the triangles are congruent (AAS congruence criterion).
Statement-2: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent (RHS congruence criterion).

In the figure, A and B are the centres of two intersecting circles. Which Euclid's axiom will prove that ABC is an equilateral triangle?

A die is rolled. If the number on the die is even, then a coin is tossed once; and if the number on the die is odd, then the coin is tossed twice. Match the events in Column I with their probabilities in Column II.

Column I	Column II
(P) Probability that two heads appear	(1)
(Q) Probability that at least 1 heads appears	(2) 0
(R) Probability that the die shows an even number and the coin shows exactly two heads	(3)
(S) Probability that the die shows an odd number and the coin shows at least one tails	(4)

The volume of the space inside a right circular conical tent is 138 m² and its vertical height is 4 m. Find the canvas required to make the tent and the cost of the canvas at the rate of Rs. 120 per m².